Numerical Study of Unsteady Laminar Natural Convection In A Square Cavity Having Partial Lengths of Vertical Walls Differentially Heated and Cooled

摘要

The present numerical study deals with transient natural convective flow in a closed square cavity with adiabatic top and bottom walls. Vertical walls of the cavity are assumed to be partially heated and cooled such that heated and cooled portions face each other in an opposed manner. Three different cases with equal and unequal lengths of hot and cold portions on the vertical walls are considered here. The corresponding governing equations of motion are non-dimensionalized and reformulated using stream function-vorticity approach. Alternating direction implicit finite difference scheme is used to solve the coupled equations. Results obtained for different values of Grashof number (Gr) and fixed Prandtl number (Pr = 0.733) are presented in the form of isotherms, streamlines, average Nusselt number and time series. Average Nusselt number is found to behave as a non-linear function of Grashof number.