The Influence of a Heat Source Position Located on the Bottom Wall Inside Square Enclosure on Laminar Natural Convection

Abstract

Natural convection in two-dimensional square enclosure is studied numerically using a finite difference method. In the present study, top wall is considered adiabatic, two vertical walls are maintained at constant low temperature, the bottom wall is maintained at constant high temperature and the non-heated parts of the bottom wall are considered adiabatic. The aim of this work is to determine the influence of the position of a small heating source located on the bottom wall of a square enclosure (aspect ratio=1) filled with air (Pr=0.71) on the natural convection flow. Three different positions are analyzed ,on the left side (δ=0.1) ,on the center(δ=0.5) and on the right side (δ=0.9). The dimensionless of the heat source length (S) is taken equal to (0.2). The three dimensional differential conservation equations of mass, momentum and energy are solved by a finite difference method for Rayleigh number varying from 103 to 106. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number at the heat source surface under different conditions. The average Nusselt number and flow behavior are symmetrical for both cases, when heat source located on the left extreme and right extreme of the bottom wall. The average Nusselt number for the extremes (left and right) is higher than the central position for (Ra≤105) because the heat source is adjacent to the cold vertical wall. The average Nusselt number for the central position is higher than the extremes ( left and right) for (Ra>105)because the vortexes rotation of the air in the center of the bottom wall is greater than extremes .The local Nusselt number is very high at the edges of the heat source and reduces towards the center.