TRANSIENT NATURAL CONVECTION INSIDE POROUS CAVITIES: HYBRID NUMERICAL-ANALYTICAL SOLUTION AND MIXED SYMBOLIC-NUMERICAL COMPUTATION

Abstract

A hybrid numerical-analytical solution for two-dimensional transient-free convection is presented and applied to a vertical porous cavity, based on application of the ideas in the generalized integral transform technique (GITT). The integral transformation process reduces the original coupled partial differential equations (PDEs), for stream function and temperature, into an infinite system of nonlinear ordinary differential equations (ODEs) for the transformed potentials, which is adaptively truncated and numerically solved through subroutine NDSolve from the Mathematica software system. All the analytical steps in the solution procedure are symbolically evaluated through the Mathematica package, mixing with the numerical computations and graphic representation.