Journal of Advances in Mathematics and Computer Science

The present numerical attempt deals with the analysis of natural convection flow in a trapezoidal cavity with triangular block embedded inside intended for various inclination angles ф. In this cavity, the bottom wall is non-uniformly heated, left and right (side) walls are cold and the top wall is well insulated. The triangular block or triangular solid body surface for different positions (LBC, RBC, LTC, RTC) inside the trapezoidal cavity is also non-uniformly heated (T_hb). A Galerkin weighted residual finite element method is applied to solve the Navier-Stokes equations and energy balance equations and to find the results in the form of streamlines, isotherms (temperature), heat function, pressure and local Nusselt numbers and average Nusselt number for different parameters. Finite element method has also been used to solve the velocity and thermal fields. The fluid is concerned for various governing parameters, such as Rayleigh number, Ra (10³≤Ra≤10⁶), Prandtl number, Pr (0.026≤Pr≤1000) and various inclination angles ф (ф = 45°,  30° and 0°). It has been revealed that due to non-uniformly heated triangular block, heatlines by connecting cold and hot walls are found to be continuous lines and also perpendicular to the isothermal walls which occur for the conduction dominant regimes. Fluid flow and heat flow occur symmetrically. The local Nusselt number and average Nusselt number for the non-uniformly heated bottom wall of the trapezoidal cavity using the inside of the non-uniformly heated triangular block are illustrated by heatlines. It has been also found that heat transfer rates significantly depend on the tilt angles (ф), non-uniformly heated triangular block and aforementioned non-dimensional parameters.