Natural Convection Study by the Direct Integration of the Momentum and Energy Equations

Abstract

In this paper, we investigate theoretically the natural thermoconvection phenomena near a vertical plate for two thermal boundary conditions at the sidewalls. A specifically developed analytical model based on the new integral method form is used for the solution of the momentum and energy transfer governing equations. From an adequate choice of velocity and temperature expressions, two new Nusselt-Rayleigh relations, depending on the sidewalls conditions, are derived for all Prandtl numbers. Comparisons among the different thermal configurations considered are reported. In particular, with reference to the typical configuration wherein the sidewalls are isothermal and in uniform heat flux, it is found that the NusseltRayleigh coefficient given via this method indicates a good agreement with the theoretical and experimental results for all Prandtl numbers.

Simulation of Solid-Liquid Phase Transition Process in Aluminum Foams Using the Lattice Boltzmann Method

“…Ibraheem Nasser and H.M. Duwairi have conducted research on convection heat transfer in porous media 7 . Mohamed Bachiri and Ahcene Bouabdallah have studied the natural convection theoretically by the direct integration of momentum and energy equations 8 . Halima Usman and others have investigated heat and mass transfer flow along a vertical channel in a porous medium with a radiation effect 9 .…”