Natural convection flow simulation for various angles in a trapezoidal enclosure with linearly heated side wall(s)

Natural convection in trapezoidal enclosures for uniformly heated bottom wall, linearly heated vertical wall(s) in presence of insulated top wall have been investigated numerically with penalty finite element method. Parametric studies for the wide range of Rayleigh numbers (Ra=103-105) and Prandtl numbers (Pr=0.7-1000) with various tilt angles of side walls (φ) have been performed. For linearly heated side walls, symmetry in flow pattern is observed. In addition, secondary circulations are observed near the bottom wall for φ=0° especially for larger Pr(Pr⩾0.7). In contrast, for linearly heated left wall and cooled right wall, the secondary circulations are stronger near the top portion of the left wall especially for larger Pr. Streamlines show that the strength of convection is larger for φ=45° and flow intensities are found to be larger for higher Prandtl numbers. Local heat transfer rates are found to be relatively larger for φ=0°. Average Nusselt number plots show higher heat transfer rates for φ=0° and the overall heat transfer rates at the bottom wall is larger for the linearly heated left wall and cooled right wall. A non-monotonic trend in average Nusselt number vs Rayleigh number due to presence of multiple circulations is observed for φ=0°.