Numerical simulation of three-dimensional natural convection in a cubic enclosure induced by an isothermally-heated circular cylinder at different inclinations

Abstract

This study numerically examines three-dimensional natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and a titled angle of the enclosure varying from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature, components of velocity and streamtraces eventually reaches a steady state for Rayleigh numbers ranging from 103 to 107 for titled inclination of 90°. However, for the remaining inclinations, Rayleigh numbers must be in the range 103–106 to avoid unsteady state which is manifested by the subdivision of the area, containing the maximum local heat transfer rate, into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper which is solely devoted to three dimensional calculations. Results indicate also that optimal average heat transfer rate is obtained for Rayleigh number set to 106 and an inclination of 90° for both cases of the inner cylinder and lateral walls of cubical enclosure.