A Comprehensive Bejan’s Heatline Approach for Natural Convection Heat Transfer Within Inclined Square Cavities

TL;DR: In this paper, the Galerkin finite element method has been used to solve the nonlinear coupled partial differential equations governing the fluid flow and thermal fields in the presence of adiabatic top wall.

Abstract: The present study deals with natural convection heat transfer within water (Pr = 7.2) filled inclined square cavities for hot bottom wall (case 1: isothermal heating/case 2: non-isothermal heating) and cold side walls in the presence of adiabatic top wall. The Galerkin finite element method has been used to solve the nonlinear coupled partial differential equations governing the fluid flow and thermal fields. This method is further used to solve the Poisson equation for streamfunction and heatfunction. The streamlines (Ψ), isotherms (θ) and heatlines (Π) are obtained for various inclination angles (φ = 0°, 30° and 60°) in the range of Rayleigh numbers (103 ≤ Ra ≤ 105). The physical significance of heatlines have been demonstrated for a comprehensive understanding of heat energy distribution within the inclined square cavities. The flow pattern is symmetric for φ = 0° whereas asymmetric flow pattern is observed for the φ = 30° and 60° due to tangential and normal components of buoyancy forces. At Ra = 103, weak fluid circulation and orthogonal heat-lines on isothermal surface, indicate conduction dominant heat transfer for both cases. Strong closed loop heatlines are found due to strong fluid convective circulation cells at Ra = 105. Heat transfer rates are obtained in terms of local and average Nusselt numbers. In general, the overall amount of heat transfer along the right wall increases with inclination angle and that decreases along the left wall with increase in inclination angle. The non-isothermal heating case exhibits greater heat transfer rates at the center of the bottom wall than the isothermal heating whereas average Nusselt number shows that overall heat transfer rate is larger for the isothermal heating case as compared to that of non-isothermal heating case.Copyright © 2012 by ASME