BIOT NUMBER EFFECTS ON THE NUMERICAL STABILITY OF HEAT AND MASS TRANSFER PROBLEMS

In many cases the mass and energy conservation equations are strongly coupled, specially at the boundaries of porous media. This strong coupling may easily cause numerical divergence when a not very robust solver is used. A dimensionless number that could numerically express when numerical instability arises is the Biot number for moisture diffusion. This number gives the relation between the convective and diffusive resistances, which means that, for high Bim numbers, the wall hygric resistance is much higher than the corresponding surface resistance. Another important dimensionless is the mass Fourier number, expressing a mesh-size parameter that could be related to a convergence error function. Therefore, we present a mathematical model to solve a heat and mass transfer problem by using two algorithms and carry out a sensitivity analysis of numerical performance in terms of: i) moisture and heat Biot Numbers; ii) moisture and heat Fourier Numbers; iii) Luikov number and iv) Posnov number. It is noted, for traditional algorithms such as TDMA, the risk of divergence arises very quickly as the moisture Biot number increases, showing a high sensitivity to this dimensionless parameter, which can be even higher than the one caused by the mass Fourier number.