Finite Element Analysis of Convective Heat Transfer in a Linearly Heated Porous Trapezoidal Cavity in the Presence of a Magnetic Field

A computational study is carried out to examine how a magnetic field affects convective heat transfer in a linearly heated trapezoidal cavity, filled with a fluid-saturated by porous medium. Both inclined walls are adiabatic, with the top wall maintaining a constant cooled temperature T_c which is moving with a constant velocity U₀ in the positive x-axis direction, and the bottom wall being heated linearly which is moving with a constant velocity that is the same as that of the top wall but in the opposite direction. The finite element technique resolves the governing equations associated with appropriate initial and boundary conditions. The resulting solutions are represented graphically for streamlines, isothermal lines, and thermal gradient magnitude for an extensive range of Darcy numbers (10^–2 ≤ Da ≤ 10^–5), Hartmann numbers (0 ≤ Ha ≤ 100), Prandtl numbers (7 ≤ Pr ≤ 50), Grashof numbers (10³ ≤ Gr ≤ 10⁶), and Reynolds numbers (10 ≤ Re ≤ 200). The findings indicate the enhancement of flow circulation concerning the higher values of Darcy number, Grashof number, and Reynolds number but the reduction of that with the higher values of Hartmann number and Prandtl number. In addition, the temperature distribution is affected by various values of the parameters mentioned above. It is also reflected that the rate of convective heat transfer declines with the growing values of the Hartmann number. In particular, the heat transfer rate experiences a decline of 2.102% and 55.44% with the application of a magnetic field respectively at Ha = 10 and Ha = 100 in comparison to the absence of a magnetic field (Ha = 0) for Pr = 10. It also reduces with the increasing value of the Grashof number and the decreasing values of the Darcy number, Prandtl number, and Reynolds number.