Natural Convection Heat Transfer in Rectangular Enclosure with Sinusoidal Boundary Condition

A. Hamid, Ib; S. Ahmed, Israa; M. Salman, Ayad

	Natural Convection Heat Transfer in Rectangular Enclosure with Sinusoidal Boundary Condition
Journal of Engineering and Sustainable Development
Article 1, Volume 16, Issue 1, 2012, Pages 287-306
Authors
ib A. Hamid; Israa S. Ahmed; Ayad M. Salman
Abstract
Natural convection heat transfer with two-dimensional in a rectangular enclo¬sure is examined numerically. The enclosure object with heated left side wall, while the right side was cold, the top and bottom walls was adiabatic. The theoretical study involved the numerical solution of the Navier-Stokes and energy equations by using finite difference method. The stream function– formulation was used in the mathematical model. The numerical solution is capable of calculating the velocity, stream function, and vorticity and temperature fields of the computational domain. A computer program in (FORTRAN 90) was used to carry out the numerical solution. Problem has been analyzed and the non-dimensional governing equations are solved using finite difference method. Enclosure is assumed to be filled with an 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 a relation between average Nusselt number and Ra number, are compared with previous works. For square enclosure filled by air (Pr=0.72). There are agreement in results and found excellent agreement which validate the present computational model.

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