Finite element analysis of convective heat transfer in a linearly heated porous trapezoidal cavity in the presence of a magnetic field

Abstract

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 Tc 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 is utilized to resolve the governing equations associated with appropriate initial and boundary conditions. The resulting solutions are represented graphically in respect of streamlines, isothermal lines, and thermal gradient magnitude for an extensive range of Darcy numbers (10− 2 ≤ Da ≤ 10− 5), Hartmann numbers (0 ≤ Ha ≤ 100), and Prandtl numbers (0.7 ≤ Pr ≤ 15). The findings indicate the enhancement of flow circulation concerning the higher values of Darcy number but the reduction of that with the higher values of Hartmann number as well as Prandtl number. In addition, the temperature distribution is affected by various values of the Darcy number and Hartmann number. It is also reflected that the rate of convective heat transfer declines with the growing values of the Hartmann number and the decreasing values of the Darcy number and Prandtl number.