Effect of Inclination Angle of a Rhombic Enclosure on Natural Convection due to Differential Heating and Rayleigh-Bѐnard Configuration

Abstract

This article analyzes the detailed natural convection phenomena for a rhombic enclosure with differential heating and Rayleigh-Bѐnard configuration. A bi-quadratic element has been used to calculate the differential fluxes in the Navier-Stokes equations. A fourth order artificial viscosity was used to stabilize the numerical residue. The present numerical solution is performed over a wide range of parameters; 10^3 ≤ Ra ≤ 10^8, 15^0 ≤ ϕ ≤ 165^0 for differential heating and 10^3 ≤ Ra ≤ 10^6, 15^0 ≤ ϕ ≤ 90^0 for Rayleigh-Bѐnard configuration. The analysis of the net convective heat transfer across the mid-passage or the mid-height is used to identify the contribution of vortex motion from conduction dominate to convection dominate. The overshoots or undershoots of this net convective contribution is highly related to inclination angle of the rhombic enclosure and also the thermal boundary conditions. The compressibility effect slightly alters the overall performance and overshoots or undershoots of the net heat transfer by less than 1% value. Average Nusselt number distributions show that heat transfer rate is maximum for ϕ=90o in differential heating case, while for Rayleigh-Bѐnard convection, the heat transfer rate is maximum for ϕ=75o except for ϕ=15o at Rayleigh number 10^3 where conduction heat transfer is dominate. There is a linearity between the average Nusselt number and log(Ra) for all the inclination angles for both cases. Results of the study shows that the slope of the linearity is steeper for smaller or wider inclination angles when convective heat transfer is dominate i.e., at larger Rayleigh number.