Modeling the Influence of Raleigh Numbers on Thermal and Fluidic Behaviors in a Trapezoid-shaped Cell

We model the influence of Raleigh numbers in a trapezoidal cavity. One wall among the sloping walls is exposed to a heat flux density Q=100 W/ m<sup>2 </sup>and the other inclined wall is kept adiabatic. The temperature of the two horizontal walls is assumed to be constant such that T<sub>sup</sub>=305K is greater than T<sub>inf</sub>=300K. The equations of heat and mass transfer which direct our template are described by the Navier-Stockes equation. These equations are discretized using the finite difference method and solved by the Thomas and Gauss-Seidel algorithms. Thus, we analyze the effects of the Raleigh numbers (<i>Ra</i>) on temperature profiles T = 303.15 K and speeds v = 0 m/s. For a variation of <i>Ra</i>=10<sup>3</sup>-10<sup>5</sup>, we note that the convective exchanges of the confined air and the different walls become preponderant with the increase in the Rayleigh number. Also, we contact that the speed of the confined air remains high along the horizontal walls for a <i>Ra</i> high number, but low near the inclined walls. These results show the effects of natural convection in this trapezoidal cavity.