An analytical solution to coupled heat and moisture diffusion transfer in porous materials

Abstract

An analytical method is proposed for solving the problem of coupled heat and moisture transfer in porous materials. The coupled partial differential equations and boundary conditions are first subjected to Laplace transformation, the equations are reduced to ordinary differential equations, then the equations are converted into a single fourth-order ordinary differential equation by introducing a transformation function. The solution of the equation can be easily obtained, and thus, the temperature and moisture distributions in the transform domain can be determined. Finally, the transformed values are analytically or numerically inverted to obtain the time domain results. Therefore, the transient solution at any given time can be evaluated. The results are identical with published analytical solutions for a special case using decoupling technique, and they agree with a published analytical solution for wood slab. The method is compact enough to be generally applied to problems of heat and mass transfer in porous media.