4 - Integral transforms for natural convection in cavities filled with porous media

Abstract

Transport phenomena in porous media represent an important segment of the heat and mass transfer field, and have a variety of applications in engineering. In terms of adopted modeling, a number of previous works show the importance of an adequate parametric range analysis of different models used to represent flows in porous media. Hybrid numerical-analytical algorithms, based on the generalized integral transform technique, developed to handle transient two- and three-dimensional heat and fluid flow in cavities filled with a porous material, are reviewed in the chapter. To illustrate the approach, specific situations of both horizontal and vertical cavities are closely considered under the Darcy flow model. The problem is analyzed with and without the time derivative term in the flow equations, using a vorticity-vector potential formulation, which automatically reduces to the stream function-only formulation for two-dimensional situations. Results for rectangular (2D) and parallelepiped (3D) cavities are presented to demonstrate the convergence behavior of proposed eigenfunction expansion solutions, and comparisons with previously reported numerical solutions are critically performed.