Essentials of Heat and Fluid Flow in Porous Media by Arunn Narasimhan
Foreword by Prof. D. Andrew S. Rees, Uty. of Bath, UK.
Porous media are ubiquitous; they appear everywhere. Examples range from clothing, through which the rain seeps, to filters and catalytic converters in our cars; brain tissue, lungs and other parts of the bodies of animals; soils, aquifers, sands and even the methane-saturated regolith of Titan. Apart from that very last example, the others frequently from an essential part of our daily lives and we depend on them functioning in order both to live and to live comfortably. Yet despite this very wide-ranging list of applications of porous media, there is little taught at undergraduate or postgraduate level outside of the disciplines of civil, chemical and geological engineering.
Perhaps one reason for this is that the simplest form of the momentum equation is Darcy’s law, which is of a lower differential order than its clear fluid equivalent, the Navier-Stokes equations. A two-dimensional flow in a porous medium is, therefore, governed by a second order equation whereas that of a clear fluid is of fourth order. This simplification appears not to have been welcomed in some quarters, but rather it has been derided as being too easy to study. I do not agree with this point of view. It has even been stated that a motivation for the study of convective flow in porous media is that it serves simply as a test-bed for methods for studying convective flows in clear fluids. I do not agree with this motivation even though it is quite true that many aspects of stability theory for the porous B’enard problem (see Chapter 5) may be undertaken using solely analytical techniques, thereby imparting much knowledge of stability theory which may then be used elsewhere.
However, while Darcy’s law in its most primitive form yields a simpler system to solve than do the Navier-Stokes equations, this ceases to be true when Brinkman effects are non-negligible (see Chapter 3). Small Darcy numbers then yield thin boundary layers near surfaces, and these need to be resolved numerically, a difficult task to do well.
Geological applications frequently have heterogeneous permeability fields where the permeability varies randomly over many orders of magnitude; the governing equations are then very difficult to solve numerically. Thus we are entering an arena where mathematicians and physicists, for example, may be called upon to employ averaging techniques in order to obtain equivalent macroscopic equations, and where numerical analysts are required to solve very detailed models with discontinuous and highly anisotropic coefficients. Therefore the study of porous media requires a great plethora of techniques and topics to cover a large range of possible applications. There is clearly a need for an interdisciplinary approach to studying porous media.
Many books on porous media have appeared in the last twenty years or so. The very well-acclaimed and popular monograph, Convection in Porous Media, by Nield and Bejan is just about to appear in its fourth edition, but it is meant to be a resource base, a one-stop-shop for researchers to find out what the state-of-the-art is in their particular niche. The two series of books, one edited by Vafai (Handbook of Porous Media) and the other by Ingham and Pop (Transport Phenomena in Porous Media), which are also excellent, provide more detailed reviews of chosen topics by experts in the field. A very recent book edited by Vafai (Porous Media: Applications in Biological Systems and Biotechnology) also consists of a set of reviews by specially chosen authors. But none of these books, as important as they have been for the research community at large, may be described as textbooks. The present book fills an important gap in the market because it has written specifically for students to acquire the basic knowledge of flows, heat conduction, convection and radiation in porous materials.
Finally, I would like to say a few words about the author. Arunn is equally at home with analytical, numerical and experimental techniques. He thinks creatively and strategically, is prolific in his research and is a conscientious teacher. In all of these respects he is following the heritage of his PhD supervisor, Prof Jose Lage, and his supervisor’s supervisor, Prof Adrian Bejan. However Prof Narasimhan is very much his own man — not content with traditional means of communication within the lecture theatre, conferences and research journals, he is also the founder of two prolific blogs, one in English, the other in Tamil, in which he discourses on a wide range of topics which includes but is not at all limited by those of his research. He has been described by Asian Scientist as “one of India’s most energetic professors — both in person and in cyberspace”. I certainly wonder how he finds the time to do all of these things!
So I welcome onto the scene this textbook which is so clearly infused with the distilled product of its author’s roving mind, and which is rooted in and motivated by the applications of the theory.
D. Andrew S. Rees
University of Bath, UK.