Magnetohydrodynamic Natural Convection Flow in an Enclosure with a Finite Length Heater Using the Differential Quadrature (DQ) Method

Analysis of heat and fluid flow transport due to natural convection and magnetohydrodynamic (MHD) flows in a square enclosure with a finite length heater has been performed using the differential quadrature (DQ) technique. The heater with constant heat flux is located on the bottom wall of the enclosure and isothermal boundary conditions are applied to the right vertical wall while the remaining walls are adiabatic. The effects of heater length (0.2 ≤ ? ≤ 0.8), heater location (0.1 ≤ c/L ≤ 0.9), and direction of magnetic force (0° ≤ φ ≤ 90°) for different values of Grashof (10³ ≤ Gr ≤ 10⁶) and Hartmann numbers (0 ≤ Ha ≤ 100) on the heat and fluid flow in the enclosure are studied. According to the results obtained, heat transfer reduces when increasing the Hartmann number. The rate of reduction is higher for high values of Grashof number. The heat transfer rate for the heater closer to the cold wall is considerably higher than the heaters far from the right wall.