Internal natural, forced and mixed convection in fluid-saturated porous medium

Abstract

This chapter summarizes theoretical and experimental studies on internal natural, forced, and mixed convection in saturated porous media in recent years. It discusses the physics of natural convection and the corresponding mathematical descriptions or the governing equations for mass, momentum, and energy based on the Darcy model. A numerical solution method is described that uses the vorticity-stream function formulation and a second-order, finite-difference method(FDM). The governing equations for transient and steady-state, 3D natural convection are solved numerically for tilted rectangular or annular porous closures with different boundary conditions to predict the flow field and temperature distribution in these geometries. This study experimentally investigates developing and fully developed forced convective heat transfer in packed channels for different fluids and differently sized porous media. The dimensionless parameters governing mixed convection in a vertical annulus filled with porous media are deduced through dimensional analysis. A criterion on Gr**Da/ReH is also suggested for identifying pure forced as opposed to mixed convection. Mixed convection in a vertical porous channel bounded by two parallel plates with asymmetrical heating is investigated with Brinkman's model in the momentum equation. In addition, criteria that identify the occurrence of flow reversals are deduced from an analytical solution of the Brinkman-Forchheimer-Darcy momentum equation for fully-developed flow.