Costa (1997) presented numerical solutions for the steady-state heat and mass transfer in a vertical stack of plane vertical square cavities separated by solid layers one-tenth the height of the cavities. This configuration was supposed to represent a building construction element. The temperature and concentration fields were assumed to be harmonic in these layers; i.e. Fourier's and Fick's Laws were assumed to hold there. Although this would be a reasonable approach for a pure heat transfer problem, it is probably too simplistic for the porous media envisaged by Costa.
According to Künzel and Kiessl (1997), the vapour flux in such materials is driven by gradients in both partial pressure (for effusion and Fickian diffusion) and relative humidity (for the transport of liquefied vapour in sorbed layers or capillaries). The energy flux is due to gradients in temperature (for conduction) and vapour pressure (for the enthalpy flux by vapour diffusion with phase changes). This leads to a nonlinear strongly coupled pair of field equations in the porous solid layers, even when advection is neglected.
Studies of the conjugate heat and mass transfer problem, such as Costa's, are necessary but they are only of value if realistic constitutive laws are employed in both phases. In addition to the oversimplified expressions for the fluxes, Costa did not use realistic values for the conductivity or diffusivity in the porous layers, only arbitrary ones. References to methods for the experimental determination of the required transport properties may be found in Künzel and Kiessl's article.