Numerical Investigation of Laminar Natural Convection in Inclined Square Enclosure with the Influence of Discrete Heat Source

Abstract

Natural convection heat transfer in a two-dimensional square enclosure at various angles of inclination is investigated numerically using a finite volume based computational procedure. The heat transfer is from a constant temperature heat source of finite length centred at one of the walls to the cold wall on the opposite side while the remaining walls are insulated. The effect of area ratio of the heat source $A$ from 0.2 to 1.0, Rayleigh number Ra from 10³ to 10⁷, and angle of inclination of the enclosure $\theta$ varying from 0° to 360° on the flow field and heat transfer characteristics are investigated. Streamline and isothermal line patterns are found to be similar at low Rayleigh numbers whereas at high Rayleigh numbers the differences are significant due to the influence of the parameters considered. Average Nusselt number decreases drastically as the position of the heat source is moved above the horizontal centre line of the enclosure. Correlation of the average Nusselt number which depends on the parameters of interest is obtained in the general form $C{\mathrm{R}\mathrm{a}}^m{A}^n$. The correlation coefficients are determined by multiple regression analysis for the entire range of Rayleigh numbers analysed and the values found by correlation equations are in good agreement with the numerical results.