Analysis of Flow and Heat Transfer in a Parallelogram Non‐Uniformly Heated Enclosure Filled with Porous Medium

Abstract

The flow and heat transfer in a parallelogram enclosure filled with a porous medium is analyzed numerically. The heated bottom wall has a sinusoidal temperature distribution and side walls cooled isothermally while the upper wall is well insulated. Dimensionless Darcy law and energy equations are solved using the finite difference method along with the corresponding boundary condition. Computations were carried out for four inclination angles of side walls (γ = 45°, 60°, 75°, 90°) with different Rayleigh numbers (100 ≤ Ra ≤ 1000) and their effects on the flow field and heat transfer are discussed. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and an increase in the angle leads to a decrease in the strength of the right vortex. The study also revealed that as the Rayleigh number increases at γ = 45°, another (third) vortex develops along the left wall and its strength enhances with Rayleigh number. At the end, a correlation is extracted from the numerical data which represents the relation between the Nusselt number, inclination angle, and the Rayleigh number.

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

“…He concluded that the heat transfer rate was increased by an increase in the thermal conductivity parameter and it was reduced in the presence of heat sources. Soleimani et al [24 ] analyzed numerically the flow and heat transfer in a parallelogram enclosure filled with a porous medium. The heated bottom wall had a sinusoidal temperature distribution and sidewalls cooled isothermally while the upper wall was well insulated.…”