Convection of Micropolar Fluid in a Square Cavity with an Inside Heater

The effect of thermal radiation and viscous dissipation on magnetohydrodynamic natural convection of a micropolar fluid in a square cavity with uniform and nonuniform heated thin plate is studied numerically. The vertical walls are cooled, whereas the horizontal top and bottom walls are considered thermally insulated. The thin plate is assumed to be isothermal with a linearly varying temperature. The governing equations were solved by the finite volume method using the second-order central difference scheme and upwind differencing scheme. The results are discussed for different combinations of physical parameters, namely, the Hartmann number, inclination angle of the magnetic field, viscous dissipation and radiation parameter, vortex viscosity, and source nonuniformity parameter. It is observed that the heat transfer rate increases with an increase in the inclination angle of the magnetic field and viscous dissipation, but it decreases with an increase in the radiation parameter, Hartmann number, and vortex viscosity parameter for both uniform and nonuniform heating parameters. In addition, the overall heat transfer rate of a micropolar fluid is found to be smaller than that of a Newtonian fluid.