Control volume finite element simulation of MHD forced and natural convection in a vertical channel with a heat-generating pipe

Using the Galerkin weighted residual control volume finite element method, the effects of magnetic field and Joule heating on combined convection flow and heat transfer characteristics inside an octagonal vertical channel containing a heat-generating hollow circular pipe at the centre is performed. The flow enters at the bottom and exits from the top surface. All solid walls of the octagon are considered to be adiabatic. Graphical representation of streamlines, isotherms, average Nusselt number and maximum temperature of fluid for different combinations of Hartmann number (Ha), Joule heating parameter (J) and Richardson number (Ri) are displayed. The results indicate that the flow and thermal fields in the vertical channel depend markedly on the above mentioned parameters. In addition rate of heat transfer is obtained optimum in the absence of both MHD and Joule heating effects.