要約

Hybrid numerical—analytical algorithms, based on the generalized integral transform technique, are developed and reviewed to handle transient two-and three-dimensional heat and fluid flow in cavities filled with a porous material. A general formulation and solution methodology for horizontal and vertical cavities is developed. To illustrate the algorithm computational behavior, specific situations are more closely considered, under the Darcy model for natural convection in porous medium filled cavities. 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 (2-D) and parallelepiped (3-D) vertical cavities are presented to demonstrate the convergence behavior of the proposed eigenfunction expansion solutions, and comparisons with previously reported numerical solutions are critically performed.