(Semi-)analytical solution of Luikov equations for time-periodic boundary conditions

The paper addresses the problem of coupled heat and moisture transfer in porous materials with the time-periodic boundary conditions applied. The solution of Luikov equations [1], which describe coupled heat and moisture transfer, is presented. Laplace transform is used, where some terms of the inverse Laplace transform ought to be solved by Gaussian quadrature, meaning that the solution is semi-analytical. The time-periodic boundary conditions are applied to simulate the humidity and temperature oscillations of natural environment. Therefore, the proposed solution is appropriate to evaluate the distribution of moisture and temperature within the porous material exposed to everyday natural cycles. The paper presents convergence tests, validation of semi-analytical solution and application to different building materials are presented in the paper.