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

• Published in: International journal of heat and mass transfer Vol. 42; no. 14; pp. 2649 - 2660
• Main Authors: Pandey, R.N., Srivastava, S.K., Mikhailov, M.D.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.1999; Elsevier
• Subjects: Applied sciences; Eigenvalues and eigenfunctions; Energy; Energy. Thermal use of fuels; Equations of motion; Exact sciences and technology; Heat transfer; Interfaces (materials); Mass transfer; Mathematical models; Matrix algebra; Partial differential equations; Porous materials; Problem solving; Theoretical studies. Data and constants. Metering; Thermal diffusion in solids; Eigenvalue problem; Linear system; Partial differential equation; Capillary structure; Porous medium; Heat mass transfer
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/S0017-9310(98)00253-1

In this paper an eigen value 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 non inclusion 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.