On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

Abstract

A three-time-level scheme is employed to obtain numerical solutions of heat and mass transfer potentials for the nonlinear Luikov system. Relative errors are examined when the numerical solutions are compared to the analytical solutions for a single layer linear problem using different finite difference techniques. As a final example, comparisons also are made when the numerical schemes are used to solve a two-layer multi-region nonlinear approach, considering that the thermal conductivity and mass conductivity of the material are dependent on temperature and moisture transfer potential respectively. List of symbolsBi m Biot number for mass transfer, a m L=k m Bi q Biot number for heat transfer, a q L=k q Fo Fourier number, a q s=L 2 Ki m dimensionless mass flux, Lw m =k m / / Ki q dimensionless heat flux, Lw q =k q t t Ko Kossovitch number, qc m /=c q t Lu Luikov number, a m =a q Pn Posnov number, d t t=c m / / r r dimensionless coordinate, r=L e phase change criterion, where, for the boundary conditions of the second kind t t ¼ t 0 ; / / ¼ / 0 and for the boundary conditions of the third kind t t ¼ t s À t 0 ;/ / ¼ / 0 À / à a m diffusion coefficient of moisture, m 2 /s a q thermal diffusivity coefficient, m 2 /s c m specific isothermal mass capacity, 1/ M c q specific heat capacity, kJ/Kg C L half thickness of the layer, m q specific heat of evaporation, kJ/kg t temperature, C r coordinate perpendicular to the surface, m a m mass transfer coefficient, kg/m 2 s M a q heat transfer coefficient, kJ/m 2 s C d thermal gradient coefficient, 1/ C k m moisture conductivity, kg/m s M k q thermal conductivity, kJ/m s C s time, s / moisture transfer potential, M w m mass flux, kg/m 2 s w q heat flux, kg/m 2 s Subscripts 0 initial s surrounds or surface à in equilibrium with surroundings j region i space node Superscript n geometry h time level IntroductionThere is a continuously increasing activity in the field of heat and mass transfer in capillary porous media due to its wide research as well industrial applications. Besides its applications as ground water pollution, heat transfer in the ground, drying processes, and multiphase flow under nonisothermal conditions, it is also been used in space research, especially in devices for liquid and energy transfer (heat pipes, heat exchangers, insulation of highly conducting wire nets, etc.) due to the fact that the performance of capillary porous materials does not depend on a gravitational field (Pandey et al., 1999). Because of the complexities of the mechanism involved, it is very difficult to model the process. The phenomena appropriate for moisture, pressure and enthalpy distributions are coupled. The transport of associated matter of all phases and the transfer of enthalpy must be considered simultaneously. Luikov (1965Luikov ( , 1966Luikov ( , 1975) developed a uniquely model for a simultaneous heat and moisture transfer in capillary porous materials, which is based on non-equilibrium thermodynamics of irreversible transfer processes. This model is applicable for both ...