Appendix I

A Brief History of Thermal Engineering of Electronic Systems

Electronic microminiaturization is affecting nearly every facet of our lives. One of the critical challenges to maintaining the past rate of miniaturization is in electronic packaging, and more specifically, thermal engineering. To put this in perspective, at the periphery of the sun the surface temperature is about 6000° 7 2 C, representing a heat flux of 10 W/m • Current microchips generate a heat flux of about 105 W/m 2 which must be cooled to around only 125° C. The applica­ tion of advanced thermal engineering techniques requires a blending of the engi­ neering disciplines of heat transfer, fluid dynamics, mathematics, and to a lesser extent, electronic theory. How did we get to this point, and what can we expect in the future? The Egyptians had learned some physiology and surgery techniques as early as 3000 B.C. Using principles of evaporation (two-phase heat transfer), con­ vection cooling, and heat radiation, they chilled their drinking water on rooftops at night. They also developed a system for measuring property lines, geometry, and a form of mathematics. The Chinese cut and stored ice for sum­ mer usage staring about 1000 B.C. They also had a system of mathematics, writing, chemistry, and astronomy. During the 6th century B.C., the abacus originated in China, and was the fundamental instrument for performing calcu­ lations until the 1500s. Geometry studies progressed in ancient Greece. Thales (640?-546? B.C.), one of the Seven Wise Men of ancient Greece, used geometry to predict a solar eclipse. He also experimented with static electricity. The Greek mathematician Pythagorus (580?-500? B.C.) formulated the Pythagorean Theorem, although its principles were known earlier. Pythagorus was probably killed in a political uprising because he organized the Brotherhood of Aristocrats. The brotherhood finally disbanded about 400 B.C. Euclid (300?-? B.C.) published The Elements,

545 546 App. I A Brief History of Thermal Engineering of Electronic Systems

a 13-volume set of books about geometry, algebra, and number theory. Students used The Elements as textbooks until the late l800s. About 200 B.C. the Indians passed on a numbering system to the Arabs. Around this time, Archimedes (287?-2l2 B.C.) was asked to find a method for detecting a fake royal crown. He realized that since gold is one of the most dense substances, mixing another metal with it would make a fraudulent crown lighter than an authentic crown. The problem became how to measure the den­ sity of an irregularly shaped object. It is said that Archimedes discovered the principle while taking a bath. When he realized that his arms and legs seemed lighter in the bath, he ran down the streets of Syracuse, wearing only a towel, yelling "Eureka! Eureka!". Archimedes' principle says that when an object is submerged, the loss of weight equals the weight of the fluid displaced by the object. Known as specific gravity, this is the ratio between the weight of the fluid and the weight of the object. Archimedes was the greatest scientist of his day and was respected in all of the civilized world. He originated processes that foreshadowed the invention of integral calculus 1800 years later. When the Romans conquered Syracuse, Sicily in 212 B.C., a Roman soldier, mistaking Archimedes for an old beggar, ran a sword through him. Although the Romans conquered many civil engineering problems, they con­ tributed little to the advancement of mathematics as a science. After the fall of the Roman Empire in A.D. 476 there were no new European developments for hundreds of years. These were the Dark Ages. European scholars had turned to theology. By the 600s the Mayans had a much better understanding of their numbering system than the Europeans had of theirs. During the 700s, the Arabs, who had taken over much of the old Roman Empire, studied the writings of the ancient Greeks. They combined those writings with the Indian decimal system. Between 813 and 833, AI-Khowarizmi, a professor in the Baghdad school of Mathematics, organized and improved the writings of Hindu and Arab scholars. When traders introduced translations of the ancient Greek books and new Arab ideas into Europe during the A.D. WOOs, the Europeans organized them to agree with their own religious views. To question the interpreted writings of the ancient Greeks was punishable by death . The head of the Franciscan Order jailed Roger Bacon (1214-1294), an English monk and one of the founders of present day science, for "suspect innovations" in his work. Progress in the sciences began again in the l400s, the European Renaissance. Leonardo Da Vinci (1452-1519) studied the sciences as an engineer, geologist, astronomer, and botanist. Among his many accomplishments was a canal sys­ tem with locks that is still used. His sketches provided insight into the turbulent flow of liquids. In 1585, Galileo Galilei (1564-1642) invented the hydrostatic balance. This device is still used to find the specific gravity of objects by weigh­ ing them in water. Later in 1593, Galileo invented the thermoscope. The appa­ ratus, similar to a thermometer, consisted of an inverted tube of water in a bowl. App. I A Brief History of Thermal Engineering of Electronic Systems 547

It had no degree scale, and measured only temperature differences, not temper­ ature. Galileo spent his last years confined to his villa by the Inquisition. He wrote about his theories of motion, acceleration, and gravity. His work provided the basis for Sir Isaac Newton' s laws of motion. At about the same time Galileo was experimenting with fluids, William Gilbert (1540-1603), physician to Queen Elizabeth I, began to experiment with static electricity. He used the words electrum and electrica in his reports. A contemporary of Galileo ' s, Sanctorius, introduced the first scale for the thermoscope in 1611. The low point temperature was when covered by snow. The high point was when a candle was held underneath. This scale had 110 units and was the first actual thermometer. The measurements were inaccurate because atmospheric pressure altered the readings. A more accurate thermome­ ter using alcohol was invented in 1641. John Napier (1550-1617), a Scotsman, published the famous Mirifici Loga­ rthmorum Canonis Descriptio in 1614. His logarithms converted the lengthy procedures of multiplication and division to the faster processes of addition and subtraction. He also invented so-called "bones" or "rods" for multiplying and dividing, and for extracting square and cube roots. He published many formu­ las used in spherical trigonometry. Blaise Pascal ' s (1623-1662) father taught his son only the subjects he thought a son should know, mostly ancient dead languages. By the age of 12 Blaise had taught himself geometry, and at the age of 16 published a book titled The Geometry of Conics. His father relented and allowed the boy to study physics and mathematics when the famous philosopher and mathematician Rene ("I think, therefore I am") Descartes (1596-1650) took an interest. At the age of 19, noting his father's long hours spent calculating as a tax collector, he built the first calculating machine. His mechanical device added and subtracted by turning small wheels. The idea didn't catch on with the hand-calculating clerks in France for reasons of job security, so Blaise turned his attention to the study of fluid pressure. Pascal' s Law says that the change of pressure at any point in a confined fluid is transmitted undiminished in all directions to all points within the fluid. Later, along with the French mathematician Pierre De Fermat (1601-1665), Pascal invented the theories of probability and statistics, and explained their uses in card games and gambling. In 1643, the Italian mathematician Evangelista Torricelli (1608-1647) pro­ posed that atmospheric pressure determines the height of a fluid in an inverted tube over a container of the fluid. Torricelli was Galileo's successor at the Flo­ rentine Academy. This theory led to the development of the barometer. As court mathematician and philosopher to Grand Duke Ferdinand II of Tuscany, Torri­ celli proved what is now known as Torricelli ' s theorem. This theorem says that the velocity of a liquid through an opening equals the velocity of a free-falling body from the surface of the liquid to the opening. 548 App. I A Brief History of Thermal Engineering of Electronic Systems

The problem of a thermometer responding to atmospheric pressure changes was solved in 1644 when Grand Duke Ferdinand III of Tuscany (1608-1657) introduced the sealed thermometer, To further the experimentation and manu­ facture of accurate thermometers, the Academia de Cimento in Florence was established in 1657. The Florentines filled these thermometers with red wine because it expands faster than liquid metal. Robert Boyle (1627-1691), an Irish chemist, studied the changes in volume of a gas as he varied the pressure. The result was Boyle's Law: P = constant/V. This shows that at a given temperature and volume, all gases will exert the same pressure, and became the general gas law: 9ft = PVInT. He also studied the boil­ ing and freezing of liquids at reduced pressures. The English astronomer Edmund Halley (1656-1742) predicted the return of the comet of 1682, studied compass needle deviations, and mapped the stars. Robert Hooke (1635-1703) stated Hooke's Law of proportional stress and defor­ mation and discovered plant cells. Sir Christopher Wren (1632-1723), the Eng­ lish architect and mathematician, redesigned all or part of 55 out of 87 churches that were destroyed in the Great Fire of London in 1666. One day in 1684 these three men were discussing the law of force that guided the planets around the sun. They could not solve the problem, so Halley traveled to Cambridge to con­ fer with Sir Isaac Newton (1642-1727). Newton displayed the complete proof of the law of gravity that he had discovered 17 years earlier along with calcu­ lus, and the laws of color and light. He had made these discoveries during an 18-month period from 1665 to 1667. Newton disliked the negative criticism that accompanies new scientific discoveries so he concealed his work. In 1671, the German mathematician Gottfried Wilhelm von Leibniz (1646-1716) constructed a stepped-wheel device for multiplying by means of repeated additions. Scientists used his device in limited numbers. Leibniz did not attempt to popularize his invention. He believed that a man should just accept his lot in life, not try to change things, and make the best of it. The quote "This is the best of all possible worlds" is attributed to Leibniz. He also shares the credit for inventing calculus with Sir Isaac Newton. Daniel Bernoulli (1700-1782), whose father and uncle were also famous Swiss mathematicians and physicists, discovered the relationship between fluid velocity, density, pressure, and height. Bernoulli's Law, published in Hydrody­ namica in 1738, explains that as the speed of a fluid increases, the pressure of the fluid decreases. In this work Bernoulli also explained his kinetic theory of gaseous pressure in a container. Bernoulli collaborated with Leonhard Euler at the St. Petersburg Academy of Sciences. The German physicist Gabriel Daniel Fahrenheit (1686-1736) made the ther­ mometer more accurate in 1714 by using mercury instead of alcohol, and devel­ oped the temperature scale named in his honor. The Swedish astronomer Anders App. I A Brief History of Thermal Engineering of Electronic Systems 549

Celsius (1701-1744) made a great impact on thermometers. Two years before his death he chose a fixed water freezing point, a water boiling point, and the division of the interval into 100 equal graduations (centigrade). Celsius origi­ nally called the ice point 100 and the boiling point zero. Charles Francois Du Fay (1698-1739), King Louis XV's Superintendent of Gardens, found that a static electricity charge can be deposited on any object. In 1733 he wrote about two different types of electricity: vitreous and resinous. Benjamin Franklin (1706-1790), Minister and frequent visitor to France, became interested in electricity about 1746. He called Du Fay's electricities pos­ itive and negative. He conducted his famous kite experiment in 1752 and proved that lightning is electricity. Franklin continued to experiment with electricity even though he was knocked unconscious several times. Leonhard Euler (1707-1783) became famous for his wide range of work in mathematics. Most of his work in number theory, probability, geometry, acoustics, mechanics, algebra, optics, finance , calculus, statistics, and algebra was accomplished after he went blind in 1766. In the period between 1726 and 1800, Euler's 866 books and articles represented one-third of all the research on mathematics, theoretical physics, and engineering mechanics. A Swiss society started to publish his work in 1909. After 50 years and 47 volumes they were still not finished. The Scottish scientist William Cullen discovered the principles of artificial refrigeration in 1748 at the University of Glasgow. While experimenting with ethyl ether, he evaporated it into a partial vacuum. This event was the dawn of vapor cooling. In 1760, a Scottish physician, Joseph Black (1728-1799), demonstrated that heat does not have weight and devised the theory of latent heat. Another Scot­ tish inventor, James Watt (1736-1819), patented an improved steam engine in 1769. Watt used steam coils to heat his office in 1784. His inventions include the engine governor, a throttle valve, and a type of double-acting engine. He per­ formed research in chemistry and metallurgy and retired as a wealthy man in 1800. The Watt equals one volt driving one ampere. About this time, the French scientist Charles Augustan De Coulomb (1736-1806) formulated Coulomb's Law. This says that the force between two electric or magnetic charges varies inversely as the square of the distance between them. The Coulomb is equal to the quantity of energy in 6.242 X 1018 electrons. Alessandro Volta (1745-1827), an Italian physicist, invented the electric battery. The volt is named in Lord Volta's honor. Count Rumford (1753-1814) was born Benjamin Thompson, in Massachu­ setts. Loyal to the crown during the American Revolution, Thompson moved to London in 1776. Thompson was knighted in 1784, and became a count of the Holy Roman Empire in 1791. In 1797 he designed an experiment to prove that 550 App. I A Brief History of Thermal Engineering of Electronic Systems

heat was not a fluid-like substance. He concluded that heat is not a fluid, but a form of mechanical motion. His research led to improvements in heating and cooking equipment. Although it had been written about since 1670, the French Revolution caused the adoption of the metric system in 1799. A group of 12 mathemati­ cians and scientists met with French King Louis XVI to discuss the adoption proposal. Signing of the order was delayed because the King tried to escape France and the murderous peasants. King Louis finally signed the proclamation from his jail cell. In 1811, Amadeo Avogadro (1776-1856) suggested that: at any temperature and pressure, the number of molecules per unit volume is the same for all gases. This became known as the Avogadro number (6.022 X 1023 atoms per mole). Interestingly, Avogadro himself had no idea what this number might be. He was also the first to distinguish between molecules and atoms. Nicolas Leonard Sadi Camot (1796-1832) originated the field of thermody­ namics. This French engineer and physicist worked to improve the efficiency of the steam engine. His conclusions apply to all devices that convert heat into work. He found that the efficiency of a reversible engine depends on the tem­ peratures between which it works. The French mathematician Joseph Fourier (1768-1830), like Leonhard Euler, was trained as a priest. Fourier did not take his vows and turned to mathematics. In 1799 he accompanied Napoleon's army in the conquest of Egypt. There he studied archaeology, the pyramids, and the sphinx. In 1822 he became famous for his mathematical treatment of the theory of heat. He established the partial differential equations governing heat diffu­ sion and solved them by using an infinite series of trigonometric functions , known now as the Fourier series. One of the first to work in the new field of electricity was Heinrich Geissler (1814-1879). Geissler removed the air from glass tubes and found that they glowed with colors when an electrical current was passed through them. Thomas Edison (1847-1931) found that by inserting a small metal plate into the tube he could cause current to flow from the filament to the plate. This was called the Edison Effect. Edison patented the device and called it the Thermionic Tube. William Thomson (1824-1907) was knighted and became Lord Kelvin after laying the Atlantic Cable in 1866. Later, he described absolute zero as the tem­ perature of a reservoir to which a Carnot engine would reject no heat. He later developed the absolute temperature scale, graduated in degrees Kelvin. This scale does not rely on a thermoelectric property of a substance so there is no problem of deciding which thermoelectric property or substance to use. In terms of the Celsius thermometer, absolute zero is defined as -273.15°C. Absolute zero is often considered the point at which all random molecular motion stops. Although this is not a true definition, it is very close. App. I A Brief History of Thermal Engineering of Electronic Systems 551

In 1804, the French inventor Joseph Jacquard (1752-1834) demonstrated his loom for Napoleon. The loom used punched cards to weave complex textile pat­ terns. Mobs of silkworkers, angry at the automation of their craft , destroyed looms all over Europe. The Engli sh mathematician Charles Babbage (1792-1871 ) built the first true computer. Babbage also invented the speedome­ ter and the cow-catcher. In 1822, incensed by the inaccurate mathematical tables of his time, he constructed a system of cogs and gears called the "Difference Engine." The engine could rapidly and accurately calculate long lists of func­ tions. Only one was built. After further experimentation he conceived of the more complex "Analytical Engine." He produced thousands of drawings for this programmable device, which had data storage, logic circuits, memory, and data retrieval. None were built. His ally, Augusta Ada Byron, countess of Lovelace , daughter of the English poet Lord Byron (1788-1824), wrote a program to cal­ culate Bernoulli numbers. She envi sioned punch card data entry similar to Joseph Jacquard's loom. The device would have been as large as a football field and would have required a power supply of six steam locomotive s to overcome the gear friction during calculations. In 1834 Jacob Perkin s, a Massachu setts inventor, patented a refrigerator employing a compressor and a closed-loop ammonia system. From 1843 to 1850, James Prescott Joule (1818-1889) published a series of papers explain­ ing his experiments to measure heat as an equal to mechanical energy. The Joule, named in his honor, is equal to the energy expended moving a one coulomb charge (6.242 X 1018 electron s) against one volt. A French engineer, Ferdinand Carre, developed the first heat absorption system between 1851 and 1855. Later, Karle von Linde, a German engineer, introdu ced the first com­ pression refrigeration system. Linde developed his ammonia refrigerant system between 1873 and 1875. The science of hydrodynamic s was established in 1851 when the British physicist and mathematician Sir George Stokes (1819-1903) described the movement of a sphere through a viscous fluid. The British system of units mea­ sures kinematic viscosity in "Stokes." In 1883, Osborne Reynolds (1842-1912) published his paper on fluid turbulence. The dimensionless number ratio of iner­ tial force to viscous force within the fluid stream is named in his honor. In 1871, the Englishman John Strutt, 3rd Baron of Rayleigh (1842-1919), explained why the sky is blue. Lord Rayleigh made many contributions to the field of wave phenomena, and laid the foundation for the distribution of energy in blackbody radiation. A dimensionless number ratio named in his honor represents the ratio of buoyant forces to viscous forces. The Grashof number is often multiplied by the Prandtl number to arrive at the Rayleigh number. The ratio of the Grashof number and the Reynolds number suggests whether natural or forced convective forces are dominant. 552 App. I A Brief History of Thermal Engineering of Electronic Systems

In 1847 the German physiologist Hermann von Helmholtz (1821-1894), a direct descendant of William Penn, published a paper that consolidated all known information about the conservation of energy . He supported his paper with mathematical arguments. He was also the first to measure the speed of nerve impulses. A St. Louis bank clerk, William Burroughs (1885-1898), devised the first commercial calculating machine in 1885. He sold it in Chicago in substan­ tial numbers. An American engineer, Herman Hollerith (1860-1929), persuaded the U.S. Census Bureau to try punched card programming for the 1890 census . Soon, punched cards were being used in many offices. In 1896 Hollerith formed the Tabulating Machine Company. Later, another firm absorbed Hollerith's com­ pany to form the Computing-Tabulating-Recording Company, which evolved to become International Business Machines Corporation (IBM). In 1904, John Fleming (1849-1945) built the Fleming Valve, a vacuum diode that could detect radio signals. After several contributions to research in photome­ try, Fleming was knighted in 1929. One year later, Lee De Forest a 33-year-old American inventor, patented the Audion Tube. It was the first amplifying triode vacuum tube. It was soon wedded with Marconi's wireless invention to produce ra­ dio. Although De Forest had a technical Ph.D., it is said that he did not understand how his device worked, and its discovery was an accident. Nevertheless, his dream was to bring his great joy (opera) into every home in America. In 1906 the German inventor Hermann Nernst (1864-1941) discovered the third law of thermodynamics. This 1920 Nobel prize law states that entropy approaches zero as temperature approaches absolute zero. He sold his patent for the Nernst lamp for one million marks, but an improved version of Edi­ son's light bulb soon replaced Nernst's lamp. A New York farmhand, Willis Carrier, was fascinated by heat transfer during his studies at Cornell Univer­ sity. One year after he graduated, he undertook the task of cooling a Brook­ lyn printer's office. His breakthrough accomplishment was to calculate and balance the airflow against the cooling effect to reduce the humidity . This bal­ ance further cooled the air. He built a very successful business. By 1930, movie theaters were advertising "Air-Conditioning" in larger letters than the movie title. 1913 saw the production of the first commercial refrigerator. The "Domelre" cost about $900 at a time when $11 was the average weekly wage. Using the ideas of Charles Babbage, Dr. Vannevar Bush (1890-1974), while Dean of Engineering at the Massachusetts Institute of Technology (MIT), built the first large-scale electromechanical analog computer, the Differential Ana­ lyzer, in 1925. In 1941 President Roosevelt appointed Dr. Bush to be the first director of the Office of Scientific Research. His proposal for a similar office, for peacetime research , led to the formation of the National Science Foundation. App. I A Brief History of Thermal Engineering of Electronic Systems 553

By the late 1920s pentode tubes had grown so large and powerful that cool­ ing fans were placed around the devices. In 1935, I. E. Mouromtseff and H. N. Kozanowski published "Comparative Analysis of Water-Cooled Tubes as Class B Audio Amplifiers." They used four gallons per minute of deionized water to cool an 11.3 kW tube. By 1942 liquid cooling was firmly established and was required to cool such new and powerful devices as the Amplitron, the Mag­ netron, and the Klystron tubes. During this time Mouromtseff devised a dimen­ 6 sionless number to evaluate cooling media, p0.8 kO. Cp 0.4/I-L 0.4. This has become known as the Mouromtseff number. The first large scale digital electromechanical computer, the Mark I, was de­ signed by Dr. Howard Aiken (1900-1973) of Harvard University in 1937. IBM built the computer in 1944. A year later, Grace Hopper, while troubleshooting the malfunctioning computer, found a moth lodged in a circuit. From that time on, a computer malfunction was said to be a "bug." In February 1946, the first electron­ ic digital computer was unveiled at the University of Pennsylvania in Philadelphia. John Mauchly (1907-1980) and J. Presper Eckert (1919-) built it for the sole pur­ pose of calculating artillery ballistic tables. The Electronic Numerical Integrator and Calculator (ENIAC) made mistakes and required repairs about every seven minutes. This milestone computer used air-conditioned hallways to cool its 18,000 vacuum tubes, 500,000 soldered joints, and 30 tons of wiring. It is rumored that the lights of Philadelphia dimmed when the machine was turned on. At a cost $500,000 (1946 dollars) it was the equivalent of today's hand-held calculator, and had a speed of 500 additions and subtractions per second. ENIAC was nonprogrammable and had to be rewired for each new problem. In 1951 Mauchly and Eckert intro­ duced the first commercially available computer, the UNIVAC I. When Bell Labs developed the transistor in 1947, most scientists thought that the burden of cooling electronics would be eliminated. It was, but only for a short time. Soon, the problem became worse. A 1949 article in Popular Mechanics contained the bold statement "Someday, computers may weigh less than 1.5 tons." By the late 1950s powerful transistors and newly developed inte­ grated circuits were in use. In 1958 J.S. Kilby invented the integrated circuit, which consists of multiple transistors on a single piece of silicon. While these new devices produced less total heat, there was now much less surface area to dissipate that heat. Consequently, Watt density (heat generation/surface area) increased. Gordon Moore, co-founder of Intel Corporation, predicted that the number of transistors produced on a single silicon wafer will double every 18 months. Moore's Law has held true for more than 30 years. By the 1960s engineers had devised indirect cooling using coldplates, and were using dielectric fluids for direct immersion cooling. Airborne military sys­ tems used coldplates with ethylene-glycol mixtures to cool their avionics. Uni­ versities began to study direct immersion cooling as a way to avoid the reservoirs , piping, leak-proof connectors, and pumps mandated by indirect cool- 554 App. I A Brief History of Thermal Engineering of Electronic Systems

ing. In 1969 Dr. De Forest, father of radio , said "[Man will never reach the moon] regardless of all future scientific advances." Although direct immersion cooling was gaining use in closely controlled environments in the 1970s, direct immersion (pool-boiling) cooling for high power assemblies was regarded with growing disfavor. Circuits had become so powerful that some fluids would boil when in contact with these circuits. Engi­ neers knew that the heat transfer coefficient increased dramatically during this phase change, but actual systems suffered from thermal hysteresis at the critical boiling temperature. Instead of the circuit maintaining the constant temperature of the boiling fluid, ICs would sometimes exceed the boiling point by 50°C before the fluid in contact with the IC would begin to boil. In 1977 Kenneth Olen, president and founder of Digital Equipment Corp, said "There is no rea­ son for any individual to have a computer in their home." Because of problems associated with direct immersion, system designers in the early 1980's began to use ideas such as helium-cooled pistons, jet-impinge­ ment, and heat pipes, for indirect cooling. These concepts were introduced in new supercomputers, most notably, the Thermal Control Module (TCM) in the IBM 3090. Because of the market pressure to develop even smaller systems, electronic companies began to provide large funds for research programs at uni­ versities. Researchers began to understand the factors involved in reducing the thermal hysteresis in prior assemblies. In 1986, ETA Inc., developed a computer that had its processors immersed in a bath of liquid nitrogen at -190°C. Today, laptop computers use liquid heat sinks. Designers use Computational Fluid Dynamics (CFD) to better understand convective cooling processes. Engi­ neering specialists use lasers to cut microchannels into an IC's surface, and force synthetic fluids costing over $300 per gallon through the microtunnels to cool the latest semiconductors. Prototype diamond substrates are now available. These substrates allow faster movement of electrons than either gallium arsenide or silicon. And, since they have a higher dielectric strength, diamonds can oper­ ate at higher power levels. Also, diamonds have the highest thermal conductiv­ ity (2000 Wlm K) of any material: Five times greater than pure copper, 17 times greater than silicon, and 40 times that of gallium arsenide. Tomorrow, superconducting circuits may be standard catalog items. Minia­ ture cryogenic systems will offer new challenges to designers. Automobiles will use liquid cooling to improve module reliability in the severe underhood envi­ ronments. "Smart" houses may have dedicated cooling for their computers. Magnetic and sonic refrigeration techniques may see commercial use. Two things are certain: circuits will grow more powerful and smaller, and the ther­ mal engineering specialists will be faced with more difficult challenges . Appendix II

Properties

Air at Sea-Level Atmospheric Pressure

Temp. Density Coef. Specific Thermal Absolute Kinematic Prandtl Exp. Heat Condo Viscosity Viscosity Number 3 6 6 (T) p 13 X 10 Cp k IL X 10 V X 10 Pr COF) COC) (kg/m ' ) (IlK) (J/kg K) (W/m K) (N s/rrr') (m 2/s)

32 0 1.293 3.664 1003.9 0.02417 17.17 13.28 0.7131 41 5 1.269 3.598 1004.3 0.02445 17.35 13.67 0.7127 50 10 1.242 3.533 1004.6 0.02480 17.58 14.16 0.7122 59 15 1.222 3.470 1004.9 0.02512 17.79 14.56 0.7118 68 20 1.202 3.412 1005.2 0.02544 18.00 14.98 0.7113 77 25 1.183 3.354 1005.4 0.02577 18.22 15.40 0.7108 86 30 1.164 3.298 1005.7 0.02614 18.46 15.86 0.7103 95 35 1.147 3.244 1006.0 0.02650 18.70 16.30 0.7098 104 40 1.129 3.193 1006.3 0.02684 18.92 16.76 0.7093 113 45 1.111 3.142 1006.6 0.02726 19.19 17.27 0.7087 122 50 1.093 3.094 1006.9 0.02761 19.42 17.77 0.7082 131 55 1.079 3.048 1007.3 0.02801 19.68 18.24 0.7077 140 60 1.061 3.003 1007.7 0.02837 19.91 18.77 0.7072 149 65 1.047 2.957 1008.0 0.02876 20.16 19.26 0.7067 158 70 1.030 2.914 1008.4 0.02912 20.39 19.80 0.7062 167 75 1.013 2.875 1008.8 0.02945 20.60 20.34 0.7057 176 80 1.001 2.834 1009.3 0.02979 20.82 20.80 0.7053 185 85 0.986 2.795 1009.8 0.03012 21.02 21.32 0.7048 194 90 0.972 2.755 1010.3 0.03045 21.23 21.84 0.7044 203 95 0.959 2.718 1010.7 0.03073 21.41 22.33 0.7041 212 100 0.947 2.683 1011.2 0.03101 21.58 22.79 0.7038

555 556 App. II Properties

Water at Sea-Level Atmospheric Pressure

Temp. Density Coef. Specific Thermal Absolute Kinematic Prandtl Exp. Heat Condo Viscosity Viscosity Number 3 6 6 (T) p 13 X 10 Cp k fL X 10 V X 10 Pr (OF) (oq (kg/m') (IlK) (Jlkg K) (W/m K) (N s/m') (m2/s)

32 0 999.9 -D.068 4217.5 0.5580 1794 1.794 13.56 41 5 1000 0.018 4202.7 0.5677 1530 1.530 11.33 50 10 999.7 0.095 4192.4 0.5774 1296 1.296 9.410 59 15 999.1 0.16 4185.8 0.5870 1136 1.137 8.101 68 20 998.2 0.22 4181.7 0.5967 993 0.995 6.959 77 25 997.1 0.26 4179.5 0.6064 880.6 0.883 6.069 86 30 995.7 0.31 4178.6 0.6155 792.4 0.796 5.380 95 35 994.1 0.35 4178.5 0.6243 719.8 0.724 4.818 104 40 992.2 0.39 4179.0 0.6325 658.0 0.663 4.348 113 45 990.2 0.42 4179.9 0.6401 605.1 0.611 3.951 122 50 988.1 0.45 4181.1 0.6472 555.1 0.562 3.586 131 55 985.8 0.48 4182.6 0.6536 512.6 0.520 3.280 140 60 983.5 0.51 4184.5 0.6594 470.0 0.478 2.983 149 65 980.8 0.54 4186.8 0.6643 436.0 0.445 2.748 158 70 978 0.57 4189.5 0.6686 402.0 0.411 2.519 167 75 974.9 0.60 4192.9 0.6724 376.6 0.386 2.348 176 80 971.7 0.63 4196.6 0.6753 350.0 0.361 2.175 185 85 968.5 0.66 4201.0 0.6778 330.5 0.341 2.048 194 90 965 0.69 4205.7 0.6797 311.0 0.322 1.924 203 95 961.7 0.72 4210.6 0.6811 294.3 0.306 1.819 212 100 958.4 0.75 4215.5 0.6822 277.5 0.290 1.715 App. II Properties 557

Perfluorocarbon FC-72 at Atmospheric Pressure (Boils at 56°C)

Temp . Density Coef. Specific Thermal Absolute Kinematic Prandtl Exp . Heat Cond o Viscosity Viscosity Number 3 6 6 (T) p f3 X 10 k fl. X 10 V X 10 Pr < 2 2/s) (OF) eC) (kg/m ' ) (IlK) (J/kg K) (W1m K) (N s/m ) (m

32 0 1740 1.601 1005.0 0.0600 1009.5 0.5802 16.91 41 5 1727 1.611 1016.2 0.0595 932.4 0.5399 15.93 50 10 1714 1.619 1025.6 0.0590 861.6 0.5027 14.98 59 15 1701 1.626 1033.2 0.0585 799.5 0.4700 14.12 68 20 1688 1.633 1039.8 0.0580 743.0 0.4402 13.32 77 25 1675 1.640 1046.6 0.0575 693.8 0.4142 12.63 86 30 1662 1.647 1053.5 0.0570 648.2 0.3900 11.98 95 35 1649 1.654 1060.8 0.0565 610.1 0.3700 11.46 104 40 1636 1.662 1068.7 0.0560 574.3 0.3510 10.96 113 45 1623 1.670 1077.5 0.0555 543.9 0.3351 10.56 122 50 1610 1.680 1087.0 0.0550 514.8 0.3198 10.17 131 55 1597 1.689 1096.5 0.0545 486 .0 0.3043 9.778 558 App. II Properties

Perfluorocarbon FC-77 at Atmospheric Pressure (Boils at 97°C)

Temp. Density Coef. Specific Thermal Absolute Kinematic Prandtl Exp. Heat Condo Viscosity Viscosity Number 3 6 6 (T) p 13 X 10 Cp k fL X 10 V X 10 Pr COF) (0C) (kg/m' ) (l1K) (J/kg K) (W1m K) (N s/m') (m 2/s)

32 0 1838 1.399 1005 0.0649 2356 1.282 36.48 41 5 1826 1.407 1016 0.0646 2117 1.159 33.30 50 10 1814 1.414 1025 0.0643 1905 1.052 30.37 59 15 1802 1.421 1033 0.0640 1719 0.9539 27.75 68 20 1789 1.429 1041 0.0637 1554 0.8686 25.40 77 25 1777 1.436 1048 0.0634 1413 0.7592 23.36 86 30 1765 1.443 1056 0.0631 1288 0.7298 21.56 95 35 1753 1.451 1063 0.0628 1178 0.6720 19.94 104 40 1740 1.458 1071 0.0625 1083 0.6224 18.56 113 45 1728 1.466 1079 0.0621 1001 0.5793 17.39 122 50 1716 1.473 1087 0.0617 927.0 0.5402 16.33 131 55 1704 1.481 1096 0.0613 862.4 0.5061 15.42 140 60 1691 1.489 1105 0.0609 805.0 0.4761 14.61 149 65 1679 1.497 1114 0.0604 753.2 0.4486 13.89 158 70 1667 1.504 1123 0.0600 706.1 0.4236 13.22 167 75 1655 1.512 1131 0.0595 662.3 0.4002 12.59 176 80 1642 1.520 1140 0.0590 622.1 0.3789 12.02 185 85 1630 1.527 1147 0.0585 584.0 0.3583 11.45 194 90 1618 1.534 1154 0.0580 548.0 0.3387 10.90 203 95 1605 1.541 1159 0.0575 513.2 0.3198 10.34

Data from Fluorinertlf Liquids Product Manual, 3M. App. II Properties 559

Thennophysical Properties of Nonferrous Metals at 20 ce

Materials Density Coef. Specific Thermal Exp. Heat Condo 6 p a X 10 cp k (kg/m' ) (IlK) (J/kg K) (W/m K)

Aluminum (1100) 2,713 23.6 921 222 Aluminum (2014) 2,796 23.0 921 192 Aluminum (2024) 2,768 23.2 921 189 Aluminum (5052) 2685 23.8 921 139 Aluminum (6061) 2,713 23.4 963 180 Aluminum (7075) 2,796 23.6 963 121 Aluminum (356) 2,685 21.4 935 159 Beryllium 1,855 11.5 1,884 151 Brass (C36000) 8,498 20.5 380 116 Bronze (C22000) 8,802 18.4 377 189 Copper (C11000) 8,913 17.6 383 391 Copper (C12200) 8,941 17.6 385 339 Copper (C22000) 8,802 18.4 377 189 Copper (Alloy MF 202) 8,862 17.0 382 150 Glass Seal (Alloy Ni 50) 8,332 8.46 482 10.4 Gold 19,321 14.2 129 313 Inconel (625) 8,442 12.8 410 9.82 Kovar 8,343 4.30 16.0 Lead 11,349 29.3 130 33.9 Magnesium (AZ 31B-F) 1,772 25.2 1026 76.2 Monel (400) 8,830 13.9 427 21.8 Nickel (270) 8,885 13.5 461 91.0 NILO (Alloy 42) 8,138 4.86 482 10.4 Palladium 12,013 11.7 244 76.2 Platinum 21,452 8.82 129 72.7 Silver 10,494 19.6 234 419 Solder (Sn60Pb40) 8,500 24.5 176 51.0 Tantalum 16,608 6.48 151 54.5 Tin 7,307 23.4 227 67.0 Titanium 4,510 9.54 531 17.5 Titanium (Ti-6AI-4V) 4,429 9.36 574 7.27 Zinc (SAE 925) 6,699 27.4 417 109 560 App. II Properties

Thennophysical Properties of Ferrous Metals at 200 e

Materials Density Coef. Specific Thermal Exp. Heat Condo 6 p a X 10 Cp k (kg/m') (11K) (J/kg K) (W/m K)

Carbon steel (AISI 1010) 7,830 6.60 434 64.0 Carbon steel (AISI 1042) 7,840 6.50 460 50.0 Cast iron (ASTM A-48) 7,197 10.8 544 50.2 Cast iron (ASTM A-220) 7,363 13.5 544 51.1 Cast steels (carbon & alloy) 7,834 14.7 440 46.7 Stainless steel (4130) 7,833 13.5 456 43.3 Stainless steel (17-4 PH) 7,778 10.8 461 18.0 Stainless steel (304) 8,027 17.3 477 16.3 Stainless steel (316) 2,685 16.0 468 16.3 Stainless steel (440) 7,750 10.1 461 24.2 App. II Properties 561

Thennophysical Properties of Plastic at 200 e

Materials Density Coe£. Specific Thermal Exp. Heat Cond o 6 p a X 10 Cp k (kg/m ' ) (11K) (J/kg K) (W/m K)

ABS (acrylonitrile butadiene styrene) 1,058 72.0 1,466 2.70 Acetal 1,415 82.8 1,465 3.01 Acrylic 1,178 81.0 1,466 2.49 Alkyd 2,206 36.0 9.87 Cellulose acetate 1,257 121 1,508 3.01 Epoxy (cast) 1,148 59.4 1,884 4.15 Epoxy (IC molding) 1,820 17.0 984 4.00 Fluorocarbon (PTFE) 2,196 90.9 1,047 2.91 Polyamide (nylon type 6) 1,247 89.1 1,675 2.08 Phenolic 1,387 37.4 1,570 1.74 Polycarbonate 1,203 67.5 1,256 2.39 Polybutylene terephthalate (PBT) 1,307 72.0 1,905 1.90 Polyester 1,287 85.5 1,780 2.29 Polyimide 1,427 47.7 1,214 8.05 Polyamide-imide 1,397 36.0 2.94 Polyetherimide 1,277 54.0 1,090 2.2 Polyetheretherketone 1,317 40.5 2.95 Polyetherketone 103 Polystyrene 1,039 72.9 1,361 1.54 Polyethylene 933 225 2,261 3.95 Polypropylene 903 86.4 1,884 2.22 Polyvinyl Chloride (PVC) 1,447 54.0 1,050 1.77 562 App. II Properties

Thermophysical Properties of Ceramics at 20°C

Materials Density Coe£. Specific Thermal Exp. Heat Condo 6 p IX X 10 Cp k (kg/m ') (11K) (J/kg K) (W/m K)

Aluminum oxide 3,982 5.67 879 30.0 Aluminum nitride 3,200 4.40 711 200 Beryllium oxide 2,900 7.00 1030 300 Boron nitride (cubic) 2,200 3.80 709 1,300 Diamond (film) 3,500 2.00 510 1,200 Fused quartz 2,200 0.50 745 1.60 Glass (die attach) 2,900 50.0 Silicon 2,300 4.20 664 83.7 Silicon nitride 3,300 2.00 624 21.0 Author Index

Abramovich,G. N., 208 Burroughs, W., 552 Addoms, J. N., 483 Bush, V., 552 Aihara, T., 389 Byron, Lord, 551 Aiken, H., 553 Carnavos, T. C., 287 Altoz, F. E., 116 Carnot, N. L. S., 550 AI-Arabi, M., 378, 381 Carri, F., 551 Annund, W. J. D., 210 Carrier, W., 552 Antonetti, V. M., 125 Carrothers, P. J. G., 211 Archimedes, 546 Catton, I., 374-376 Arnold, J. N., 376 Celsius, A., 414, 433, 549, 550 Austin, L. R., 209 Chao, B. T., 450 Avogadro, A., 550 Chen, M. M., 485, 487 Ayyaswamy, P. S., 375, 376 Chilton, T. H., 281, 282, 284, 285, 481 Babbage, c, 551, 552 Choi, H., 481 Bacon, R., 546 Chu, H. H. S., 344, 346-348, 377 Baines, W. D., 211 Chun, K. R., 481, 485, 486 Bardowicks, H., 307 Churchill, S. W., 291, 304, 318, 344, 346-348, Bar-Cohen, A., 117, 120,257,352 377,379,400,401 Berdahl, P., 434 Cichelli, M. T., 462 Berenson, P. J., 465 Clapeyron, 446 Bergles, A. E., 446 Clark, J. A., 466 Bernath, L., 464 Clausius, 446 Bernoulli, D., 158, 161, 167-172, 174-177, 197, Colburn, A. P., 256, 281, 282, 284, 285, 290, 548,551 295,481 Bernstein, M. 304, 318 Cole, R., 447 Bilitzky, A., 383, 414 Coleman, H. W., 214 Black,J., 243,406,407,410-412,417,421 ,549 Collier, J. G., 454 Blasius, H., 188, 189,289 Cooper, M. G., 119 Boelter, L. M. K., 281, 282, 284, 285 Coulomb, C. A., 549, 551 Bohn, M. S., 288 Courchesne, J., 307 Bonilla, C. F., 462 Crawford, M. E., 286, 291, 296 Boussinesq, J., 12,337,342 Cullen, W., 549 Boyle, R., 548 Da Vinci, L., 546 Bromley, L. A., 449, 466 Daile Donne, M., 215 Brown, A. I., 348, 366 Daniels, D. J., 466 Brunt, D., 434 Danielson, R. D., 456

563 564 Author Index

Darcy, H., 179 Hansen, M., 189 De Fermat, P., 547 Harper, C. A., 414 De Forest, L., 552, 554 Harris, C. H., 201, 203 Delany, N. K., 307 Hatfield, D. W., 365 Descartes, 547 Hendricks, R. C., 448 DeWitt, D. P., 516 Herbert, M. V., 210 Dhir, V. K., 461 Hetsroni, G., 446, 447, 456 Dipprey, D. F., 310 Hilpert, R., 302, 344, 347, 348, 360, 364, 366 Dirichlet, 101 Ho, C. Y., 492 Dittus, F. W., 281, 282, 284, 285 Hollands, K. G. T., 373, 375 Donaldson, E., 380 Hollerith, H., 552 Drew, T. B., 451 Hooke, R., 548 Dropkin, D., 372 Hopper, G., 553 Du Fay, C. F., 549 Hottel, H. C., 425 Eckert, E. R. G., 257, 345, 553 Howard, 425, 553 Ede, A. J., 378 Howell, J. R., 423, 425 Edison, T. A., 550, 552 Imai, K., 207 Edwards, D. K., 267, 271, 272, 277, 278, 365 Incropera, F. P., 516 Eichhorn, R., 467 IdeI' chik, I. E., 202, 203, 206 Elenbaas, M., 257, 349-351, 355, 356, 358-360, Ito, H., 204, 206, 207 386,387,389 Jackson, T. W., 345 Elizabeth I, Queen, 547 Jacob, M., 306, 308, 309, 320, 323, 329, 330, Ellion , M. E., 464 372,551 Emery, A. P., 374 Jacquard, J., 551 Euclid,545 Joule, J. P., 136,551 Euler, L., 156, 158, 165, 167, 177,548-550 Kays, W. M., 286, 291, 296 Eustis, 447 Kelvin, Lord, 399, 550 Fahrenheit, G. D., 548 Kern, D. Q., 112, 114 Fanning, 179,281,288 Khamis, M., 378 Ferdinand III, 548 Khowarizmi, 546 Ferdinand II, 547 Kilby, J. S., 553 Fleming, J., 552 Klimenko, V. V., 471 Florschuetz, L. W., 450 Kovalev, S. A., 465 Fourier, J. B. J., 51, 257, 258, 550 Kozanowski, H. N., 553 Franklin , B., 549 Kraus, A. D., 112, 114, 117, 120,257 Frederking, T. H. K., 466 Kreith, F., 288 Fromberg, R., 434 Kutateladze, S. S., 461 Galileo, G., 546, 547 Lanville, A., 307 Gebhart, B., 341 LeFevre, E. 1., 378 Geissler, H., 550, 552 Leidenfrost, 452, 453, 464, 465 Gibson, A. H., 197 Lewis, G. W., 258, 260, 480 Giedt, W. H., 302 Lienhard, J. H., 382, 461, 465, 467, 485 Gilbert, W., 547 London, A. L., 286, 548, 549 Gilliland, E. R., 480 Louis XVI, King, 550 Globe, S., 372 Lovelace , Countess of, 551 Gnielinski, V., 282, 285, 315 MacGregor, R. K., 374 Graham, R. W., 448 Madison, R. D., 206 Gregg, J. L., 378 Mahrenholtz, 0 ., 307 Halley, E., 548 Marco, S. M., 348, 366 Hamilton, J. B., 202 Martin, H., 331-333, 335, 336 Author Index 565

Martin , J. G., 425 Ramsey, J. W., 319, 325, 327 Mauchly, J., 553 Rayleigh , 3rd Baron of, 116,257,258,260,337, McAdams, W. H., 364, 366, 376, 377 343, 344, 346-349, 359, 360, 362, 364, McEligot, D. M., 270 367-369, 371, 373-375, 377, 382, 400, Meyer , L., 215 401,465,509,512,551 Mikic, B. B., 125 Reynolds, 0., 13, 175, 179-186, 189, 191, 192, Mills, A. F., 189, 214, 267, 323, 325, 326, 328, 194, 195, 210, 212 , 215, 225 , 226 , 362,421,466 228-231,235,247,248,250,253-256, Moin, P., 13 258-260, 263, 265-268, 271-273, 277, Moody, L. F., 212, 281 280-282, 284, 292, 294-304, 306, 307, Moore, G., 553 309, 311, 313-316, 323, 325-328, Mueller, c, 451 335-337, 339, 343, 390, 448, 467, 470, Muriel, M. J. B., 425 472,475,477,481,485,486,496,551 Nakai, S., 303 Rich, B. R., 362 Napier, 1., 547 Rohsenow, W. M., 350 , 352, 446 , 447 , 454, Napoleon, 551 455,481,485 Nernst , H., 552 Roosevelt, F. D., 552 Nikuradse, J., 212, 364 Rumford, Count, 549 Nukiyama, S., 451 Sabersky, R. H., 310 Nusselt, E. W. H., 192,241,249,250,253-261, Sadasivan, P., 485 263 , 266-268, 270-273, 275-279, Sanctorius, 547 281-287, 290-292, 296, 302, 303, 305, Schlichting, H., 215, 292 306, 308-310, 313-316, 318, 319, Schmidt , E., 51, 258, 260, 261, 289, 480 325-328, 332, 333, 335-340, 343, 344, Schneider, P. 1., 57 347, 348, 350-352, 355, 356, 358-360, Seader , J. D., 209 362, 364, 365, 367-369, 372-374, 376, Seban, R. A., 481, 485, 486 379, 382, 383, 387, 388, 390, 444, Seto, W. W., 534 453-455,459,460, 471, 472, 476-479, Shah, R. K., 286 481,484-486 Sherwood, T. K., 260, 261, 480 Obasaju, E. D., 307 Shlykov, Y. L., 120 Okazaki , T., 303 Sieder, E. N., 281, 282, 284, 285 Oosthuizen, P. H., 380, 381 Siegel, R., 425 Ozisik, M. N., 56 Soren sen, N. E., 307 Owe, H. J., 291 Sparrow, E. M., 310, 319, 325, 327, 378, 389 Parker, J. R., 206 Squire , H. B., 301 Pascal, B., 547 Steinberg, D. S., 366 Penn, W., 552 Stokes , G., 13, 15, 177,551 Perkins , J., 551 Strutt, J., 260, 551 Petukhov, B. S., 475 Sukhatme, S. P., 303 Pinker, R. A., 210 Sunderland, 1. E., 389 Plank, M., 402, 403, 407 Swearingen, T. W., 270 Plesset, M. S., 450 Sylvester, N. D., 212 Pohlhausen, E., 289, 290 Tate, G. E., 281, 282, 284, 285 PrandtI, L., 12, 184, 194,246,249,250,253, Taylor, R. P., 12, 66 254, 256, 258-260, 264-269, 278, 280, Thale s,545 289, 290, 294, 295, 301, 309, 325, 327, Thomp son, B., 549 337,390,400,444,454,551 Thomson, W., 550 Pythagorus, 545 Torricelli, E., 161,547 Quarmby, A., 302 Vemuri , S. B., 389 Rai, M. M., 13 Vennard, J. K., 198 566 Author Index

Volta, A., 549 Wong, P. T. Y., 465 von Karman, T., 300 Wren, c., 548 von Leibniz, G. W., 548 Yamagata, K., 454 von Linde, K., 551 Yardi, N. R., 303 Ward Smith, A. 1., 206 Yovanovich, M. M., 125 Watt, J., 5, 6, 72, 242, 338,505,522, 528, 549, Yuge, T., 378 553 Zigrang, D. 1., 212 Whitaker, S., 305 Zografos, A. I., 389 White, F. M., 215, 292, 397, 407, 411,412, 432, Zuber, N., 449, 461, 463, 464 542 Zukauskas, A. A., 302, 319, 322, 323, 325-327, Wills, M., 310, 313, 314, 316 329,330 Wong, H. Y., 425 Zwick, S. A., 450 Subject Index

Absolute, Adhesive, 22, 24-27, 33, 36 asperity angle, 119, 121, 122 Adiabatic, 59, 101, 257, 351, 526 deviation , 472 Air, 16,94,216,219,220,230,242, 348, 357, pressure, 161 519,520,526-530 scale, 538 ambient, 16, 40, 48, 93-95, 109, 248, terms, 142 324-328,353,518 zero, 431, 438, 552 bulk modulus, 132 Absolute temperature , 244, 398, 399, 402-404, convection, 90, 131, 262 434,490,491,520,521,550 density, 132,219,220,528 Absolute viscosity, 133, 134, 181, 251, 252, film, 95, 96 268,272,282,294,443,454,458 flow, 16, 17, 184,216,219,221,223-227, Absorptance, 419, 435, 496 245,255,306,323,552 energy, 399, 406, 431,440 head loss, 229, 230 heat, 132,242,348,405,406,440,441,444, inlet, 227, 235 490,496,551 interface, 116, 120-124, 136, 137,480 radiation, 3, 397, 398,407,419,433 mass, 242 solar energy, 407, 410, 429, 431-433 particles, 519, 527, 528, 530 sound, 519, 525 pressure, 131,520,528,529,538 Acceleration , 142, 144, 146, 147, 155 properties, 248, 313, 314, 356, 357, 520 components , 143, 147, 151-156, 169 space, 22, 438, 530, 532 fluid, 140, 142-148,208,297 speed of sound in, 520 gravitational, 158, 168, 223, 254, 339, 362, temperature , 93-95, 96, 248, 324-328, 345, 454 348, 353, 507, 521, 524 level, 524, 525 unstable 218 streamline, 150, 156, 157, 159, 171 Air-cooled, 3, 221, 263, 312, 438 two-dimensional, 166, 167 Algebra, 65, 253, 396,428,434, 546,549 Acoustics, 518, 529, 537, 538, 540-542, 549 Altitude, 131, 132, 142,220 Acoustic Alumina, 120, 122 doublet, 535 Aluminum, 23, 36, 46, 71, 108, 120,410 impedance, 529, 532 bracket, 33, 35, 76, 90 intensity, 528, 531 core, 46 power, 522, 525, 537, 542 emittance, 399, 407, 410 pressure, 527, 528, 531-533, 535, 536, 543 heat sink, 23, 92,102,105, 120,417 resistance, 529 heat spreader, 45 unit, 538, 540, 541 interface, 120, 122, 124 wave, 520, 524, 526-532,542 wall, 71

567 568 Subject Index

American, 259, 549, 552 pressure, 131, 142,220,221,439,441,520, American Revolution, 549 528,529,538,547,548 Amplitude, 99, 194,531,535,536,538,542, radiation and, 429, 433, 434 544 standard, 179,223,439,520,528 Analog, 552 Atomic, 3, 22, 23 Analogic, 51 Automotive, 211, 456 Analogy, 250, 281, 292, 293, 295, 310 Average, 293, 386,387, 406, 420, 528, 542, 552 Analysis, 152,224,382,461,465,466,517,553 density, 90, 92 acoustic, 526, 541 directional, 408, 419 conduction, 57, 59, 89, 128 flow, 148,330,469,531 convection, 382 friction coefficient, 185, 186, 191,214,246, dimensional, 250, 253-255, 461 248,249,295 finite element, 9, II, 13, 15, 382 gap, 119 finite difference, 11, 12,63 heat transfer coefficient, 259, 272-274, 278, finite volume, 11, 12 279,291,303,318,335,336,383,466, fluid flow, 131, 148, 165, 174, 259, 260, 485- 487 280, 288, 289 heat flux, 429 thermal, 16, 17,51,57,249,517 Nusselt number, 250, 259, 261, 268, 277, turbulence, 12 282, 287, 291, 296, 302, 303, 305, 306, whole-field, 12 308, 309, 318, 325-328, 332, 333, 335, Analytic solution, 52 336, 364, 367, 369, 376, 382 Anechoic chamber, 536 pressure, 140, 524 Angular, 301, 302 properties, 149, 491, 527 Annular, 102, 105, 106, 108,425,469 roughness, 121, 122,225 Apparent, 23, 116, 117, 120, 121, 123, 194,260, Sherwood number, 261 337 sound pressure level, 524, 525 Approximate, 65, 69, 149, 156, 291, 434, 468, Stanton number, 262 492,534 temperature, 64, 87, 94-96 , 125, 269, 270, Arabs, 546 277-279 ,293,332, 366,368-371,386, Area, 2, 6, 107, 115-117, 125,288,294,515 387,507 cross-sectional, 3, 102, 123, 148, 163,224, time, 12, 192, 194 230,271 ,288,467 velocity, 179, 182,284,438 surface, 2, 6, 48, 92, 105, 115, 125, 278, Avogadro number, 550 304,325,349,389,398,414,508,535, Axial, 11, 13, 60, 61, 116,216, 218, 221, 267, 553 534,535 unit, 22, 99, 179, 191, 193,237,251,270, Azimuth, 408, 419 293,294,402,448,492,528 Baffle, 534, 535 Arrangement, 316, 318, 323, 326, 328, 535 Balance, 79, 81, 178,275,434,446,478,546, Array, 16,64,105, 149,312,319,534,535 552 finned, 102, 108, 115, 129,389,414,417 energy, 48, 65, 74, 75,84, 86, 90,101,405, jet, 331, 332, 333 406,419,421,475 pin-fin, 316, 318-320, 322, 323, 326, Band,397,524,525,539-542 328-330, 389, 390 Bar, 117, 120,257,350,352,474 plate, 352, 353, 381, 382, 383, 414, 417 Barometer, 547 printed circuit board, 351, 353 Base, Aspect, 206, 302,374-376,542 area, 107, 115 Asperities, 117-123,212, 309,310 heat flow, 112 Asymmetric, 351-353 , 382 heat sink, 319, 323, 324, 382, 384, 389, 390, Atmosphere, 222, 232, 233, 262, 434, 451, 455, 417 456,458,490 logarithmic, 521, 523, 524 Subject Index 569

Bathtub drain vortex, 170 transient, 84, 89, 96 Beam, 535 Boundary layer, 187, 188, 191,257,296,297, Bel, 521 301,349 Bend, 172,204-206,224,233,268 displacement, 185, 186,215,247-249,292, Bernoulli, 311 constant, 158 flow, 260, 361, 374 equation, 158, 161, 167, 169-172, 174-177, thermal, 185, 241, 245-249, 263, 265, 274, 197,551 288-290,362 numbers, 551 thickness, 185, 186, 189,215,245,246,248, terms, 168 249,290,292,302,311,362 Bernoulli's law, 548 velocity, 184-186,203,245,246,248,249 Bessel functions, 105, 110, Ill, 113, 534 Boussinesq Binaural,543 approximation, 342 Biot number, 86, 96, 129, 255, 256 concept, 12 Blackbody, 398, 399, 402-407 , 419, 430, 431, number, 337 433,434 Bracket, 33, 35, 36, 73, 74, 76, 90, 91 Blackbody radiation, 260, 402, 403, 407, 419, Branch, 207, 208 431,551 Breakdown, 23 Blade, 219, 519 British, 181,260,551 Body, 13,406,438,519 Btu (British Thermal Unit), 5, 21, 22, 49, 402, falling, 161,547 403 fluid, 145,237,262,296,297 Bubble Reynolds number, 448 force, 341, 342 Bubbles, 15, 139, 161, 437, 439, 444-452, heated, 445,461,465 459-46 3,468,469,471,478,496 shape factor, 4 Buckingham 7T, 250, 252, 254, 442, 443 solid, 256 Bulk, I, 8, 132, 180, 273-275 , 302,438,445, Boiling, 237, 437, 439, 441, 444, 445, 450-453 , 464,466,520,526 458,459,466-468,470,478,479,516 Bulk temperature, 245, 268-270, 282, 284, 285 film, 452, 464-466 Buoyancy, 254, 258,374,551 flow, 444,466,467,468,471,496 force, 339-342, 361, 362, 371, 376, 437, liquid, 101,516,548 443,444,446,448,466 nucleate, 446, 448, 450-452, 454, 455, 459, Burnout, 453 460,463,464,468,471,476,496 Calculus, 546, 548, 549 point, 137,442,456,458,461,496,549 Calorie, 241 pool, 444, 450, 451, 453, 454, 460, Capacitance, 70, 74, 75, 85, 86, 89, 92, 94-96, 464-466,554 129 saturated, 445 Capacity, 241, 242, 288, 492 spontaneous, 161 Capillarity, 137 subcooled, 444, 445 Carbon, 410, 457 transition, 452 Carbon dioxide, 397 viscosity, 268 Card, 45, 225, 547, 551, 552 Boundaries, 45, 89, 101, 148, 156, 172, 295, Carnot engine, 550 330, 353 Case, 5, 243, 335, 338,396,412,499,505 Boundary conditions, 15, 100, 102, 189 temperature, 511, 514 acoustic, 527, 530 Casting, 212, 309 conduction, 39, 44, 47, 52, 55-57, 64, 75, Catalog, 554 77, 128, 129 Cavitation, 15, 161 convection, WI, 102,289 Celsius, 414, 433, 550 phase change, WI, 102,491-493 Center, 59,159,160,221,330,374,411,525 radiation, WI frequency, 530, 541 570 Subject Index

Center (cont.) heat source, 125, 126, 128 line, 44, 45, 47, 48, 60, 61,424 Circular tube, 274, 275, 281, 315 of curvature, 141, 169, 170, 171 Classical thermodynamics, 6 of tube or cylinder, 38, 60, 61, 176-178, Clausius-Clapeyron relation, 446 265,268,297,469 Clean, 464, 483 to center, 210, 214, 225,310,312,316,323, Closed system, 7 390,474 Coefficient, 75, 461, 481, 536 Central Processing Unit (CPU), 16, 276, 306, mass transfer, 261, 479-481 307,309,333,335,336 drag, 191,298,301,304,305,307,448 Centrifugal, 216, 218-221 friction, 179, 186,248-250,261,281,288, CFD, see Computational Fluid Dynamics 290,295,296,309,310 Change, 7, 9-11, 84, 89, 220, 273, 342, 343, heat transfer, see heat transfer coefficient 397,422,525,527,528,530,554 interlace, 116, 119, 120,454,457,459,460 momentum, 469, 470, 475, 478 loss, 195, 197, 198,200-208,210,211,223, phase, 15, 102, 135, 237, 437-439, 441, 229,230,232-235,238 444,470,490,491,496,554 momentum, 195,292 pressure, 132, 144,207,208,216,237,520, thermal expansion, 243, 254, 339, 458 547,548 skin friction, 185, 191, 246, 256 rate of, 6, 86 surface tension, 136, 137,441 temperature, 27, 87, 142,243,256,437,438 Collector, 547 volume, 132, 243, 548 Combination, 1,7, 10, 120, 133, 161,382,389, Channel, 181, 208, 212, 309-314, 316, 349, 439,516 353,358,359,382-387,389,414,417 liquid/surface, 454, 456, 457 flow, 184, 207, 215, 224-226, 257, 277, Combine, 81-83, 105, 176, 177,251,259,294, 311,314,355,356 492,540 Characteristic, 216, 221, 223, 243, 252, 254, Combined, 90, 219, 223, 231, 253, 499, 518, 298,445,462,529,534 538,546 dimension, 181, 191, 253, 332, 335, 336, head loss, 227, 229, 231, 235, 236 355, 356, 378, 382, 386-388, 463, 509, heat transfer, 15,39, 128,499,501,506,516 512 resistance, 70, 82, 515 length, 263, 314, 315, 364,446,448,449, Commercial, 13,407,410,552,554 459-461 ,471,476,478 Compact, 204 Chassis, 16,33,36,45,51,71,218,221-223, Complex, 5, 6, 10, II, 36, 56, 241, 275, 496, 236-238, 263, 312, 338, 349, 396, 412, 527,529,551 429 flow, 201, 204, 262, 270, 280, 296, 316, Chilton-Colburn 331,389 analogy, 281 geometries , 12,51,52,57,289,305,376, correlation, 282, 284,285 423,435 factor, 481 sound, 541, 542 Chimney, 258 Component, 71, 76, 143, 151, 155, 169,221, Chinese, 545 225,242,305,309,310,429,438 Chip, 5, 124,276-279,307,309,312,333,338, acceleration, 152-155, 169 413,499 active, 23, 45, 51, 71 Churn, 469 height, 310, 314, 315 Circuit, 26, 46, 472, 482, 516, 539, 553, 554 directional, 10, 11 board, 45, 222-225, 309, 311-313, 349, temperature, 73, 74, 76, 116 351,353,366,499,506 velocity, 10, 11, 151, 169, 176, 177, 188, Circular, 16, 60, 102, 103, 106, 153, 273-275, 189, 192, 259, 280, 361 285,337,425,530,532,533 Composite, 36, 37, 39,46,71,501,502 duct, 212, 273-275, 281, 285, 315 Compressibility, 10, 15, 131, 132, 156,280 Subject Index 571

Computational Fluid Dynamics (CFD), 9-11, Continuity equation, 163, 164, 171 , 187, 188 13,554 Contraction, 201, 203, 204, 227, 229-231, 243 Computer, 9-13 , 85, 129, 150, 165, 338, 382, Control, 75, 216, 288, 300,431 ,451 ,453,518, 493,522,536,553,554 531,542,554 Computer program, 423, 435 Control surface, 8, 516 Concentrate, 52 Control volume, 7-9, 15,77,87 Concentric cylinders and tubes, 60, 376, 412, Convection, 67, 77, 336, 339, 401, 434, 503, 421,425 506 Condensate, 483, 486-488, 496 forced, 10,49 , 131,222,252,253,262,263, Condensation, 437, 439, 442-444, 483-487, 273, 274, 276, 280, 285-289, 292, 296, 489,496,527,528,531-533 304, 305, 309, 316, 330, 337, 338, 340, Conditioned, 553 343,438,466-468,518 Conduct, 21, 102, 108 heat transfer, 39, 89, 109, 241, 252, 262, Conductance, 79, 102, 104, 116, 117, 12~123 , 442,479,480,505,506,509,512 128,301-303,488,489,492 natural, I, 10, 22, 49, 90, 105, 109, 237, Conduction, 2, 3, 21, 76, 116, 241, 245, 337, 242, 245, 253, 254, 257, 258, 260, 262, 374,434,465,503 268, 336, 337, 339-341, 343, 345, 348, complex, 51, 53, 57, 60, 61, 65-67 349, 361, 366, 371, 376, 378, 38~382, electrical, 22, 23 389,451,496,509-513 heat, 1,28,29,32,33 ,38,42,51,57,61,68, Convective heat transfer coefficient, 6, 49, 92, 84,97, 123,128,257,263,489,501,502 93, 98, 115, 253 simple, 32, 33, 38, 39, 42, 48 Convective mass transfer coefficient, 261 thermal, 22, 24, 32, 74, 507 Convergence, II transient, 68, 74, 84-86, 89, 129 Conversion, 132,261,410 Conduction equation, 32, 33, 38, 53, 57, 61, Cool, 3, 85, 137,225 ,323,331,333,335,337, 245,257,491 364,397,438,439,443,516,553,554 Conductivity, 256, 292, 294, 335, 366, 367, 369, Coolant, 1,2,162,173,222,341,456,474 382 fluid, 2, 209, 212, 309, 316 thermal, 3, 21-24, 27, 49, 59,119,120,122, media, 1, 2, 85, 86, 304 268 Cooling, 16, 27, 131, 133, 269, 331, 336, 348, Cone, 380, 381 464,482,490,506,552 Conical, 197-199,203 air, 3, 221, 263, 312, 438 Conjugate, 15 conduction, 413 Conservation, 15,64,289,421,516,517,552 convection,48,309,349,390,518,545,554 of energy equation, 251, 253, 258 liquid, 39, 242, 438, 553, 554 of energy law, 7 radiation, 396, 397, 414 of mass, 10, 12, 187 Coordinate, 10, 11, 28, 29, 32, 33, 66, 75, 76, Constant, 57, 132, 133, 168, 188,220,274,429, 152 454,461,463,520,527,528,530 Copper, 5, 6, 22, 23, 45, 124,276, 277,410, Stefan-Boltzmann, 3, 102, 398, 402, 404, 457,474,475,477,554 411 Correlation, 280, 286, 319, 322, 327, 390, numerical, 54, 71, 76, 98, 101, 135, 146, 509-513 147, 180, 194, 260, 265, 267, 270, 275, Addoms,483 276,289,301,349,448,483,494,542 AI-Arabi-EI-Rafaee, 381 of integration, 44, 47 Al-Arabi-Khamis , 378 Construction, 223 Arnold,376 Contact, 5, 24, 116, 117, 119-124, 133,456 Ayyaswamy-Catton, 375, 376 Contact resistance, 6, 16, 102, 108, 115, 116, Brown-Marco, 348 119, 123, 129 Brunt, 434 Continuity, 167, 169, 197 Catton, 374 572 Subject Index

Correlation (cont.) conduction in, 32, 38, 46-49, 60, 61, 86 Chen, 487 convection on, 255, 274, 296-304, 318, 319, Chilton-Colburn, 282, 284, 285 325,327,341,366,376,378,389 Chun and Seban, 481, 485 radiation on, 412, 421, 425 Churchill, 379, 400, 401 Cylindrical coordinate, 29, 32 Churchill-Chu, 344, 346-348, 377 Damage, 1,221,538 Collier, 454 Darcy friction factor, 179 Dipprey-Sabersky, 310 Dark Ages, 546 Dittus-Boelter, 281, 282, 284, 285 Decibel, 521, 535, 538, 542 Edwards, 267, 277, 278 Density, 21, 140-142, 148, 158,220,268,339, Elenbass, 351 365, 443, 458, 461, 480, 526-529, 531, Globe-Dropkin, 372 532 Gnielinski, 282, 285, 315 gas, 132,219,244,475,477,520,528,529 Hatfield-Edwards, 365 liquid, 146, 160,237,243,475,477 Hilpert, 344, 347, 348, 360, 364 mass, 31, 134, 160,454,470,475,477,520, Hollands, 373, 375 526 Jacob, 308, 309, 329, 330 solid, 492, 546 Klimenko, 471, 472 Departure, 447, 448, 450, 496 Kovalev, 465 Design, 1,5,6,92,221,243,249,257,467,520 LeFevre-Ede, 378 Diameter, 60, 139,202,227,235,304,389,461, Lienhard-Eichhorn, 467 487 MacGregor-Emery, 374 bubble, 449, 450, 476, 478 McAdams, 376 hydraulic, 181-183, 225, 226, 263, 265, Mills, 323, 325, 326, 328 267,314,315,332,481 Nakai-Okazaki, 303 inner, 34, 39, 108, 288, 474 Petukhov, 475, 477 outer, 39, 108,302 Rich-Mills, 362 Diamond,5, 22, 23, 307, 554 Rohsenow, 454, 455 Diaphragm, 534, 542 Shlykov, 120 Dielectric, 22, 24-26 , 553, 554 Sieder-Tate, 281, 282, 284, 285 Difference, 12,52,66,70,95,237,337,342, Sparrow-Ramsey, 319 443,543 Swearingen-McEligot, 270 equation, 63-65 , 67, 69 Whitaker, 305 pressure, 138, 142,341 Wills, 310, 313, 314, 316 temperature, 58, 59, 69, 71, 85, 87, 89, 97, Zukauskas, 302, 319, 322, 323, 325-327, ll2, ll5, ll6, 254, 257, 274, 275, 290, 329, 330 336,349,396,405,444,446,483,492, Cover, 10, 375 502, 514, 547 CPU, see Central Processing Unit Differential, 54, 149, 151, 157, 165-168, 177, Critical, 49, 162, 182, 253, 260, 349, 371, 375, 188,241,330,422,434,550,552 376,439,455,545,554 element, 140,408 heat flux, 448, 453, 460-464, 467,468,496 equation, 169, 189,495,526 radius, 48, 50 pressure, 209, 222 Rayleigh number, 260, 371 temperature, 3, 22, 57-59, 69, 71, 85-89, Reynolds number, 181, 191,292,296 97, ll2, ll5, ll6, 242, 254, 257, 274, Crossflow, 181, 186, 191,292,301,303,304, 275,290,346,349,396,405,444,446, 467,468 452,483,492,502,514,547 Cryogenic, 554 Diffuse, 402, 420, 421, 427, 428 Current, 13,23,46, 117,447,545,550,552 Diffusion, 12, 100, 101, 186,259-261,480,550 Cylinder, 149, 175-177, 181, 376-378, 461, Diffusivity, 31, 49, 97, 251, 254, 257, 259-261, 465-468 264,294,464,492 Subject Index 573

Dimension, 51, 102,252-254,340, 348, 349, Dry, 482 446,461--463 Dual Inline Package, 59, 216 characteristic, 181, 191,253,332,335,336, Duct, 133,212,216,218,274,285-287,309, 355, 356, 378, 382, 386-388, 463, 509, 319,323,325-328 512 Ducted,316 Dimensional, 148-151, 156-159, 165-167,252, Dynamic, 13, 15, 140, 156, 159, 177, 184, 195, 260-262 216 one-, 3, 32, 33, 36, 51, 68, 101, 128, 148, Ear, 519, 537-543 149, 156-159, 161, 165, 167, 520, 526, Eckert number, 257 530 Eddy, 180,204,263 three-,ll, 13, 16, 57, 63, 116, 148-150, Eddy heat conductivity, 292, 294 156, 161, 204, 262, 300, 362, 378, 382, Eddy viscosity, 12, 194, 195,292,294,337 390,424,519,530 Edge, 56, 61, 180, 181, 191,215 ,257,268,292, two-,ll, 13,36,51, 53, 57, 59, 63, 64, 77, 301,311,312,343,364,424 149, 151, 165-167, 169, 171, 192,261, Effectiveness, 15,21,48, 101, 103, 133,220, 301 223,260,316,348,349,363,433,527, Dimensional analysis, 63, 250, 253-255, 461 528 Dimensionless, 212,448,551 emittance, 414, 417 equation, 493 Efficiency, 103-106, 108-112, 133, 180, 216, form, 39,178,261 218,219,221 ,237,331,390,406,538, group, 181,250-254,257-259,442,444 542, 550 number, 250, 551, 553 fin, 6, 103-105, 108-111, 115, 129, 324, parameter, 258, 260, 442, 461, 471, 476, 478 387, 388 stream function, 188 Egyptians, 545 DIP, see Dual Inline Package Elasticity, 21, 132,518,519,526,538,542 Direct, 12, 13,23,237,390,429,507,552-554 Elbow, 268 Directional, 407, 408, 419, 420, 534 Electrical, 22, 23, 136,441 ,549,550 Directivity index or gain, 535 Electroacoustic, 543 Dirichlet, 101 Electromagnetic, 3,13,397,405,406,519 Discharge, 220, 221 ElectroMagneticInterference, 209 Disk, 61, 539 Electron, 21 Displacement, 3, 134, 151 ,216,220,301,362, Electronic, 2,137,161 ,218,222,238,257,263, 405,519,526-528,531-533 349,366,431 ,482,553,554 boundary layer, 185, 186, 215, 247-249, cooling, 12, 13, 15, 16, 27, 38, 129, 131, 292,311 135, 156,216,221 ,296,331,348,378, Dissipation, 6, 10, 12,48,90, 109, 111, 112, 397, 406, 407, 420, 438, 456, 464--467, 156,340,389,510,513,536 472,490,496,503,506,529 Dittus-Boelter correlation, 281, 282, 284, 285 device or component, 1, 15, 221, 242, 396, Double, 138,349,423,427,549,553 429,434,518,520 Doublet, 535 packaging, 6, 100, 102, 116,518,545 Drag, 133, 184, 195, 209, 212, 265, 288, Electronicequipment, 1,21, 115, 148,209,241 , 296-298,300,304-307,309 243,496,516,518,521,525,541,544 Drag coefficient, 191,298,301,304,305,307, Element, 76, 138, 139, 141, 159, 169, 170,254, 448 408 Drop, 170 finite, 9, 11-13, 15 pressure, 179,204,208,209,212,221,223, fluid, 1, 140, 142-144, 156, 178,342 262,263,277,296,309,316,319,320, EMI see ElectroMagneticInterference 323,329,330,467,469,470,496 Emissivity, 3, 396, 398, 399, 402--404, 406, temperature, 86 411,412,414,417,419,422,431--435, Droplet, 139,469,483 506 574 Subject Index

Emissivity (cont.) conduction, 28, 32, 33, 38, 53, 57, 61, 245, factor, 102, 405 257,491 hemi spheric~ ,408 ,410 empirical,6, 117,241,249,260,301 directional, 407, 408 energy balance, 12,48,86, 187,251,253, Enclosure, 90, 243, 366, 371, 372, 374, 375, 258,260 399,412,417,427-429,438,439 gener~, 28, 29,36,47,365,438 Energy, 2, 6, 8, 86, 89, 99, 293, 405, 419, 431, heat transfer, 39, 257, 402 438,440,479,518,528,531,551 Navier-Stokes, 13, 15, 177 conservation, 7,10,251 ,253,258,289,421, rate, 7, 9, 49, 517 516,552 wave, 526,527,530 heat, 5, 7, 21, 71, 180,242, 259, 280, 397, Equivalent, 181,214,304,521,524,534,553 406,411,441,448 Error, 57,67, 69, 70,86,97,104,270,278,280, kinetic, 7, 8, 12, 21, 22, 216, 301 282,538 potential, 7, 8, 136,441 Ethylene, 553 Energy balance, 48,65,74,75,84,86,90, 101, Euler equation, 156, 158, 165, 167, 177 405,406,419,421,475,478 Eustis number, 447 Energy conservation equation, 289 Evaporation, 437-439, 438,443,471,479, 481, Energy density, 528, 531-533 496,545 Engineering, 15, 148, 161, 259, 261, 280, 398, Excess temperature, 444, 451, 454, 455 411,419,453,467,499,546,549,552 Exchanger, 108, 288 thermal, 9, 396, 545, 554 Expansion, 1,6, 12,51,66, 131-133, 197-200, English, 142,222,342,546,548,551 204,232-236,458,516,521 English system, 5, 22, 25, 26, 36, 42, 46, 50, 63, abrupt, 197,232-235 73, 91-93, 95, 96, 105, 111, 122, 139, gradual, 198, 224, 233 145, 147, 155, 161, 164, 174, 176, 183, therm~ , 133,242,243,251,254,339,343 184, 186, 200, 223, 226, 230, 232, 233, Explicit, 11, 12, 75, 212 235,241- 243, 248, 272, 273, 277-279, Exponential, 88, 527 284,285,306,307,309,313-315,324, Extend, 265, 323, 397,445 326, 329, 336, 339, 347, 348, 356, 358, Extended, 129,414,534 360,367,368,371,385,387,401,414, Extended surface, 102, 256 418,431,433,440,441,460,463,477, Falling, 161,481,487,547 488,489,496,506,511 Fan, 1, 16, 17,90, 216, 218-220, 222, 223, Enhancement, 13, 102, 310 236-238,262,263,338,519 ENIAC, 553 Fanning friction coefficient, 179,281,288 Enlargement, 199-201 Fatigue, 15, 538 Enthalpy, 8, 11,251,274,437,494 FC, see F1uorinert Entrance, 201-203, 223, 229, 230, 233, 265, Filament, 550, 552 268,271,272,274,276,282,349 Film, 95, 96, 269, 345, 410, 445, 481, 483, 484, effect, 182, 267, 277, 278 486,487 Entropy, 9,552 Film boiling, 452, 453, 464-466 Entry, 490, 551 Film evaporation, 471 Environment,5,16,92,105,120,194,366,482, Film thickness, 134, 485 505,510,513,520,522 Fin, 102, 106, 107, 112-114, 248, 382-384, ambient, 4, 6, 101, 112,222,242,362,379, 386,414,417 429,499 pin, 16, 103, 174,273,296,316,319,320, Epoxy, 33, 36, 124,411,432,505 322,323,325,327,389 Equation, 11, 54, 81, 96, 142, 165, 185, 208, Fin efficiency, 6, 103-105, 108-111, 115, 129, 289,389,446,493 324,387,388 Bernoulli, 158-161, 167, 169-172, Finite, 16,71 ,75, 102, 126-128, 149 174-177, 197,238 Finite difference, 11, 12, 15,52,63-67,69,70 Subject Index 575

Finite element, 9, 11-13, 15 friction, 191,237,256,261,475,477 Finned, 105, 115, 288, 387, 388 particle, 140, 142, 148, 151, 152, 184, 191, Fit, 237 192, 194,245,246,292,293,296,304, Fitting, 382 438 Flat, 149, 218, 247, 291, 292, 296, 341, 343, Fluorinert, 137, 182, 183,277,333,443,456, 345,413,428,461 ,465,481,524 458,474,482,487,488 plate, 13, 181 , 182, 184, 185, 191,245,248, Flux, 51 250, 263-265, 273, 289, 290, 302, 310, heat, 33, 57, 67, 77, 97, 98, 101, 102, 257, 340, 348, 378, 390 262, 270, 274, 275, 277, 287, 343, 350, surface, 107, 181, 185,214, 246, 288, 295, 366,384,429,438,445,448,451,453, 414,463,485 454,456,459-465,467,468,496,545 Florence, 548 Foil, 123, 124,410 Flow, 15, 131, 184, 197,216,223, 235, 242, Force, 11, 134, 140, 169,204,220-222,251, 262, 297, 301, 310, 330, 361, 378, 468, 441,530,548,554 470 buoyancy, 339-342, 361, 362, 371, 376, heat, 2, 3, 21, 32, 33, 36, 38,39,51,53,54, 437,443,444,446,448,466 57-59 , 70, 72, 75, 81, 112, 114- 116, drag, 209, 298 120, 255, 258, 268, 294, 382, 398, 492, inertial, 181,260,300,551 502,514 shear, 133, 177, 191, 341, 342 laminar, 10, 13, 133, 177, 179, 180, 182, viscous, 181, 184,254,258,260, 263, 371, 186, 191, 192,209, 212, 215, 250, 259, 374,551 260, 263, 265-267, 269, 273, 274, 279, shear, 133, 177, 191,341 ,342 286,289-292,296,300,302,309,311, Forced,48, 184,212 ,221,245,258,471,542, 322,342,367,369,376,481,483 551 turbulent, 10-13, 133, 148, 177, 180-182, Forced convection, 10,49, 131,222,252,253, 191 , 192, 194, 195,204,205,209,212, 262, 263, 273, 274, 276, 280, 285-289, 260, 263, 269, 280-282, 286-288, 292, 292, 296, 304, 305, 309, 316, 330, 337, 295, 296, 302, 309, 315, 343, 344, 348, 338,340,343,438,466-468,518 362,363,377,481,546 Form, 32, 57, 64, 136,298,349,439,441,445, internal, 265, 269, 270, 273, 466, 467, 496 451,483,526 external, 13,288,296,466,467 Forward difference, 69 Flow rate, 2, 3, 162-164, 179,221,236,251, Fourier, 270-272,466,467,483 law, 97, 241 volumetric, 199,200,219,227,228,230 modulus, 257, 258 Flow regime, 180 number, 257 Flowfield, 11, 12, 148, 149, 150, 151, 165, France, 547, 549, 550 167-175,204,364, 389 Free, 5, 219, 280, 288, 314, 330, 353, 520, 521, FI

Friction, 133, 156, 161, 184-186,208,216,329, Head, 142, 158, 161 ,237,296,542,546 342,469 Head loss, 195, 197, 199-201,209,223-227, coefficient, 179, 185, 191, 246, 248, 250, 229-236,238,279 256,261 ,281,288,295,296,309,310 Hearing, 518, 538,539, 542, 543 Factor, 195,209,212,222,225,226,229,231, Heat, 5, 47, 71, 79, 86,93, 103, 117, 126,243, 235,238 ,279,285,315,470,475,477 264, 340, 348, 407, 488, 495, 549-551, Fanning, 179,281,288 553 Darcy, 179 energy, 7, 21, 242, 397, 406 Frictional, 133, 156,208,235,238,296,341, specific, 11,31 ,87,90, 113, 114, 133,241, 342 242,251,252,440,441 ,443,454,458, Fully-developed, 178 491,520 Gamma, 397 Heat conduction, 1,28,32,38,42,51,57,61, Gap, 119-121, 123,257,312,494,495 68,84,97, 123, 128,257,263,489,501 Gas, 21, 22, 27, 131-133, 156,237,243,268, Heat exchanger, 108, 288 269,280,306,397,441,515,516,548 Heat flow, 2, 3, 21, 32, 33, 36, 39, 51, 53, 54, constant, 133, 244, 480 57-59 ,70,75,81, 112, 114-116, 120, molecules, 133,429,433,439 255, 258, 268, 294, 382, 398, 492, 502, Gaussian, 97, 542 514 General, 13,55,75, 131, 148, 150, 165, 170, Heat flux, 33, 57, 67, 77, 97, 98, 101, 102,257, 379,412,526,527,530 262, 270, 274, 275, 277, 287, 343, 350, equation, 28, 29, 32, 33, 36, 38, 47, 53, 365, 366,384,429,438,445,448,451,453, 438,491 454,456,459-465,467,468,496,545 gas law, 244, 548 Heat sink, 3-6 , 16, 17,23,92, 101, 109, 116, Geometric, 102, 265, 325, 328, 383, 385-388, 120, 123, 276, 316, 323-329, 384, 385, 435 387-389,417,418,492,499 German, 184,258,259,261 ,548,551,552 Heat spreader, 45, 333, 335, 336, 456, 459, 460, Glass, 9, 49, 405, 410, 422, 550 463,505 Gradient, 135, 170, 179, 191, 297, 301, 341, Heat transfer, 15,22,53, 101, 114, 125,256, 469,470,474-478 263, 288-290, 294, 295, 353, 374, 399, temperature, 3, 21, 22, 33, 85, 86, 102,246, 516 257, 264, 265, 274, 290, 293, 382, 389, average coefficient, 87, 259, 272-274, 278, 495,501 279, 291, 303, 318, 335, 336, 466, Graph,238 485-487 Graphical, 51, 57, 58, 128, 135,243,534 coefficient, 4, 6, 48, 49, 92, 93-95, 98, 108, Grashof number, 254, 258, 260, 268, 337, 339, 109,115,116,121,122,132,133,172, 343,367,368,376,379,444,551 241,245,249-251,253,255,258,261, Gravitational, 299, 337, 342, 444, 469, 470, 262, 266, 268, 270, 280, 282, 286, 290, 475,478 302, 305, 308-310, 313-316, 325-328, acceleration, 158, 168, 223, 362, 454 330, 337, 343, 349, 352, 355-362, 365, constant, 299, 342, 454 367- 371, 387-390, 401, 402, 438, 442, Gravity, 140, 173,221,254,337,339,363,469, 452,456, 459, 460, 471, 476-480, 483, 476,478,483,509,512,546-548 489,490,496,505,506,509-513,554 Grease, 120-124 conduction, 3, 21, 33, 76, 129 Greece, 545 convection, 2, 6, 21, 23, 37, 39, 49, 89, 92, Ground, 120, 150,457 93, 98, 109, 115, 148, 237, 241, 249, Growth, 301, 444, 450 252, 253, 262, 330, 390, 442, 479, 480, Half, 35, 36, 194,300,316,535,538,540 503,505,506,509,512 Hard, 116,410 local coefficient, 265, 301, 484 Hardness, 119, 120, 122 overall coefficient, 37, 39, 40, 42, 472, 474, Harmonic,529, 531, 532 494,514,515 Subject Index 577

radiation, 3, 4, 23, 75, 396-398 , 402, 404, medium or substrate, 61, 126,305,399,463 423, 434, 453, 465, 506, 510, 513, semi-, 61, 96 515 Infinite cylinder, 425 Height, 102, 112-114, 140-142, 160-163,212, Influence, 185, 237, 246, 280, 342, 364, 382, 225,309-311,319,366,386, 387 454,461,518 Helium, 554 Infrared, 397,407,429,431 Helmholtz instability, 449 Initial, 33, 64, 88, 243, 263, 450, 466, 491, 527, Hemisphere, 408, 420, 537 530 Hemispherical, 402, 403, 408, 410, 419-422, Inlet, 204, 221, 222, 224, 227, 229, 230, 235, 535 263,270,277, 335,349 High power, 554 Inner, 48, 60, 102, 108,421,474 High speed, 257, 438 Input, 84, 384, 441 Hindu, 546 Inquisition, 547 Hollow, 32 Inside, 139,205,243,281,288,316,396,412, Homogeneous, 469,470, 526, 534 417,425,427,429,456,506,515,536 Horizontal, 61, 141, 153, 199,373,378,381, Insulation, 48, 49, 57 389,390,465,469,470,486-490 Insulator, 33, 505 cylinder, 366, 376, 377, 461, 466, 483 Integral, 45, 108, 168, 172,423,427,450,546 plate, 361, 363, 364 Integrated circuit (IC), 537, 553, 554 surlace, 364, 366-371,464,509,512 Integrating , 39, 47,89,167,168,170,191,194, Hot, 1,2,246,397,405 ,452,466 ,467 ,503 ,515 259,276,290,291,295,493,495 Hottel's rule, 425 Intensity, 407, 408, 419, 521-524, 528, 531, Hydraulic , 216, 265 532,535,536,538-541,543 diameter, 181-183,225,226,263,267,314, Intensity of radiation, 422 315, 332, 481 Interlace , 6, 102, 115, 123, 124, 129, 184,241, radius, 225, 226, 383, 386-388 245,256,268,331,491-493 Hydrodynamic, 132, 185, 188,265,289,461 thermal, 5, 108, 116, 119, 120 Hydrostatic balance, 546 Interlace resistance, 116, 117 Hyperbolic, 16, 106 Interfacial, 485 IBM, 552-554 Internal, 133, 180,243,287,468 IC, see Integrated Circuit energy, 7, 8, 86, 89, 97, 251, 431 Ice, 439-441,444,494,495, 545, 549 flow, 13,265,269,270,273,466,467,496 Ideal, 140, 148, 156, 158, 161 , 169, 173, 174, heat, 31-33, 40, 46, 53, 64, 68, 84 177,184,216,297,343 temperature, 85, 86, 444,501 Immersion, 84,131,148,181,451,520,553, Inviscid, 184 554 Irradiation, 405, 419-422 Impedance, 222, 223, 237, 483, 529, 532, Irreversible, 9 534-536 Irrotational, 168-170, 297 Impeller, 220, 221 Isentropic, 133 Impinge, 162 Isotherm, 54 Impingement, 131,221,310,330-332,554 Isothermal, 57, 85, 132, 256, 269, 274-276, Implicit, 11, 12,75 281,348,427,446 Indians, 546 plate, 290, 291, 349-353 Induced, 15, 148,242,361,362,467 surlace, 59, 67, 247, 291, 362, 364 Inertial, 175, 180, 181,260,300,551 Isotropic , 526, 534 Infinite, 56, 85, 89, 135, 463, 480, 530, 534, Italian, 547, 549 535,550 Iteration, 314 dimension, 61, 96, 126, 139,201 ,229,230, Iterative, 12, 275 352,412,413,421,424,425,428,461, Jacob correlation , 308, 309 520 Jet, 137, 139, 161-165,333,443,540,554 578 Subject Index

Jet impingement, 131,330-332 unit, 40, 42, 48, 179,210,298,474 Joule, 136 Lewis number, 258, 260, 480 Junction, 1,4-6,46, 207,396,413,414,499 Life, 1, 15, 26, 243, 244, 548 Kelvin, 399 Liquid, 27, 133, 137, 161 , 237, 243, 268, 442, Kinematic viscosity, 133, 134, 181, 251, 254, 443, 446, 452, 464, 466, 469, 470, 479, 260, 261, 264, 551 554 Kinetic, 7, 8, 12, 21,22, 216, 280, 301,448, flow, 101, 220, 269,467,468 519,528,531,548 immersion, 131, 520 King, 549,550 molecule, 438, 439 Klystron, 553 phase, 437, 439,454 Laminar, 180-182, 194, 273, 274, 277, 289, surface, 136,441 ,444,445,451 291, 292, 296, 343, 348, 485, 486, 509, temperature, 450, 492 512 Liquid metal, 548 flow, 10, 133, 177, 179, 180, 182, 186, 191, Liquid-cooled, 39, 438 192, 209, 212, 215, 250, 259, 260, 263, Lobe, 535 266, 267, 274, 279, 286, 289-292, 300, Log, 380,521-525,535 302, 309, 311, 322, 342, 367, 369, 376, Logarithm, 521, 523, 524, 538 481,483 Logarithmic, 39, 521 external flow, 13, 288, 296, 466, 467 Logic, 551 internal flow, 265, 269, 270, 273, 466, 467, Longitudinal, 119, 318, 323, 519, 520, 526, 496 543 Laplace equation or transform, 31, 51, 57 fin, 102, 103, 105, 106, 112, 113, 287,414 Large scale, 191, 195,292,552,553 Loop, 551 Latent, 437, 440, 441, 443, 444, 454, 461, 483, Loss, 24, 86, 198, 216,269,479,538,543,546 485,488-490,492,549 coefficient, 195, 197, 198, 200-208, 210, Lattice, 3, 23 211, 223,229, 230,232-235 , 238 Law, 7-9 ,402,405,411, 547,549,553 head, 195, 197, 199-20 1, 209, 223-227 , Boyle's, 132, 244, 548 229-236, 238, 279 conservation, 15,516,517 heat, 42, 86, 101 ,402 Fourier' s, 21, 22, 25, 33, 57, 86, 97, 101, minor, 195 116, 241,547 pressure, 131, 178, 195,204, 205,222, 223, Newton's, 140, 142, 143, 156, 157, 165, 261 166, 169, 170,304,342 Loud, 538,540 thermodynanrics,6-9,132,552 Loudness,538-542 Lay, 118, 119 Loudspeaker,524,525 Layer, 23, 71, 120, 268, 293, 309- 311, 373, Low, 23, 102, 137, 165, 219, 327, 382, 396, 452,453,483,502 448,465,470,539,541-543,547 thermal boundary, 185, 241, 245-249, 263, power, 5 265,274,288-290,362 pressure, 216, 218, 221, 238, 262, 439 thickness, 185, 186, 189,215,245,246,248, Reynolds number, 297, 301, 309, 316, 325 249,290,292,302,311,362 thermal conductivity, 5, 6, 27, 265, 452 velocity boundary, 184-186,203,245,246, velocity, 10, 17, 182,337,467,468 248, 249 Lumped, 85, 86, 89,94-96,129 Lead, 5, 21, 57, 68, 124,296, 389 Mach number, 131,257 Least, 63, 115, 220, 221, 456 Major, 9, 51, 466 Length,191 , 229,231 ,233,397,404,407,408, Mark I, 553 419,422 Mass, 10, 12, 136, 142, 143, 157, 167, 187, 193, characteristic, 263, 314, 315, 364, 446, 448, 241,243,269,474,478,490,536 449,459-461,471 ,476,478 density, 31, 134, 160,454,470,475,477, flow, 181, 235,296, 316 520,526 Subject Index 579

flow,179, 220, 242, 251, 270, 271, 272, 466, Module, 59, 63, 456, 506, 507, 510, 511, 513, 467,481,483 514,554 unit, 8, 9, 339, 340, 437 Modulus, 132,257,258,399,520,526 Mass transfer, 256, 258, 260, 261, 289, 337, Molar, 188 479~81 Mole, 550 Mathematical, 256, 258, 259, 280, 550-552 Molecular, 11, 12,22, 133, 186,241 ,268,310, Matrix, 81, 510, 513 441, 480, 550 Maximum, 108, 115, 162, 216, 218, 297, 302, diffusivity of heat, 264, 294 340,404,444,535,544 diffusivity of momentum, 264 heat, 49, 102, 112,352,353,357,452,461, Molecule, 22, 133, 136,402,438,441 462,467 Momentum, 7, 10, 15, 16, 180, 186, 193-195, temperature, 1, 5, 6, 23, 26, 45, 46, 48, 197,264,280,292,476,478,485 90-92,94,96,396,414,434 change, 342,469,470,475 velocity, 178,316,318,324,325,327,331, diffusivity, 259-261 448,449,460 equation, 11, 12, 187-189,260 Mayan, 546 Monochromatic, 403 Mean, 12, 117, 203, 212, 280, 286, 337, 472, Moody chart, 212, 281 523,524,527,530,538 Motherboard, 16 temperature, 269, 270, 293 Mouromtseff number, 553 velocity, 171, 173, 174,481 Move, 22, 131, 133, 146, 151, 179, 180,221, Mean value, 192, 193,429,525 262,296,349,364,519 Mel, 541 fluid, 220, 238 Melting, 101,437,451,491 Moving, 6, 133, 134, 148, 182, 184, 216, 238, Melting and freezing, 490, 496 245,260,262,439,551 Membrane, 530 Multidimensional, 51, 53, 57-59, 128 Memory, 551 Multiple, 267, 423, 514, 553 Mesh, 57, 63, 66, 67, 227 Natural,48, 131, 184,438,527,537,551 Metric, 342,440,441,463,550 Natural convection, 254, 258, 336, 337, 339, Microminiaturization, 545 349,376,382 Micron, 405, 408, 419 flow, 257, 262, 340, 34 1, 343, 371, 378, Microphone, 525 379,389,509,512 Microprocessor, 59, 85, 116, 120, 323, Natural convection heat transfer coefficient, 109 411~13 ,456 ,459,460,462 Near, 67, 216, 218, 243, 265, 268, 297, 302, temperature, 325-329 340,397,534 Military (MIL), 26, 27, 243, 553 Net, 209, 342, 399,422,423,448,479 Minimum, 49, 117,218,302, 353, 379, 453, Network, 57, 63, 64, 70, 71, 499 464,465 Newtonian, 2, 15, 135,403 Minor, 195,356,357,535 Neumann boundary, 101 Mist, 469, 471 Nodal, 63-65, 71, 75, 76 Mixed, 191, 195, 269, 338 Node, 63-65 , 67, 74, 77, 81, 83, 84 Mixed boundary layer, 260, 296, 348 Noise, I, 218-220, 263, 286, 518, 521, Mixing, I, 12, 16, 244, 266, 280, 293, 337, 536-538,540-543 546 Nonuniform, 171 Mixing cup, 269 Non-Newtonian, 15, 135 Model, 6, 10, 15, 16,85,86,96,97, 116, 193, Normal, 91,119,153,159,169,187,193,195, 280,467,469,503,515 219,361,371,519,527,538,542 flow, 11-13 convection, 331,466 e,12 operation, 1,516 Modified, 113, 177,257, 350, 386, 387, 447, Noy,540 485,488,489 Nozzle, 162-164,330-332,335 580 SUbject Index

Nucleate boiling, 446, 448, 450-452, 454, 463, Octave, 525, 541, 542 464,466,468,496 Octave band, 525, 541 dominates, 471, 476, 478 Offset, 60, 142 Nusse1t number, 455, 459, 460 One-third, 525, 541, 549 Nucleation,448, 454, 456 Opaque, 396,419,422 Number, 36,58,64, 131,262,378,411,456, Open, 90, 146, 181,209,228,230,268,288, 480,494,502,532-534,540-543,553 330,385,387 Biot, 86, 96, 129, 255, 256 Optimization, 10, 112 Elenbaas,257,349,350,355, 356,358-360, Optimum, 112-114,333,352,353,389 386, 387, 389 Order of magnitude, 259 Grashof, 254, 258, 268, 337, 339, 343, 367, Orientation, 16, 119,361,363,380,381,384, 368,376,379,444,551 389,509,512 Jacob, 444, 494 Outer, 38, 47-49, 60, 74, 102, 108, 396,421, Nusse1t, 192, 241, 249, 250, 253-261, 263, 487 266-268, 270-273, 275-279 , 281-287, Outlet, 39, 204, 209, 218, 221, 222, 263, 273 291, 292, 296, 302, 303, 305, 306, Outside, 136, 139, 184, 187,205,297,390,441, 308-310, 313-316, 318, 319, 325-328, 490,515,516 332, 333, 335-340, 343, 344, 347, 348, Overall, 4, 71, 115, 116, 120, 122, 127, 133, 350-352, 355, 356, 358-360, 362, 364, 195,331,502,538,541 365, 367, 369, 372-374, 376, 379, 382, Overall heat transfer coefficient, 37, 39, 40, 42, 383, 387, 388, 390, 444, 453-455, 459, 472,474,494,514,515 460,471 ,472,476-479,481,484-486 Parabolic, 16,44, 106, 178, 179,268,274 Prandt1, 246, 249, 250, 253, 254, 256, Partial, 52, 152, 165, 167, 177, 188,434,452, 258-260, 264-269, 278, 289, 290, 294, 492,526,549,550 295,309,325,327,337,390,444,454, Particle, 157,397,527-529,531-533 551 fluid, 140, 142, 148, 151, 152, 184, 191, Rayleigh, 116, 257, 258, 260, 337, 343, 344, 192, 194,245,246, 292, 293, 296, 304, 346-349, 359, 360, 362, 364, 367-369, 438 371,373-375,377, 382,400,401,465, Particular, 148,259,285,330,492,541 509,512,551 PCB, see Printed Circuit Board Reynolds, 13, 175, 179-182, 185, 186, 189, Peak, 16,27 , 117, 120,462 191, 192, 195,210,212,215,225,226, Peclet number, 259, 291 228-231, 235, 247, 248, 250, 253-256, Penetration, 15 258-260, 263, 265-268, 271-273, 277, Pentode, 553 280-282, 284, 292, 295-304, 306, 307, Perceived, 540 309, 311, 313-316, 323, 325-328 , Perfect, 76, 132, 133, 257, 367, 369, 396, 399, 335-337, 339, 343, 390, 448, 467, 470, 405,406 472,475,477,481 ,485,486,496,551 Perforation, 207, 209-211, 224, 231, 232 Numerical, 13, 15, 16,51, 52, 128,301, 517, Periodic, 99, 464, 519, 544 553 Phase, 10, 99, 101, 102, 131, 135,453,454, Nusse1t number, 192, 241, 249, 250, 253-261, 492,535 ,541,543-544,554 263, 266-268, 270-273, 275-279, two-, 15, 16,466-472,474,475,477, 479, 281-285, 287, 290-292, 296, 302, 303, 496, 545 305, 306, 308-310, 313-316, 318, 319, Phase change, 15,237,437-439,441 ,444,490, 325-328, 332, 333, 335-340, 343, 344, 491,496 347, 348, 350-352, 355, 356, 358-360, Phon, 538 362, 364, 365, 367, 369, 372-374, 376, Piece, 259, 553 379,382,383,387,388,390,444,454, Pin, 273, 390 455,459,460,471 ,472,476-479,481, Pin-fin, 16, 103, 174,296,316,319,320,322, 484-486 323,325 ,327,389 Subject Index 581

Pipe, 11,39,40, 149, 159, 181, 182, 197-201, maximum or full, 91, 94 204,212,238,310,376,451 pumping, 179, 180,288 Pitch, 541-543 sound, 521, 522, 525, 536, 541, 544 Plane, 141, 146, 151, 193, 194,294, 297,331, Prandtl number, 246, 249, 250, 253, 254, 256, 466,514,521,534 258-260, 264-269, 278, 289, 290, 294, acoustic wave, 520, 524, 526-529 295, 309,325,327,337,390,444,454, surface, 67, 77, 107, 149 551 Plane wall, 32, 33, 38, 39, 43, 44, 46, 60, 67, 85, Pressure, 5, 115, 139-141, 158, 174, 237, 280, 515 300,434,461 ,474-478,526,550 Plastic, 5, 39, 412 absolute, 142, 161 ,244 Plate, 54, 73,102,133,180,209,249,307,330, atmospheric, 131 , 142,220,221,439,441, 355-360,363,369,381,414,550 520,528,529,538,547,548 flat, 13, 181, 182, 184, 185, 191 ,245,248, constant, 27, 28, 144,243,252,443,520 250, 263-265, 273, 289, 290, 292, 296, difference, 138, 142, 341 302,310,340,341,345,348,378,390, drop, 179,204, 208, 209, 212, 221, 223, 413 262, 263, 277, 296, 309, 316, 319, 320, horizontal, 361, 364 323,329,330,467,469,470,496 isoflux, 291, 296, 350-353 fluid, 160, 173, 187,209,216,221,261, isothermal, 290, 291, 349-353 296, 547 parallel, 181 ,267,270,349,412 gage, 142, 173, 175 perforated, 209, 211, 231, 232 sound, 521, 523-525, 527, 529, 532, 533, rough,214 540-542 vertical, 257, 341, 343, 344, 349, 353 static, 159, 160, 208, 216, 218, 219, 222, Point, 151, 158,216,222,237,280,397,454, 223, 527, 538 527, 530, 535 total, 159,207,216,469 alphanumerical, 7, 12, 63, 146-148, 153, Pressure loss, 178, 195,204,205,222,223,261 155, 160, 161, 163, 164, 172-174, 185, Primary, 1,4,22,118,131 ,175,193,250,253, 246,296,301,303,428,439,452,453, 331,389 460,461,491,528,534,550 Primary dimension, 252 boiling, 137, 442, 456, 458, 461, 496, 549, Principle, 421, 546 554 Printed Circuit Board (PCB), 6,15,45,46,331, contact, 116, 117, 120-122 351,353,411 grid or nodal, 12, 13,64,65 Probability, 280, 547, 549 initial or starting, 142, 185,245 ,246,297 Process, 7,9,101 ,133,243,275,439,441,445, stagnation, 172-175, 296, 297, 301-303 , 483,492,496,526 330,331 boiling, 444, 446 time, 52, 66, 88, 148,453 freezing, 493 Polar, 11, 151, 152 transfer, 280,337,444,479,516 Pool, 447, 554 Profile, 57, 134, 171, 189, 195,265,266,268, Pool boiling, 444, 450, 451, 453, 454, 460, 274,281,330,342 464-466 rectangular, 105, 106, 112,414 Porosity, 179,209-211,228,230,232,259,438 temperature, 275, 289, 340 Potential, 7, 8, 32, 136, 159, 161 ,275,441,502, triangular, 106, 112-114 514,519,528,531 Propeller, 216 Potential flow, 297, 300 Properties, 6, 21, 75, 131, 149, 192, 242,442, Power, 5, 93, 95, 121 , 172, 216,256,263,338, 466,488,492,516,527,538,545,550 399,434,451,490,537,542,553 air, 248, 313, 314, 338, 345, 354, 356, 357, component, 23, 33, 34, 36, 71, 92, 101, 108 385,399,482,508 dissipation, 6, 510, 513 fluid, 28,148,156,181,187,188,241 ,257, emissive, 396, 402-404, 408, 422 260,268,269,272,297,302,458 582 Subject Index

Properties (cont.) fluid, 156, 175, 177, 289,297,390 material, I I, 12,74, 120, 122, 133 flow, 149, 156, 170, 177, 184,297,390 variation, 268, 269, 270, 272, 281, 467 object, 405, 406, 419 Prototype, 554 surface, 399, 407 Public domain, 129 Reciprocal, 6, 257 Pulsating, 530, 534, 535 Reciprocity, 428 Pump, I, 180, 220-222, 262,466 Rectangular, 31, 54, 61, 63,103,1 27, 206, 233, Pumping power, 179, 180, 288 234, 286, 287,424,530 Quality, 466, 470, 474, 475, 478, 541, 542 coordinate, 28 Radial, 11,31,38, 39,46, 102, 169, 170, 174, duct, 309 176, 274, 530-532 fin, 104, 114 Radiation, 1,3, 10, 15,49, 84, 90, 101, 116, profile, 105, 106, 112,414 241,400,408,413,420,429,432,499, Rectilinear, 175 516,545 Reflectance, 398, 405, 406, 420, 421, 427, 515 blackbody, 260, 398, 399, 402-405 , 407, Relative, 2, 86, 134, 140, 142, 177, 260, 399, 419,430,431 ,433,434,551 463,467,492,535,538 graybody, 399 Reliability, 1, 554 heat transfer, 23, 75, 396-398, 402, 404, Reliable, 28 423,434,453,465,506,510,513,515 Renaissance, 546 impedance, 534-536 Resistance, 76, 89, 117, 177, 238,371,466, pattern, 534 469,470,475,478,493,503,516,529 view factor, 16, 396, 422-424, 427, 428, contact, 6,16,102,108,115,116,119,123, 435,507 124, 129 Radius, 49,60,102,118,139,169,170,175, flow, 221 461, 535 thermal, 4-6 , 9, 22, 23, 26, 27, 36, 39, 43, bubble, 446, 450 45, 49, 65, 70-75 , 79, 86, 94, 95, 107, critical, 48, 50 116, 121, 123, 125, 129,251, 255, 256, hydraulic, 225, 226, 383, 386-3 88 262,499, 502, 505, 506, 515 Random, 13, 133, 136, 191,441 ,542, 550 Resistance-Capacitance, 70 Rankine, 399 Resistor, 49-51, 84 Rapid, 161 Restriction, 252 Rate, 6,23, 135, 142,237,262, 340,441,450,501 Reverberation, 521 equation, 7, 9 Reynolds analogy, 250, 292, 295 energy, 87, 257, 293, 398 Reynolds number, 13, 175, 179-182, 185, 186, flow, 2, 3, 163, 164, 179, 199, 200, 219, 189, 191, 192, 195, 210,212,215,225, 221, 227, 228, 230, 236, 251, 270-272, 226, 228-231, 235, 247, 248, 250, 466,467,483 253-256, 258-260, 263, 265-268, heat flow, 2, 3, 53, 57, 58, 70, 75, 398, 492, 271-273 , 277, 280-282, 284, 292, 502 295-304, 306, 307, 309, 311, 313-316, heat transfer, 4, 7, 21, 39, 42, 48, 53, 54, 58, 323, 325-328, 335-337, 339, 343, 390, 59,89, 113-115, 184,245,257,261, 448,467,470,472,475,477,481,485, 276, 290, 293-295, 399, 438, 496, 503, 486,496,551 506, 514 Reynolds stress, 194 Rayleigh number, 116,257,258,260,337,343, Rocket, 522 344, 346- 349, 359, 360, 362, 364, Romans, 546 367- 369, 371, 373-375, 377, 382, 400, Room, 396, 520, 525, 528 401,465,509,512,551 Root mean, 527 Reaction, 534, 535 Rotary, 220 Real, 48, 85, 104, 114, 116, 161, 194, 244,348, Rotating, 216, 220, 221, 374 411,421,435,492,527, 529,534 Rotational, 168, 221 Subject Index 583

Rough surfaces, 115, 309 Similarity, 188 Roughness, 181, 195,267,287,291 Simple, 1,59,71,86,89, 102, 107, 141, 148, RMS, 117, 119-122 165, 172, 187,221,366,371,465,492 surface, 117, 156, 180,212,214,263,281, correlation, 322, 509, 511 282, 309, 310, 456 geometries and shapes, 32, 52, 128, 129, Round-off, 184 147,174,177,390,428 Safety, 90, 209, 221 source, 530, 535 Sand, 309 Simultaneous, 167,204,253,255,499,506 Sand grain, 212 Single, 16,33, 114, 135, 170,232,251, 310, Satellite, 432 365,374-377,501,538 Saturation, 438, 439, 447, 450, 464, 480, 483, cylinder, 302, 389 486,496 jet, 330, 332 Saturation temperature, 443-446, 479 phase, 467-470, 472 Scalar, 151,337 point, 12,532 Scale, 13,57,191 ,195, 197,292,467,521 ,538, Sink, 5, 6, 16, 17, 23, 92, 101, 116, 276, 540,547,548,550,552,553 323-328 , 384, 387, 388, 417, 418, 492, Scatter, 433 499 Schmidt number or method, 51, 258, 260, 261, Sinusoidal, 520, 527 289,480 Skin friction, 185, 191,246,256,300,301 Scottish, 549 Sky, 260,434, 551 Screen, 209-211, 224, 345 Slope, 118, 120, 122, 144-147,243 Second law, 9, 142, 143, 156, 157, 165, 166, Slow, 10 169,170,342 Slug, 5, 6, 144, 146, 160 Secondary, 150,204,331,374 Slug flow, 469 Segment, 13 Solar, 407, 410, 429, 431-433, 545 Semi, 12, 61, 96 Solder, 124 Semiconductor, 1,4-6, 10,45 Solid, 2, 21, 23, 86, 96, 99, 101, 117, 132, 172, Separation, 184,204,297,300--302,314,315 243,256,297,437,439,491,492,494 Series, 37, 56, 71,297,411,492,495,499,502, Solidification, 437, 492 503,527,542,544,551 Sone, 538 Fourier, 51, 550 Sonic, 554 Taylor, 12, 66 Sound, 218, 518-520, 528, 531, 534, 535, Series and parallel, 36, 70, 219, 501, 502, 516 537-539,543 Shape, 102, 110, Ill, 197,267,285,296,304, Sound power, 521, 522, 525, 536, 541,544 307-309,330,366,403,530,534 Sound pressure, 521, 523-525, 527, 529, 532, arbitrary, 382, 527 533, 540-542 factor, 4, 58-61, 63, 128 Source, 4, 11, 74, 123-128, 221, 397, 434, velocity profile, 265, 268 516, 519, 525, 528, 530, 532, 534, 537, Shear, 140, 161, 191,251 ,341,485 543 Shear stress, 134, 135, 177, 179, 185, 194, 195, Source strength, 535 246,294 Space, 7,52,119,221 ,309,337,372,431 ,490, Sherwood number, 260, 261, 480 525, 532 Short, 10,26, 191,265,285,310,382,424,483, Spacecraft, 4, 429 490,541,553 Spacing, 27, 61, 117,318,323,358,385-387, Shroud, 316 389 SI,22, 186,222,279,284,285,508 center, 210, 214, 316, 390, 474 SI system, 142,223,241,348,518 plate, 270, 349, 350,352,353, 355-357 Silicon, 23, 25, 26, 124,505,506,553,554 Species, 188,289,480 Silicone, 124,411,443 Specific, 12,81, 112, 142, 160, 168, 173-175, Silver, 23, 411 249, 310,368-371,460,521,532 584 Subject Index

Specific heat, 11,31,87,90,113,114,241,242, free, 185, 187, 189, 191,246,289,290,296, 251,252,440,441,443,454,458,491, 297, 306 520 Streamline, 148-151, 153, 155-160, 168-172, Spectral, 403, 407, 408, 410, 421 238, 362 distribution, 402, 404 Streamtube, 148, 149, 156, 159 irradiation, 419, 420 Stress, 13, 15, 133-135, 177, 179, 185, 194, reflection, 420, 427 195,246,294,337,548 Speed, 133, 180, 182,220,221,257,397,402, String, 343,422,428 438,460,519,532,548,552,553 Strip, 127 Speed of sound, 520, 521, 524, 529 Sublimation, 437, 439 Sphere, 32,42,46,60, 86, 181,297 , 304, 305, Submerged,330, 333, 546 366,378,396,399,461,466,530,534, Substantial, 382, 414, 552 551 Substrate, 126-128 Spherical, 42, 519, 530-532,534,535,547 Superheated,445, 446, 465 Spherical coordinate, 29, 32, 76 Surface, 3, 61, 86, 102, 184,245,305,331,361 , Spine, 102, 103, 106 410,421,435,453,479,496,510,534 Spiral, 287, 288 area, 2,4, 6,48, 87, 92, 104, 105, 107, 115, Spread, 125,519,520,530 116, 125, 136,278,279,290,304, 307, Spreader,45,333 , 335, 336,456,459,460,463, 325- 328,349,364,389,398,399,414, 505 441,508,511,535,536,553 Spreading, 123, 125 flat, 107, 181, 185,214,246,288,295,414, Stability, 12,75 ,364,445,461,464 463,485 Staggered, 316, 318-320, 322, 323, 326, heated, 101, 284, 343, 364, 365, 374, 328-330,389 450-452,456,460,461,465,466 Stagnation, 175 temperature, 2, 4, 44, 48, 59, 99, 101, 125, Stagnation point, 172-174,296, 297, 301-303, 268-270, 272, 273, 275, 282, 289, 290, 330, 331 313, 314, 324-329, 338, 383, 414, 465, Stagnation pressure, 159 468,483,545 Standing, 353, 529, 530 Surface tension, 15, 136-139, 161, 237, 251, Stanton number, 250, 256, 261, 262, 290, 310 437,441-444,446,454,458,462,467 State, 6, 7, 9, 131, 148, 195,340,439,479,516, Swedish, 548 526,544 Swirl, II steady, 15, 16,22,31 ,32,38,60,64,66,67, Swiss, 548, 549 84-86, 90, 91, 93-95, 109, 128, 153, Switch,543 265,431 ,482,511,513 Symmetrical,45, 46, 296, 297, 350-353, 534 Static, 140, 141, 146, 161,209, 519, 529, 545, System, 6-9, 46, 85, 89, 165, 222, 238, 280, 547,549 330-331,515,521,545,554 pressure, 159, 160,208,216,218,219,222, cooling, 39, 173,216,221 ,482,490 223,527,538 coordinate, 10, 11,28,29,32,66,75,76 Steady, 134, 148, 151, 166, 168, 187,221,544 English, 5, 25, 26, 122, 145, 147, 155, 161, Steady state, 15, 16, 22, 31, 32, 33, 38, 60, 64, 164, 174, 176, 183, 184, 186, 200, 226, 66, 67, 84-86, 90, 91, 93-95, 109, 128, 230, 232, 235, 241-243, 248, 272, 153,265,431 ,482,483,506,511 ,513 277-279, 284, 307, 309, 314, 315, 326, Stefan-Boltzmann, 3, 102,398,402,404,411 329, 336, 339, 347, 348, 356, 358, 360, Stokes, 13, 15, 177, 551 368,371,387,414,460,477,506,511,551 Straight, 102, 204 fluid, 166, 167, 260 Strain, 132, 134, 135,337,538 one-dimensional, 3, 33, 101 Stratified, 263 two-dimensional, 53, 59, 63 Stream, 151, 181, 184, 188,208,212,245,247, SI, 142,223,241,342,348,463,518,550 260,302,303,309,542,551 sound,537,539,542 Subject Index 585

Taylor series, 12, 66 Thermometer, 546-548, 550 TCM, see Thermal Control Module Thennoscope, 546, 547 Tee, 268 Three-dimensional, 13,57, 63, 116, 161,262, Temperature, 21, 73, 83, 98, 142, 265, 343, 399, 362, 378, 382, 390,424,519,530 408,434,439,445,451 ,479,496 flow, 16, 148-150, 156, 204,300,378 air, 93-95, 248, 324-328, 345, 348, 353, problem, 11, 149 507,521,524 Threshold, 538, 539, 542, 543 difference, 3, 22, 57-59, 69, 71, 85-89, 97, Timbre, 541, 542 112, 115, 116, 242, 254, 257, 274, 275, Time, 10, 11,98, 194,429,492,553 290, 336, 349, 396, 405, 444, 446, 452, constant, 88, 91, 94, 95 483,492,502,51 4,547 interval or step, 7, 9, 74, 75, 524 distribution, 42, 44, 47, 48, 54, 56, 57, 64, Tip, 102, 383 69,86, 261, 289 Torricelli, 161,547 factor, 506 Total, 89, 172, 216, 298, 300, 307, 403, 469, fluid, 246, 268-270, 275, 277-279, 282, 511,513,514,523 302,335,356,357,386,387,469 hemispherical emittance, 408 junction, 1,4-6,396,413,414 rate, 53, 54, 58, 115, 290, 294, 502, 506 maximum, 1,45,46,48,90,91, 92, 94,96 thermal resistance, 5, 6, 49, 70, 71, 73, 505, operating, 1, 23,26,90 506 potential, 275, 502, 514 Transfer, 193, 194, 220, 264, 411-413, 422, rise, 2, 3, 6, 22, 25-27, 32, 35, 36, 45, 46, 481,519 50,51, 59, 63, 89-91, 93-96, 122, 127, Transferred, 3, 5, 21, 103, 399-402,423,444, 242, 243, 257, 270, 277- 279, 283-285, 483,503,515,51 6,519 306,308,309,313,314,336,348,355, Transformer, 90, 91 357, 358-360, 367-371, 387, 388, 440, Transient, 13, 15, 16, 68, 84-86, 89, 91, 96, 441,509,511,51 2,514 128,129,255,490,496 scale, 548, 550 Transient heat conduction, 257 surface, 2, 4, 44, 48, 59, 99, 101, 125, Transistor, 33, 34, 36, 92-94, 108, 553 268-270, 272, 273, 275, 282, 289, 290, Transition, 203, 234-236, 453, 464 313, 314, 324-329, 338, 383, 413, 414, laminar to turbulent, 133, 181, 182, 191, 465,468,483,545 215, 260, 273, 274, 280, 282, 291, 292, Test, 119, 129, 136, 254, 302, 310, 521, 536 296,300,302,311,3 15,343 Thermal, 9, 43, 74, 89, 94, 242, 256, 275, 343, Transition boiling, 452 352,441 ,496 Transrrrission, 22, 215, 264, 398, 405, 406, 422, boundary layer, 185, 241, 245, 246, 248, 518 249, 263, 265, 274, 288- 290, 362 Transport, 12, 180, 191 ,259,260, 397 conductance, 79, 116, 121-123 Transverse, 119,215, 259,260, 316, 318,323, conductivity, 3, 21-23 , 27, 49, 59,11 9,120, 526 122, 268 Traveling, 17, 238, 397, 482, 527- 529 contact, 115, 116, 124, 129 Triangle, 287, 424, 428 diffusivity, 31, 49, 97, 251, 254, 257, 259, Triangular, 106, 112-114,286 264,464,492 Tube, 38, 39, 48, 160, 173, 178, 179,233 ,263, radiation, 421 276, 280, 285, 287, 468, 474, 486-490, Thermal Control Module, (TCM), 554 515 Thermal resistance, 4, 6, 22, 23, 26, 27, 70, 75, round, 177, 181,206,234,265,266,270, 86, 121, 123, 125,499,502,51 6 274, 275, 281, 288, 315, 469 total, 5, 49, 71, 505, 506 vacuum, 378, 550, 552, 553 Thermionic Tube, 550, 552 wall, 265, 270, 274, 275, 282, 469 Thennodynarrrics, 6-9 ,132, 258,550,552 Tubular, 148 Thermoelectric, 550 Turbulence, 12, 13, 16, 195, 280,303 586 Subject Index

Turbulence (cont.) phase, 437, 439,454 full, 181,260,263,323 pressure, 161,438,439,445,480 transition to, 181, 182, 191, 215, 273, 274, water, 397, 434, 444 291,292,296,311 Vaporization,161,441,454,458,461,462,485 Turbulent exchange coefficient, 292 Variable, 12, 49, 66, 84, 140, 142, 209, 220, Turbulent flow, 12, 13, 194, 195,263 ,281 252-254, 257, 258, 269, 289, 396, 444, larrrinarto, 10, 133, 180-182, 191,215,260, 466 273,274, 280, 282, 291, 292, 296, 300, Varied, 241,285, 548 302,311 ,315,343 Vector, 8, 53, 148, 150, 151,408,419 Turbulent rate of heat transfer, 293, 294 Velocity, 10, 151, 174-177, 182, 192,228,316, Turbulent shearing stress, 337 467,470,535 Turning, 439, 547 boundary layer, 184-186, 203, 245, 246, Two-dimensional, 11, 13,36,51,53,57,59,63, 248,249 64,77,166,171 , 192,301 fluid, 134, 163, 164, 184, 195, 197, 199, flow, 149, 151, 165, 167, 169,261 245,260,265,284,298,340,343,548 Two-phase , 15, 16, 466-472, 474, 475, 477, head,197,222,223,226,227,229-236,296 479,496,545 particle, 528, 529, 531-533 Ultimate, 4, 101 profile, 134, 171, 189, 195,265,268,274, Ultraviolet, 397,429 281,330,342 Unheated, 268 Vena contracta, 201, 203 Uniform, 86, 158, 274, 348, 534 Vertical,140, 147, 153, 165, 173,297,364,368, heat flux, 287 380,383,385,387,389,390,486,487 Units, 91, 136, 233, 273, 285, 302, 433, cylinder or tube, 61, 341, 345, 366, 378, 440-442,482,488,489,521,538 468,489,490 area, 22, 29, 99, 179, 191, 193,237,251, height, 141, 160, 161, 237, 349 270,293,294,402,448,492,528 plate,257 ,340,341,343-345,349,353,378 English system, 5, 25, 26, 122, 145, 147, surface, 361, 366, 367, 369, 370, 371, 374, 155, 161, 164, 174, 176, 183, 184, 186, 464,466,485,509,512 200, 226, 230, 232, 235, 241-243, 248, Vibration, 3, 21, 161,518,524,526, 534, 541, 272, 277-279, 284, 307, 309, 314, 315, 542,544 326, 329, 336, 339, 347, 348, 356, 358, View, 4, 16, 52, 116, 148, 151, 396, 397, 360,368, 371, 387,414,460,477,506, 422-424, 427, 428, 435, 507, 510, 513, 511 541 length, 40, 42, 48,179,210,298,474 Viscosity, 12, 140, 156, 177, 237, 269, 284, mass, 8, 9, 339, 340, 437 285,470 SI system, 142,223,241 ,348,518 absolute, 133, 134, 181,251,252,268,272, time, 22, 179 282,294,443,454,458 volume, 11,243,528,531,550 eddy, 12, 194, 195,292,294,337 Unit surface conductance, 302, 489 kinematic, 133, 134, 181, 251, 254, 260, UNIVAC I, 553 261,264 Universal, 133, 480 Viscous, 13, 133, 180, 181, 184, 186,220,254, Unsteady, 84, 469 258, 260, 263, 268, 298, 300, 371, 374, Vacuum, 3, 21, 117, 142,378,397,402,431, 551 549,552,553 Void, 116, 117, 119, 120 Vapor, 443,448,458,461,464-467,470,479, Voltage, 84 482,483,486,492,496,549 Volume, 12, 16, 74, 132, 220, 221, 243, 343, bubble, 161, 439, 445-447, 449, 450, 456, 450,548 460,469 control, 7-9, 15, 75, 77, 87 column, 445, 449, 451 flow, 219, 238, 316 layer, 452, 453 unit, 11, 528, 550 Subject Index 587

Vortex, 170,212,300,301,309 Wavelength, 397, 404-408, 419, 422, 449, 520, Vorticity, 13, 168 534,544 VVake, 221, 297, 300, 301, 316, 389 VVaviness, 119 VVml,37 , 71, 108,201, 215,263,270,282,311 , VVavy, 483, 485,486 439,477,503,524 VVeber number, 467 chassis, 33, 36, 45, 51, 412 VVeight,90, 141, 156, 159,243,480,546,549 friction, 161, 195, 203,204,469,470 specific, 133, 142, 146, 160, 161, 173-175, heated, 341, 374,444,446,450 460 plane, 32, 33, 38, 39, 43, 44, 46, 60, 67, 85, VVet, 258, 460 515 VVetted, 104, 182,456,480,481 surface, 105, 107, 186, 191,269,272,273, VVidth, 61, 112, 113,301, 332, 365, 414, 424, 331,341,349,444,446,515, 516 461, 535,541,542 VVater, 135, 137, 185, 216, 241-244, 330, plate or board, 231, 290, 314 439,441,443,451,452,457,494,546, unit, 185, 247,481,485 549 VVire, 209-211, 227, 228, 230,292, 343, 451 deionized, 199, 242,282,493,529,553 VVork, 7, 212, 251, 258, 267, 310, 441, 452, vapor, 397, 434 538, 546-550 velocity head, 226, 227, 229-236 Yield, 49,51,58,112,133,159,285,294,427, VVatt,5,6,72, 242,338,505,522,528 ,549,553 451,462,521,535 VVave, 84, 260, 518, 527, 530, 532-534, 541, Zenith, 408, 419 543,544,551 Z-axi s, 140, 147, 362 acoustic, 519-521, 524, 526, 528, 531 Zuber constant, 461, 463 Author Biography

Ralph Remsburg is currently President of Electronic Packaging Associates, Inc., a consulting firm with offices in Austin, Texas, and headquartered in Sarasota, Florida. Formerly, Mr. Remsburg had held engineering positions up to the direc­ tor level, before becoming a consultant. Ford, Chrysler, Delco, Hghes, Loral, and Dell Computer are just a few of the companies that have used his services. Mr. Remsburg has 17 patents, five published papers, is a member of Mensa, and is listed in Who's Who. Mr. Remsburg can be contacted at [email protected].

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