USE OF THE FINITE-ELEMENT METHOD IN PROBLEMS OF HEAT AND MASS TRANSFER IN POROUS BODIES* R. W. Lewis, G. Comiai and C. Humpheson UDC 536.24.02 Two-dimensional isoparametric finite elements are used to solve problems of heat and mass transfer in porous bodies. A comparison of the numerical calculations with the analytic solu- tions of one-dimensional problems shows a very good agreement. Using thermodynamics of irreversible processes, Lykov [1] obtained the widelyaceeptedmathemati- cal model of heat and mass transfer in capillary-porous bodies. The analytic solution of the corresponding system of partial differential equations is connected with considerable mathematical difficulties. There- fore, we know only a fe~r solutions, first and foremost for one-dimensional problems - problems with boundary conditions not depending on time and with constant coefficients [2, 3]. Finite-difference methods [1, 4, 5] are widely used in engineering problems. In this paper another possible approach to numerical analysis is proposed; it is based on the finite-element method. The dis- cretization obtained by this has considerable advantages for multidimensional problems in regions with complicated geometry or in cases with nonconstant physical properties of the materials. The finite-element method was applied to a problem of nonstationary heat conduction for the first time in [6], whilecertain calculation schemes are given in [7]. Mutually connected electrical and hydrodynamic fluxes are studied in [8], and, subsequently, the finite- element method is applied to electroosmotic flows in soils in [9]. However, the boundary conditions of the problems in [8] and [9] essentially differ from those considered in the present work. The connected problems of heat and mass exchange in the case of convective boundary conditions lead, in the case of finite elements, to systems of algebraic equations with asymmetric matrices. Since this is undesirable, in the investigation we propose such dimensionless parameters which lead to systems with symmetric matrices. The distribution of temperature and moisture in each zone ~e of a moist body ~ can be described by the Lykov system [3]: Ot _ ~ { O~t 02t , 02t ~ , Ou ocq a~ \--07~ + --T oF-z~ -~oc~ --,a~ (1) pc~ & Ox ~ § - - + ~- ~m - - ~- , (2) Oy~ ~z ~ ] Ox~ Oy2 Oz ~ where t and u are potentials of heat and mass transfer, while the constants p, Cq, c m, kq, km, e, and 6 are taken as constant and equal to the mean values, respectively, in each zone ~e. *Edited by M. D. Mikhailov. Sofia, Bulgaria. Padua, Italy. Translated from Inzhenerno-Fizieheskii Zhurnal, Vol. 29, No. 3, pp. 483-488, Septem- ber, 1975. Original article submitted December 20, 1974. 9 76 Plenum Publishing Corporation, 22 7 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microft'lming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00. 1154