Integral transform solutions of transient natural convection in enclosures with variable fluid properties

Abstract

This paper is aimed at the application of the Generalized Integral Transform Technique to the transient version of the classical differentially heated square cavity problem, considering both constant and variable fluid properties. The streamfunction-only formulation of the flow equations and the associated energy equation under laminar flow regime are employed in seeking a hybrid numerical–analytical solution to this natural convection problem. The computational procedure is carefully validated and a thorough convergence analysis is undertaken, yielding sets of reference results. The computed transient behavior of the coupled heat and fluid flow phenomena is compared to some previously reported results. The solution for variable fluid properties with partial Boussinesq approximation (density variation in the body force term only) is presented and compared with the constant properties results. Both models are investigated for different values of the Rayleigh number, from 10 3 to 10 5, and Prandtl number equal to 0.71.