A comprehensive heatline based approach for natural convection flows in trapezoidal enclosures: Effect of various walls heating

摘要

The present numerical study deals with natural convection flow in closed trapezoidal enclosures. The detailed analysis is carried out in two cases: (1) linearly heated side walls; (2) linearly heated left wall and cold right wall. In both the cases bottom wall is uniformly heated and top wall is well insulated. A penalty finite element method with bi-quadratic elements is used to obtain the results in the form of isotherms, streamlines and heatlines and local and average Nusselt numbers. Numerical results are obtained for various values of Rayleigh number Ra (10~3 ≤ Ra ≤ 10~5), Prandtl number Pr (0.015 ≤ Pr ≤ 1000) and inclination angles (φ = 45°, 60° and 90°). Results signify that, at low Ra (Ra = 10~3) heat transfer is conduction dominant. At Ra = 10~5, multiple circulations of streamlines and heatlines results in enhanced convection. For linearly heated side walls (case 1), symmetric pattern in fluid flow and heat flow is observed. Enhanced thermal transport is observed from bottom wall to top portion of side walls via dense heatlines along the vertical center line. It is found that, less intense circulations occurs in square cavity (φ = 90°) compared to other cavities φ = 45°, 60°. In case 2, the cold right wall receives larger amount of heat from bottom wall compared to that of linearly heated left wall. The formation of boundary layer on the walls is explained based on heatlines. The local and average Nusselt numbers are also illustrated using heatlines. It is found that, Nu_b distribution exhibits sinusoidal variation at Pr = 1000 in case 1. It is also found that, Nu_l and Nu_r display wavy pattern at higher Ra for all Pr in case 2. Finally, it is concluded that, overall heat transfer rates are larger for square cavity (φ = 90°) compared to other angles (φ = 45°, φ = 60°) irrespective of heating patterns for side walls.