TITLE:
Numerical Solutions of 2-D Laminar Free Convection in an Isoceles Triangular Cavity Filled with a Darcy-Brinkman Porous Medium: Effect of Heat Source Size
AUTHORS:
Giovani Elie Baptista Malomar, Omar Ngor Thiam, Cheikh Mbow
KEYWORDS:
Free Convection, Partially Heating, Porous Media, Numerical Study
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.15 No.4,
December
16,
2025
ABSTRACT: In this work, a numerical study of free convection in an isoceles porous triangular cavity with a partially heated horizontal base and cooled upper walls is analysed. The uniform heat source is located centrally at the base wall. Darcy-Brinkman model is used; it is also assumed that the fluid used is incompressible and obeys the Boussinesq approximation. The non-dimensionless governing equations, stream function-vorticity, momentum and energy are discretized by finite difference method and solved using the successive over-relaxation (SOR) method. Streamline and isotherm patterns were presented at different lengths of heater (
0.25≤ϵ≤1
), Darcy number (
10
−4
≤Da≤
10
−2
), Prandtl number (
0.7≤Pr≤7
) and for different Rayleigh number (
10
3
≤Ra≤
10
6
). On the basis of the results, it is observed that the presence of a localized heat source may slightly accelerate the flow, but does not change the fundamental mode of convection. Beyond the critical value of Rayleigh number, the average Nusselt number characterizing overall heat transfer increases rapidly with decreasing source size.