HEAT TRANSFER Notes on the Origins and Evolution of the Subject of Heat Transfer "We are picking fruit from an orchard that we have been cultivating for a long time, more than we are cultivating next year's orchard. It is easy to let the heart go out of our work when we do this. we are at our best when we mix abstract and applied thinking ... " John H. Lienhard Dept of ~~ech ., ell Engineerong University of Houston Houston Texas and Chairman, ASME Committee K 8 of •re Heat Transfer D v Joseph Black died quietly in his chair on November 26, to James Watt who had long been both his, and Black's, 1799, with a cup of tea balanced in his lap. Five years personal friend. (He attnbuted Watt's invention of the earlier, Antoine Lavoisier's head had been publicly re­ separate condenser to Black's tutelage In Glasgow. Watt moved by the French Revolutionary Tribunal. These two privately muttered that this was not at all the case. The men defined our understanding of heat phenomena on underlying ideas were, he felt, his own.) the eve of the 19th century: The closeness of the intellectual community comes home to us in one of the magnificent ironies of the new The Turn of a Century century. In 1805, the widow Lavoisier was remarried to Lavo1s1er was a key person in replacing the concept of the first modern opponent of the caloric theory, Count heat as phlogiston with the idea of caloric. Phlogiston Rumford. Rumford was a product of the 18th century who was thought to be a component of matter that was liber­ fairly hurtled into the 19th. While he was far from being ated or consumed in chemical reactions. It was some­ the greatest sc1entif1c luminary of the time, his life tells us times called the "matter of fire." Caloric was an invisible, much about how things were changing, and about how elastic fluid that could neither be created nor destroyed. It the scientific study of heat was starting to turn into the was not a component, but an occupant, of matter that technical study of heat transmission. flowed from any hot body to neighboring cold bodies. Rumford was born Benjamin Thompson in Woburn, Calonc was the first really useful tool for describing heat Mass., outside of Boston, in 1753. His catch-as-catch­ transfer processes. can education was partially achieved in the study-group Black, on the other hand, provided us with the con­ system advocated by Benjamin Franklin. It was a kind cepts-and the first measurements-of specific and la­ of backwoods reflection of the 18th century "Enlighten­ tent heats. Although his colleague, Cleghorn, had codi­ ment' -that mounting intellectual revolution that even­ fied the rules governing the behavior of caloric, Black tually led to populist upheavals of all sorts. The first himself did not embrace a theory of heat He took a of these revolutions occurred in the American Colonies restrained operational view of heat phenomena. He was shortly after Thompson had gone to Concord, N.H. a keen observer-disinclined to extend his claims be­ (which had previously been named Rumford), as its new yond what he knew with certainty. 18-year-old schoolmaster. Within a year he married the Black s lecture notes on the • General Effects of Heat" 33-year-old widow of Concords wealthiest citizen, and were published posthumously in 1803 by a former stu­ thereafter became seriously involved in spying on revolu­ dent, John Robison, who edited them heavily. The notes tionaries for the English governor. In 1776 he had to flee reveal several things at once: Robison s adulation of to England, deserting his wife and new daughter. Sara. Black, the nsing concern that educated people had in During the next quarter century, revolution engutted 1800 for learning about heat, Black's own clear-headed­ France and then continental Europe. Only England es­ ness, and the peculiar closeness of the technical scien­ caped real violence, for its revolution of the lot of the tific community at that time. Robison dedicated the work common man was industnal rather than political, and 'Sources of biographical information are g,ven in the Read ngs at the end surely more significant in its effects. When Napoleon of the ante e declared himself emperor of France in 1804 the revo- 20 JUNE 1983 MECHANICAL ENGINEERING Date 1750 1800 1850 1900 1950 1983 I< s, the Vatt The i,..----• Black -----.i• i-------Joute------i •------watt ______... ..., ______ Stokes----------i n es i-----Lavoisier·----i 1-----•Clausius------i new 1---Thomson/Rumford....--! Kelvin,-------i d to 1-------• Junt 1--Napoleon Bonaparte--! ........ Maxwen----i ho i,..---Fourier ----111 i,..---Stefan-----i emg i-------Bio1 ---..,l:;===r--Rayteigh -----­ s us OW i----Poisson,----• i,.---· Boltzmann,----- the ~ Carnot---j i------Klein------t '-------Plafl"M I >U rn, -----wien1------i itch· oup •-----Prandtll-------1 kind ,______ Nussett:------1 1ten· ------schmidt:-------1 .ven· .______ Boelter·-----• first )nies i.------ Eckert------•••• N. H. Revolutions new ~ Reign of Queen Victoria- I d the I-{ and H Wars and Revolutions Amer. French .)£ !VOIU· s:, Q. o flee Industrial 1-1 1--1 CJ) ~--­ ~ WWI WWII ,ara. ~ I U.S.-Mex. U.S. Julfed iRei9nofl France Civil Electronic Austria d es· Napoleon I c omputers )f the Prussia l I··· Italy , and Crimean 10leon revo- The dates of some people and events MECHANICAL ENGINEERING / JUNE 1983 / 21 lutions were finished and the world was a very differ- that by doing work one could create heat 1ndefm1tely, but ent place. · he did not advance a numerical equivalence. However, Thompson moved about this changing Europe with subsequent students were able to mfer a rough value Byzantine guile. He was a master of exaggeration, par­ from his data. laying every minor success into a major accomplishment. One other extremely important product of 18th-century He immediately established himself on the right hand of revolution was 19th-century education. Between his re ­ the English Secretary to the Colonies. He raised a regi­ turn to England in 1799, and 1802, Rumford's chief ef­ ment and returned to fight the Americans briefly m North forts went to formmg the Royal Institution of Great Britain. Carolina (against Marion's Raiders) and in Long Island. He had meant to form a school for educating the lower He became a Fellow of the Royal Society for his fairly classes in technology, although it rather quickly reverted straightforward studies of ballistics and gun powder. He to a higher social stratum. The French Revolutionary worked with the British Navy on signal systems and ship government had also formed an Ecole Polytechnique in design. In 1783 he left England and took up the post of 1795. Both institutions had a great deal to say about heat aide to the Elector of Bavaria. In this position his efforts transfer, but during its first 30 years the Ecole Polytech­ produced a record of really sohd accomplishment that nique set the very foundations of the subject. won him the title of Count in 1792. For his new title he The French took the name of his old town of Rumford. N.H. Rumford s instincts for political intrigue and his aspira­ Napoleon was a strong supporter of the Ecole Poly­ tions to scientific respectability might better have been technique and when he invaded Egypt at the turn of the placed in the courts and salons of 18th-century France, century he included a young professor of mathematics but his place in history was gained by his 19th-century from the school in his entourage, Joseph Fourier, who genius for social reform and thermal systems develop­ held several administrative posts in the campaign. Fouri­ ment. He was an elitist, determined to make the poor er began working on the problem of heat flow while he useful and happy by attending to their basic needs. He was in Egypt, and continued when he returned to Gre­ set up poorhouses and public works programs in Munich, noble m 1802 as Prefect of the region of !sere. By 1803 and then concerned himself with the elemental problems he had failed in his attempts to describe conduction of food, warmth. and light in these mstitut1ons His ac­ among a series of connected elements. (This is what we complishments included: do more successfully on the computer, today). He might • countless designs and innovations in stoves, ovens, have done no more, but in 1804, Joseph Biot suggested and lighting systems, and in their cleanliness and fuel another approach. economy. Biot recognized that the problem should reduce to • his famous cannon-boring experiments, which led a second order linear partial differential equation; but him to conclude about heat: "Anything which any in­ he failed to write the equation, and he did not see that sulated (system) can continue to furnish without limi­ one had to impose independent boundary conditions on tation cannot possibly be a material substance and 1t it. Fourier appears to have been reenergized by Biot's appears to me extremely difficult, if not impossible, to insight. He returned to the problem and by 1805 pro­ form any distinct idea of any thing, capable of being duced an 80-page manuscript that included the differen­ excited and communicated in the manner the heat was tial equation: excited and communicated in these experiments, except aT (constant) \'2T = -:-t + hT it be motion ... cl • a set of experiments that led him to assert that the most important element m an insulating material was the The problem with this equation is that it includes the heat entrapped air pockets that it contained; and other experi­ convection effect, hT, which, we realize today, must be ments that showed how important convective currents administered as a boundary condition.