On the solution of non‐linear drying problems in capillary porous media through integral transformation of Luikov equations

The generalized integral transform technique is employed to provide hybrid numerical–analytical solutions to the non-linear Luikov equations, that govern drying within capillary porous media. The coupled equations for moisture and temperature distributions are integral transformed to eliminate the spatial co-ordinates, yielding an ordinary differential system for the time variation of the transformed potentials, which is readily solved through scientific subroutine libraries with automatic error control schemes. The analytical inversion formula is then recalled to provide explicit expressions for the original potentials at any desired position. The convergence behaviour of the proposed eigenfunction expansions is illustrated, and a parametric study is performed, for the drying of a slab subjected to non-linear radiative boundary conditions.