COUPLED HEAT AND MASS TRANSFER PROBLEM WITH DEPENDENT HEAT CONDUCTIVITY PROPERTIES AND ITS SEMI-ANALYTICAL SOLUTION

Abstract

Present paper proposes a computation method for a coupled heat and mass transfer problem within the porous media where the heat conductivity properties of the media undergo changes caused by the mass transfer. Heat and mass transfer processes are coupled through the inclusion of evaporation and condensation phenomena which in turn require the solution to an another the vapour transfer problem. This complex coupled problem re-sults in a system of both linear and non-linear second order partial differential equations that are spatially discre-tized by Finite Element Method. Temporal integration is carried out analytically. Thus, the proposed system of equations covering linear vapor transfer problem, linear filtration problem and non-linear heat transfer problem is transformed into a system of both linear and non-linear first order ordinary differential equations being solved by semi-analytical method. Picard approach of successive iterations is used for linearization of the equations. Convergent solution is achieved which is demonstrated on a sample problem herein below. Proposed method gives good insight on the processes taking place within the structures being subjected to temperature and vapor pressure gradients, including the residual effects of moisture accumulation, and assesses its impact on heat con-ductivity of materials that the structures consist of. Present study is a part of more extensive research on the ap-plication of semi-analytical methods in heat transfer problems, therefore it is not exhaustive and complete. Shortcomings of the method and its possible work-arounds as well as the topics for further studies are discussed in Conclusions and Further Studies section.

Keywords

• Heat and mass transfer problem, coupled problem, non-linear, finite element method, semi-analytical method