Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept

Heat flow patterns in the presence of natural convection within trapezoidal enclosures have been analyzed with heatlines concept. In the present study, natural convection within a trapezoidal enclosure for uniformly and non-uniformly heated bottom wall, insulated top wall and isothermal side walls with inclination angle φ have been investigated. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively, such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. Parametric study for the wide range of Rayleigh number (Ra),103⩽Ra⩽105 and Prandtl number (Pr),0.026⩽Pr⩽1000 with various tilt angles φ=45°,30° and 0°(square) have been carried out. Heatlines are found to be continuous lines connecting the cold and hot walls and the lines are perpendicular to the isothermal wall for the conduction dominant heat transfer. The enhanced thermal mixing near the core for larger Ra is explained with dense heatlines and convective loop of heatlines. The formation of boundary layer on the walls has a direct consequence based on heatlines. The local Nusselt numbers have also been shown for side and bottom walls and variation of local Nusselt numbers with distance have also been explained based on heatlines. It is found that average heat transfer rate does not vary significantly with φ for non-uniform heating of bottom wall.