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

摘要

This article analyzes the detailed natural convection phenomena for anrhombic enclosure with differential heating and Rayleigh-Bѐnardnconfiguration. A bi-quadratic element has been used to calculate thendifferential fluxes in the Navier-Stokes equations. A fourth order artificialnviscosity was used to stabilize the numerical residue. The present numericalnsolution is performed over a wide range of parameters; 10n, Kuan-Lin Chen and Yu-Ta Hsun3≤Ra≤ 108,n150≤ϕ ≤1650 for differential heating and 103≤Ra≤ 106, 150≤ϕ ≤900 fornRayleigh-Bѐnard configuration. The analysis of the net convective heatntransfer across the mid-passage or the mid-height is used to identify thencontribution of vortex motion from conduction dominate to convectionndominate. The overshoots or undershoots of this net convective contributionnis highly related to inclination angle of the rhombic enclosure and also thenthermal boundary conditions. The compressibility effect slightly alters thenoverall performance and overshoots or undershoots of the net heat transfernby less than 1% value. Average Nusselt number distributions show that heatntransfer rate is maximum for ϕ=90o in differential heating case, while fornRayleigh-Bѐnard convection, the heat transfer rate is maximum for ϕ=75onexcept for ϕ=15o at Rayleigh number 103 where conduction heat transfer isndominate. There is a linearity between the average Nusselt number andnlog(Ra) for all the inclination angles for both cases. Results of the studynshows that the slope of the linearity is steeper for smaller or widerninclination angles when convective heat transfer is dominate i.e., at largernRayleigh number.