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A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure (with aspect ratio of one) filled with a compressible fluid (Pr = 0.72). One of the vertical walls of the enclosure is kept at a higher temperature than the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The compressibility of the working fluid is represented by an ideal gas relation. Thermodynamic and transport properties of the fluid are assumed to be function of temperature. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing based on Taylor expansion for time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried out on different mesh sizes and also on a stretched orthogonal mesh to determine the accuracy of the square mesh adopted for the present study. Numerical experiments were carried out for a benchmark case (driven cavity flows) to verify the accuracy of the CMSIP, the proposed solution procedure. Numerical experiments were then carried out to simulate the development of the buoyancy driven circulation patterns for Rayleigh (Ra) numbers between 103 and 106 . Also a parametric study was carried out (where Ra number was kept constant) to determine the effect of variations in wall temperature difference and reference length on the velocity and temperature fields. The effects of variable fluid properties on circulation patterns, temperature distributions, vertical and horizontal velocity profiles, and heat transfer from the walls of the enclosure were determined in a separate set of numerical experiments. Finally, unsteady thermal and hydrodynamic behavior of the working fluid was studied by imposing a sudden wall temperature change in the square enclosure. It is concluded that there is notable difference between the results of the variable property and the constant property models. Also, the variable property model predicts lower values for wall heat fluxes and Nu number than the constant property one. This seems to be more true when the temperature difference between the hot and cold walls of the enclosure is larger.Copyright © 2009 by ASME

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Variable Thermodynamic and Transport Properties