Analytical solution for heat and moisture diffusion in layered materials

Abstract

The study of heat and moisture flows in multiple layers of different materials that make up the unsaturated zone is of great importance when characterizing the behaviour of these materials. In the present paper, analytical solutions of the one-dimensional heat and moisture coupled diffusion problem for layered materials under two different sets of boundary conditions are proposed. The coupled flow of heat and moisture are assumed to follow the theory of Philip and De Vries, and the solutions are derived analytically using integral transform methods. A comparison between the analytical and numerical solutions for one example problem shows satisfactory results. Furthermore, a procedure is presented for estimating heat and moisture distribution profiles in any layered materials using the derived analytical solutions. It is expected that the proposed analytical solutions will be used effectively for preliminary analyses of coupled heat and moisture movements in unsaturated porous media.