Publication date: February 2000
The prediction of radiant energy transfer in absorbing, emitting and scattering media is critical to advanced development of many important processes at both high and low temperatures, from porous combustors, furnaces and fires, to advanced insulation systems for cryogenic super-conducting devices.
During the last half-century, research into the solution to radiative heat transfer in enclosures has mushroomed in numerous directions. It has been an ongoing task at the International Flame Research Foundation - IFRF, at many university laboratories, and at other research organisations. This task has brought forth a hierarchy of more or less numerical models for the prediction of radiative heat transfer, due to the complexity inherent in its physical and mathematical descriptions.
All the models developed so far, which certainly have good physical foundations, are based on a large number of simplifications or uncontrolled assumptions. They all give, numerically, candidates to the solution of the radiative heat transfer problem in enclosures, and some of these numerical solutions have became part of the folklore. But how reasonable and consistent, and reliable these approximations are; that is, with which accuracy they approximate the actual solution, if this solution exists, remain unanswered.
At the onset of the 21st century, accurate design of efficient sources of energy, thermodynamic processes, and high temperature combustion equipment is of utmost importance. The driving forces behind these are advanced technology requirements, the costs of large-scale experimental work, and the limitation of physical modeling. Thus, the control of heat transfer, particularly radiative heat transfer, in these systems cannot be based on a black box principle fed with temperature distributions and species concentrations. The ever more stringent requirements for efficient production and use of energy and heat from combustion chambers call for prediction algorithms of higher accuracy and more detailed radiative heat transfer calculations.
"Radiation in Enclosures - Elliptic Boundary Value Problem" comprehensively explains an algorithm for such calculations. It is an advanced textbook essentially self-contained, which chronicles briefly the events of the last fifty years, and describes in details the latest state of the art in radiative heat transfer theory. The book is concerned with both the formulation and the general solution of the radiative heat transfer problem in enclosures of any geometrical shape, and for any temperature distribution and material properties. It provide an exhaustive theoretical examination of the radiative heat transfer equation and dwells on a unique and the most reliable theoretical and its associated numerical method for calculating radiant heat exchanges in enclosures. The discussion in this monograph is directed towards the relevant basis of a mathematically exact technique, and averse to merely formal improvement of existing methods. It is a balance work that is both useful to the practicing design engineers and stimulating to researchers and scientists in both industry and academia.
Existence, uniqueness, solution's reliability are shown in the monograph. Convergence and robustness of the numerical approximation are established too. Error estimates and optimal order of convergence of the numerical solution, in the sense of finite element are derived and demonstrated. In this regard, we would like to remind our readers of the fundamental fact that the meaning of a numerical solution (or a numerical method), specifically for radiative heat transfer problem which is governed by an integro-differential equation, is not precise and may lead to speculations unless it is supplemented by an estimate of the errors occurring; that is, unless it is accompanied by a definite knowledge of the degree of accuracy attained. Such speculations can be read in the existing literature on radiative heat transfer models, where, for example:
Up to now, trends and fashions in the study of radiation heat transfer have weakened the connection between the physics, the engineering, and the mathematics of radiation.
Physicists and most engineers have ceased to appreciate the attitude of mathematicians, and have avoided sophisticated mathematical developments for radiation transfer. Throughout the years, they have put forward many hypotheses and numerical models to explain the physical phenomena of radiation heat transfer and to calculate the radiant heat exchanges in enclosures. These hypotheses and the associated numerical models were tested against experimental evidence until they fail, and were overtaken by new hypotheses and numerical models. Thus, the picture of radiative heat transfer in enclosures was continually altered, if not rubbed out, and relegated to the difficult topics area of study. The conclusion, based on those hypotheses and numerical models, are merely consider highly likely dependent on the experimental evidence available. We should recall that a conclusion should not merely describe a known phenomenon, but predict the results of other phenomena.
Mathematicians on the other hand have overlooked the relevance of their science to the physics and the engineering of radiation, and have emphasized the postulation and abstract side of mathematics, as always. For every problem, the route of approach for mathematicians is to begin with a series of statements or axioms, which can be true or, which are self-evidently true. Then by arguing logically, step by step, one arrives at a conclusion. We should also recall that the mathematical conclusion is undeniable and free of inconsistencies, if the statements are correct and the logic flawless. That is to say, having shown that a conclusion (theoretical or numerical) is true by one method, it should not be possible to show that the same conclusion is false via another method, unless there is an inconsistency inherent in one of the method. Thus, proof being what rests at the heart of mathematics, once something is proved, it is proved forever, with no room for changes.
True to its title, the monograph, "Radiation in Enclosures - Elliptic Boundary Value Problem", extends beyond the spectrum of applied mathematics, to includes contribution from physics and engineering. It reunifies the divergent trends, between the physics, the engineering, and the mathematics of radiation, by clarifying their common features and interconnections for scientific and advanced high performance modeling in enclosures. Also, we have endeavored to provide sufficient explanations, and fathom some of the fundamental points for readers having a less deeper knowledge of the subject.
The book covers a wide range of topics: from physical and mathematical modeling, via appropriate functional and numerical analysis, to the computational algorithm and computational results. It is written to meet the need of advanced heat transfer calculations, at a level that is appropriate for readers who have completed an ordinary training or a course of study in transport phenomena and/or in mathematical physics. Readers will notice a fairly complete and comprehensive combination, clearly discussed, of:
This combination renders the monograph a unique textbook in radiative heat transfer, a textbook far from being dry, which possesses the ingredients guaranteed to delight the reader; the textbook that members of heat transfer community have been waiting for, for the last half-century. To read it is to gain insights into the astounding world of heat transfer by radiation. It will do much to enhance the study of heat transfer in general as a core text for mainstream courses in the subject.
Due to the interdisciplinary character of this monograph, graduate students at the MSc and PhD level, and researchers in all areas of thermal sciences, who wish to apply themselves to the particular case of radiative heat transfer in enclosures, will find it extremely useful, especially for scientific modeling. Upon using a multi-grid approach, the algorithm developed in the monograph can be incorporated into computer programs that either perform an overall energy balance of a system or simulate fluid flow and heat transfer problems.
Contents: Introduction.- Physical Model.- Computational Techniques for Radiant Heat Exchange Problems.- Mathematical Model.- Numerical Approximation.- Numerical Simulations in Specific Cases.- Spectral Properties of Gases.- Application to a Semi-Industrial Scale Gas Fired Furnace.- Radiation in Scattering Media.
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