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

A two-dimensional mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid where one of the vertical walls of the enclosure is kept at a higher temperature than the opposite one. Fluid thermodynamic and transport properties are assumed to be functions of temperature. The governing equations are discretized using second order accurate differencing for spatial and temporal derivatives and then linearized using Newton\u27s linearization method. The resulting set of algebraic equations is solved using the Coupled Modified Strongly Implicit Procedure for the unknowns of the problem. The results of this study show that the variable property model predicts lower values for wall heat fluxes and Nu number than the constant property one for Rayleigh numbers between 104 and 105