Natural Convection Heat Transfer in a Porous Rhombic Annulus

Abstract

Numerical solutions are presented for laminar natural convection heat transfer in a fluid saturated porous enclosure between two isothermal concentric cylinders of rhombic cross-sections. Simulations are conducted for four values of Raleigh number (Ra = 10⁴, 10⁵, 10⁶, and 10⁷), three values of Darcy number (Da = 10⁻¹, 10⁻³, and 10⁻⁵), three values of porosity (ϵ = 0.3, 0.6, and 0.9), four values of enclosure gap (E _g  = 0.875, 0.75, 0.5, and 0.25), and two values of Prandtl number (Pr = 0.7 and 5). The results are reported in terms of streamlines, isotherms, mid-height velocity and temperature profiles, and local and average Nusselt number values. The flow strength and convection heat transfer increase with an increase in Ra, Da, E _g , and/or ϵ. At low E _g values, the flow in the enclosure is weak and convection heat transfer is low even though the total heat transfer is higher than at higher E _g values, due to an increase in conduction heat transfer. An increase in Pr is associated with a decrease in the flow strength and an increase in total heat transfer. Furthermore, predictions indicate the presence of a critical Ra number below which conduction is the dominant heat transfer mode. Convection starts affecting the total heat transfer at Ra values higher than the critical one. The critical Ra decreases with increasing Da and/or ϵ, and increases with decreasing E _g .

The financial support provided by the University Research Board of the American University of Beirut is gratefully acknowledged.