Analytical Solution for Transient Laminar Fully Developed Free Convection in Open-Ended Vertical Concentric Porous Annuli

Abstract

Free and mixed convection problems in a vertical porous annulus have been extensively studied. These studies use numerical or experimental techniques to investigate the thermal behavior of the mental porous annulus. Parang and Keyhani have obtained closed-form solutions for the special case where the inner and outer walls are heated by uniform but unequal heat fluxes. The lack of analytical solutions for transient fully developed laminar natural convection in vertical concentric porous annuli, with different fundamental combinations of isothermal and isoflux thermal boundary conditions, motivated the present work. The purpose of this paper is to present, in closed forms, transient fully developed free convection solutions, corresponding to four fundamental thermal boundary conditions in vertical concentric annuli. The solutions obtained, which take both Darcian and Brinkman effects into consideration, may be used as a preliminary check for numerical solutions of more practical situations. 4 refs.