Natural convection in an inclined parallelogrammic enclosure: Effect non-uniform heating

Abstract

In this paper, numerical simulations are presented to understand the influence of inclination angle of a tilted parallelogrammic enclosure. The upper and lower boundaries of the enclosure are treated as thermally insulated; right wall is uniform cooled while the left wall is non-uniformly heated with either sinusoidal or linear thermal profiles. Using Darcy law, the momentum equations are modeled and unsteady energy equation is considered. The model equations are numerically solved using finite difference method, in particular, using ADI and SLOR methods. Based on standard coordinate transformations, the governing equations are transformed to rectangular shaped enclosure computational domain. In this analysis, due to large number parameters, the inclination angle of the enclosure is fixed. The flow and thermal processes are depicted through streamlines and isotherms, while the thermal transport rates are illustrated through Nusselt number profiles. Numerical simulations capture the effects of side wall inclination angle and non-uniform thermal conditions on the flow and thermal patterns, heat transport rates for various parametric ranges of the problem.