Effect of heated wall position on magneto-hydrodynamic mixed convection in a channel with an open cavity

Abstract

The effect of heated wall position on magneto- hydrodynamic mixed convection in a channel with an open cavity has been investigated numerically. Magnetic field is acting countering the fluid flow, normal to the vertical wall of the cavity. Three different cases were considered based on heater position in the cavity as the left vertical side (Case 1), bottom side (Case 2) and right vertical side (Case 3). An external flow enters through an opening located at the left side of the channel, passes through the cavity and finally leaves the channel through an exit at the right side. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. Using a class of appropriate transformations, the governing equations along with the boundary conditions are transformed into non-dimensional form, which are then solved by employing a finite-element scheme based on the Galerkin method of weighted residuals. Results are presented in terms of streamlines, isotherms, average Nusselt number along the hot wall, average fluid temperature at the exit port, pressure and temperature gradient in the domain for different combinations of the governing parameters namely Rayleigh number (Ra) at selected values of Hartmann numbers (Ha) and cavity aspect ratio AR. The results indicate that both the flow and the thermal fields strongly depend on the aforesaid parameters. Comparisons with previously published work are performed and the results are found to be in excellent agreement.