Natural Convection Heat Transfer in Rectangular Enclosure with Sinusoidal Boundary Condition

Abstract

Natural convection heat transfer with two-dimensional in a rectangular enclo¬sure is examined numerically. The enclosure object with a heated left side wall, while the right side was cold, and the top and bottom walls were adiabatic. The theoretical study involved the numerical solution of the Navier-Stokes and energy equations by using the finite difference method. The stream function– formulation was used in the mathematical model. The numerical solution is capable of calculating the velocity, stream function, vorticity, and temperature fields of the computational domain. A computer program in (FORTRAN 90) was used to carry out the numerical solution. The problem has been analyzed and the non-dimensional governing equations are solved using the finite difference method. The enclosure is assumed to be filled with air with a Prandtl number of 0.71. The problem is analyzed for different values of the Rayleigh number in the range from 103 to 105, aspect ratio parameter (AR: 1, 3, and 5). It is found that for small Ra, the heat transfer is dominated by conduction and begins to be dominated by convection with increasing Ra, and the Nusselt number Nu decreases with increasing AR due to decreasing the volume of the enclosure. In order to validate the numerical model, the results of variation local Nusselt number and relation between average Nusselt number and Ra number, are compared with previous works. For square enclosure filled with air (Pr=0.72). There is an agreement in results and found excellent agreement which validates the present computational model.