The transport of heat through a porous medium in the presence of exterior forces, generally produced by the Earth's gravitational field and/or a pressure gradient, is called conduction when the Darcean fluid is static (motionless), and convection when the Darcean fluid is in motion. It is customary to use the term convection also to describe the motion which arises from the density differences due to temperature gradients within the Darcean fluid. We think that because this last phenomenon is more general it should be given a specific name; here we call it thermal flow. In the sense of the above definitions, convection and thermal flow are two distinct phenomena (they occur together, in underground combustion for instance), and the convective motion which arises when a Darcean l'luid is in contact with a source of heat is a particular case of thermal flow. Thermal flow occurs naturally and is important in many geophysical and industrial problems, particularly in oil exploration, and in the petroleum, chemical and nuclear industries (for instance, in the evaluation of capability of heat-removal from a hypothetical accident in a nuclear reactor). It can play a part in the transfer of heat from the deep interior of the Earth to a shallow depth in the geothermal regions. However, in the field of energy conversion little attention has yet been paid to the insulating characteristics of the saturated porous materials introduced in some enclosures (storage tanks) to decrease the convective and radiative transfer of heat.
Introduction PART I. SINGLE PHASE FLOW Chapter 1. The Homogenization Method for the Study of Fluid Flow in Porous Media 1. Homogenization of Second-Order Equation 2. Darcy's Law and Continuity Equation 3. Thermal Equation for Flow in Porous Media 4. Natural Convection 5. Convergence of the Homogenization Process 6. Boundary Conditions 7. Dimensionless Parameters 8. Comments and Bibliographical Notes Chapter 2. Natural Convection in Bounded Domains 1. The Steady Case. Basic Results 2. The Small Rayleigh Number Case. Asymptotic Expansions 3. The Structure of Steady Solutions 4. The Evolution Case 5. Comments and Bibliographical Notes Chapter 3. Natural Convection in Unbounded Domains 1. Horizontal Porous Layer 2. Exterior Problem 3. Natural Convection Between Two Horizontal Concentric Cylinders 4. Thermal Boundary-Layer Approximately for Vertical Flow 5. Comments and Bibliographical Notes PART II. MULTIPHASE FLOW Chapter 4. Macroscopic Equations 1. Equations for the Pore Level 2. Macroscopic Balance Equations 3. The Macroscopic Entropy Balance Equation 4. Simplifying Assumptions 5. Comments and Bibliographical Notes Chapter 5. Underground Combustion 1. Different Models 2. Equations for Combustion with Reaction Zone 3. The Thin Reaction Zone 4. Numerical Examples 5. Comments and Bibliographical Notes Appendix 1. Balance Equations for Continuous Media Appendix 2. Distributions and Sobolev Spaces References Index of Symbols Subject Index
Series: Theory and Applications of Transport in Porous Media
Number Of Pages: 194
Published: 31st August 1987
Country of Publication: NL
Dimensions (cm): 24.44 x 15.6
Weight (kg): 0.48