A Uniform Theoretical Model for Fluid Flow and Heat Transfer in Porous Media

Abstract

To comprehensively study fluid flow and heat transfer in porous media, a uniform model that is valid for both a regular microscopic geometry, e.g., spheres and cylinders, and irregular microscopic geometries, such as metal foams or ceramic, is needed to connect the macroscopic and microscopic flow and heat transfer. In this chapter, the microscopic governing equations and volume averaged macroscopic governing equations for flow and natural convection heat transfer are presented. As defined in Chap. 1, the dimensionless geometry factor connects the macroscopic and microscopic drag and heat flux between the solid and fluid phases in a porous medium. Based on this geometry factor, the closure models are presented based on the microscopic drag coefficients and heat transfer correlations in a uniform form for porous media of arbitrary microscopic geometry. Also, relationships between the microscopic drag coefficients and permeability, Forchheimer coefficient, and Ergun constants are presented.