1 INTRODUCTION AND SOME USEFUL REVIEW 1.1 A MESSAGE FOR THE STUDENT Fundamentals of Momentum, Heat, and Mass Transfer, 4th edition, Welty, Wicks, Wilson, and Rorrer. This is an advanced-level book based on a course sequence Fluid Mechanics for Chemical Engineers, 2nd edition, taught by the author for more than 20 years. Prior exposure Wilkes. to transport phenomena is assumed and familiarity with the Vectors, Tensors, and the Basic Equations of Fluid classic, Transport Phenomena, 2nd edition, by R. B. Bird, Mechanics, Aris. W. E. Stewart, and E. N. Lightfoot (BS&L), will prove par- ticularly advantageous because the notation adopted here is mainly consistent with BS&L. In addition, there are many other more specialized works There are many well-written and useful texts and mono- that treat or touch upon some facet of transport phenom- graphs that treat aspects of transport phenomena. A few of ena. These books can be very useful in proper circumstances the books that I have found to be especially valuable for and they will be clearly indicated in portions of this book engineering problem solving are listed here: to follow. In view of this sea of information, what is the point of yet another book? Let me try to provide my rationale Transport Phenomena, 2nd edition, Bird, Stewart, and below. Lightfoot. I taught transport phenomena for the first time in 1977– 1978. In the 30 years that have passed, I have taught our An Introduction to Fluid Dynamics and An Introduction graduate course sequence, Advanced Transport Phenomena 1 to Mass and Heat Transfer, Middleman. and 2, more than 20 times. These experiences have convinced Elements of Transport Phenomena, Sissom and Pitts. me that no suitable single text exists in this niche, hence, this Transport Analysis, Hershey. book. Analysis of Transport PhenomenaCOPYRIGHTED, Deen. So, MATERIAL the course of study you are about to begin here is the Transport Phenomena Fundamentals, Plawsky. course sequence I provide for our first-year graduate students. Advanced Transport Phenomena, Slattery. It is important to note that for many of our students, formal exposure to fluid mechanics and heat transfer ends with this Advanced Transport Phenomena: Fluid Mechanics and course sequence. It is imperative that such students leave the Convective Transport Processes, Leal. experience with, at the very least, some cognizance of the The Phenomena of Fluid Motions, Brodkey. breadth of transport phenomena. Of course, this reality has Fundamentals of Heat and Mass Transfer, Incropera and profoundly influenced this text. De Witt. In 1982, I purchased my first IBM PC (personal computer); Fluid Dynamics and Heat Transfer, Knudsen and Katz. by today’s standards it was a kludge with a very low clock rate, Transport Phenomena: An Introduction to Advanced Topics, By Larry A. Glasgow Copyright © 2010 John Wiley & Sons, Inc. 1 2 INTRODUCTION AND SOME USEFUL REVIEW just 64K memory, and 5.25(160K) floppy drives. The high- that particular scenario. But, blind acceptance of black-box level language available at that time was interpreted BASIC computations for an untested situation is foolhardy. that had severe limits of its own with respect to execution One of my principal objectives in transport phenomena speed and array size. Nevertheless, it was immediately appar- instruction is to help the student develop physical insight and ent that the decentralization of computing power would spur problem-solving capability simultaneously. This balance is a revolution in engineering problem solving. By necessity I essential because either skill set alone is just about useless. became fairly adept at BASIC programming, first using the In this connection, we would do well to remember G. K. interpreter and later using various BASIC compilers. Since Batchelor’s (1967) admonition: “By one means or another, 1982, the increases in PC capability and the decreases in cost a teacher should show the relation between his analysis and have been astonishing; it now appears that Moore’s “law” (the the behavior of real fluids; fluid dynamics is much less inter- number of transistors on an integrated circuit yielding mini- esting if it is treated largely as an exercise in mathematics.” I mum component cost doubles every 24 months) may continue also feel strongly that how and why this field of study devel- to hold true through several more generations of chip devel- oped is not merely peripheral; one can learn a great deal by opment. In addition, PC hard-drive capacity has exhibited obtaining a historical perspective and in many instances I exponential growth over that time frame and the estimated have tried to provide this. I believe in the adage that you can- cost per G-FLOP has decreased by a factor of about 3 every not know where you are going if you do not know where you year for the past decade. have been. Many of the accompanying problems have been It is not an exaggeration to say that a cheap desktop PC developed to provide a broader view of transport phenom- in 2009 has much more computing power than a typical ena as well; they constitute a unique feature of this book, university mainframe computer of 1970. As a consequence, and many of them require the student to draw upon other problems that were pedagogically impractical are now rou- resources. tine. This computational revolution has changed the way I I have tried to recall questions that arose in my mind approach instruction in transport phenomena and it has made when I was beginning my second course of study of trans- it possible to assign more complex exercises, even embrac- port phenomena. I certainly hope that some of these have ing nonlinear problems, and still maintain expectations of been clearly treated here. For many of the examples used in timely turnaround of student work. It was my intent that this this book, I have provided details that might often be omitted, computational revolution be reflected in this text and in some but this has a price; the resulting work cannot be as broad as of the problems that accompany it. However, I have avoided one might like. There are some important topics in transport significant use of commercial software for problem solutions. phenomena that are not treated in a substantive way in this Many engineering educators have come to the realization book. These omissions include non-Newtonian rheology and that computers (and the microelectronics revolution in gen- energy transport by radiation. Both topics deserve far more eral) are changing the way students learn. The ease with consideration than could be given here; fortunately, both are which complicated information can be obtained and diffi- subjects of numerous specialized monographs. In addition, cult problems can be solved has led to a physical disconnect; both boundary-layer theory and turbulence could easily be students have far fewer opportunities to develop somatic com- taught as separate one- or even two-semester courses. That prehension of problems and problem solving in this new envi- is obviously not possible within our framework. I would like ronment. The reduced opportunity to experience has led to a to conclude this message with five observations: reduced ability to perceive, and with dreadful consequence. Recently, Haim Baruh (2001) observed that the computer rev- 1. Transport phenomena are pervasive and they impact olution has led young people to “think, learn and visualize upon every aspect of life. differently.... Because information can be found so easily 2. Rote learning is ineffective in this subject area because and quickly, students often skip over the basics. For the most the successful application of transport phenomena is part, abstract concepts that require deeper thought aren’t part directly tied to physical understanding. of the equation. I am concerned that unless we use computers wisely, the decline in student performance will continue.” 3. Mastery of this subject will enable you to critically eval- Engineering educators must remember that computers are uate many physical phenomena, processes, and systems merely tools and skillful use of a commercial software pack- across many disciplines. age does not translate to the type of understanding needed 4. Student effort is paramount in graduate education. for the formulation and analysis of engineering problems. In There are many places in this text where outside read- this regard, I normally ask students to be wary of reliance ing and additional study are not merely recommended, upon commercial software for solution of problems in trans- but expected. port phenomena. In certain cases, commercial codes can be 5. Time has not diminished my interest in transport phe- used for comparison of alternative models; this is particularly nomena, and my hope is that through this book I can useful if the software can be verified with known results for share my enthusiasm with students. DIFFERENTIAL EQUATIONS 3 1.2 DIFFERENTIAL EQUATIONS Students come to this sequence of courses with diverse math- ematical backgrounds. Some do not have the required levels of proficiency, and since these skills are crucial to success, a brief review of some important topics may be useful. Transport phenomena are governed by, and modeled with, differential equations. These equations may arise through mass balances, momentum balances, and energy balances. The main equations of change are second-order partial differ- ential equations that are (too) frequently nonlinear. One of our principal tasks in this course is to find solutions for such equa- tions; we can expect this process to be challenging at times. Let us begin this section with some simple examples of ordinary differential equations (ODEs); consider dy = c (c is constant) (1.1) dx FIGURE 1.1. Solutions for dy/dx = 1, dy/dx = y, and dy/dx = 2xy. and = = dy depend on the product of a and b.Ifweleta b 1, then = y.