Solutions of Luikov equations of heat and mass transfer in capillary porous bodies through matrix calculus: A new approach

Abstract

In this paper an eigenvalue analysis approach is employed to obtain the solutions of the Luikov system of linear partial differential equations addressed to the most general type of boundary conditions. The Luikov equations provide a well established model for the analysis of various simultaneous heat and mass diffusion problems in capillary porous bodies. However, analytical methods to achieve a complete and satisfactory solution of these equations is still lacking in the literature because of noninclusion of the existence of a countable number of complex roots in almost all the solutions. A specific example on contact drying of a moist porous sheet with uniform initial temperature and moisture distribution is considered. The influence of the complex roots on the dimensionless temperature, moisture content, and the local rate of drying is demonstrated. A set of benchmark results is obtained for reference purposes.; In this paper an eigenvalue analysis approach is employed to obtain the solutions of the Luikov system of linear partial differential equations addressed to the most general type of boundary conditions. The Luikov equations provide a well established model for the analysis of various simultaneous heat and mass diffusion problems in capillary porous bodies. However, analytical methods to achieve a complete and satisfactory solution of these equations is still lacking in the literature because of noninclusion of the existence of a countable number of complex roots in almost all the solutions. A specific example on contact drying of a moist porous sheet with uniform initial temperature and moisture distribution is considered. The influence of the complex roots on the dimensionless temperature, moisture content, and the local rate of drying is demonstrated. A set of benchmark results is obtained for reference purposes.