The book is devoted to the heat and mass transfer in porous media with the aim to describe and to solve phenomenological laws of diffusion which are of great interest in the technology of drying.
Chapter 1, the Introduction, starts with fundamental principles of transfer phenomena. Linear laws such as Fourier’s law of heat conduction, Ohm’s law of electrical conduction, and Fick’s law for diffusion which are characterized by the proportionality between the fluxes and the gradient of the thermal and electrical potentials, and of the gradient of the concentration, respectively, all being valid only at low intensity, are formulated including cross phenomena known as Peltier, Soret and Dufour effect describing thermo-electric, thermal, and diffusional thermo transfer behavior. Phenomena with significant coupling effects taking into account the interaction between different processes, including Thomson’s and Helmholtz’s symmetry assumptions, and Onsager’s reciprocal relation giving rather complicated expressions are presented. The main part of the introductory Chapter is dedicated to the interaction of the heat and moisture process in porous media. The porous medium is assumed to be a continuum, and the bound matter filling the voids is considered to be in an unsaturated state to develop the equations for heat and moisture transfer.
To go into detail, the porous body is considered as a multicomponent system of vapour, solid in form of ice, moisture, inert gas and the skeleton body. The volume concentration of the bound matter is defined. The conservation laws of the mass sources and the fluxes of heat and moisture, and finally the system of differential equations describing the heat and mass transfer including the initial and boundary conditions describing the interaction between the body surface and the surrounding are formulated. Introducing dimensionless variables and similarity numbers the number of variables is reduced and the results are generalized. The chapter contains also some historical remarks and an overview about the contributions to the subject with a total of 57 references which cover the period between 1857 and 1988.
Chapter 2 starts with the formulation of the set of differential equations for the transfer potentials of heat and moisture including the corresponding initial and boundary conditions. A dimensionless form of the equations is derived using dimensionless variables and similarity numbers (Luikov, Posnov and Kossovich number). The solution is determinated for an infinite cylindrical geometry and for spherical cases applying integral transforms (Laplace and Hankel transform, and Fourier sine and Laplace transform, respectively) to an auxiliary problem.
In Chapter 3 the author formulates extended equations for the heat and mass transfer including chemical reactions and phase transitions and corresponding initial and boundary conditions. The solution is developed for a spherical geometry applying the Laplace transform. The results are analysed and presented in form of graphics and tables.
Chapter 4 deals with the set of differential equations which describe the drying of an infinite plate. Molecular transfer and filtration of energy and matter have to be taken into account. The solution of the problem is again obtained by the application of the Laplace transform to the equations and the boundary conditions. The results are graphically presented.
The subject of the last chapter is freeze drying where the material to be dried is frozen in tubular form. The capillary body is filled with ice, supercooled liquid and gas. Assuming the fluid to be incompressible the mathematical model for heat and moisture transfer is formulated and solved by the usual procedure.
An Appendix contains the description of the integral transforms of Laplace and Hankel, and of the Fourier sine transform including frequently used properties of the Laplace transform and transforms of a number of functions.
In all chapters the author prefers a detailed derivation of the mathematical calculations. Numerical methods for more complicated geometries are not treated. The author mainly presents results which are connected with his research during the mid 1970s. The contributions of other scientists are well documented. The monograph is designed for graduate students, engineers and applied mathematicians.