Finite Element Simulations of Natural Convection in a Right-Angle Triangular Enclosure Filled with a Porous Medium: Effects of Various Thermal Boundary Conditions
The phenomenon of natural convection in a right-angle triangular enclosure filled with a porous matrix has been studied numerically. A penalty finite element analysis with biquadratic trapezoidal elements is used for solving the Navier-Stokes and energy balance equations. The detailed study is carried out in two cases, depending on various thermal boundary conditions: (1) the vertical wall is uniformly or linearly heated, while the inclined wall is cold isothermal; and (2) the inclined wall is uniformly or linearly heated, while the vertical wall is cold isothermal. In all cases, the horizontal bottom wall is adiabatic, and the geometric aspect ratio is considered to be 1. It has been found that at low Darcy numbers (Da ≤ 10-5), the heat transfer is primarily due to conduction, irrespective of the Ra and Pr. As Rayleigh number increases, there is a change from a conduction-dominant region to a convection-dominant region for Da = 10-3, and the critical Rayleigh number corresponding to the onset of convection is obtained. Some interesting features of the stream function and isotherm contours are discussed, especially for low and high Prandtl number limits. Complete heat transfer analysis is performed in terms of local and average Nusselt numbers. It is observed that the average Nusselt number for the vertical wall is √2 times that of the inclined wall for all cases, verifying the thermal equilibrium of the system.