Modelling and simulation of energy transfer in a saturated flow through a porous medium

• Published in: Applied mathematical modelling Vol. 16; no. 11; pp. 589 - 597
• Main Authors: Costa, Maria Laura Martins, Sampaio, Rubens, da Gama, Rogério Martins Saldanha
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 1992; Elsevier Science
• Subjects: Applied sciences; Devices using thermal energy; Energy; energy transfer; Energy. Thermal use of fuels; Exact sciences and technology; Finite difference method; Heat exchangers (included heat transformers, condensers, cooling towers); Heat transfer; Mathematical models; Porous materials; porous medium; theory of mixtures; energy transfer; porous medium; theory of mixtures; Numerical simulation; Packed bed; Modeling; Heat exchanger; Heat transfer; Porous medium
• ISSN: 0307-904X
• DOI: 10.1016/0307-904X(92)90034-Z

Using the continuum theory of mixtures (a generalization of classical continuum mechanics), a model for a local description of the energy transfer in a saturated flow of a newtonian fluid through a rigid porous medium is proposed. It considers the fluid and the porous matrix as continuous constituents of a binary (solid-fluid) mixture. Both constituents coexist superposed in the whole volume of the mixture, so there exist simultaneously at each spatial point two temperatures and two velocities, giving rise to an energy generation and a momentum generation, which provide thermal and dynamical interactions, respectively. The forced convection heat transfer between the fluid and the solid constituents, when the fluid flows past a porous channel bounded by two isothermal parallel plates, is simulated by using a finite difference approach. The effects of some dimensionless parameters, such as β (relating the heat transfer between both constituents to the fluid constituent conduction), γ (relating both constituent's conduction), the aspect ratio, the fluid constituent's Péclet number, and the solid constituent's Nusselt number (at the channel's inlet and outlet) are discussed.