Effects of Rayleigh Number on MHD Heat Transfer and Fluid Flow in Two-Dimensional Open Square Cavity with Heat Generation

The present work is devoted to investigating heat transfer and fluid flow in a two dimensional square open cavity containing a heated circular cylinder at the centre. A constant heat flux is set at the left sidewall; high and low temperatures are fixed at the bottom and top walls of the cavity respectively. The right side of the cavity is open. Galerkin Weighted Residual Finite Element Analysis is used to visualize the heat transfer and fluid flow solving two-dimensional governing mass, momentum and energy equations for steady state, heat transfer and fluid flow in presence of magnetic field in side an open square cavity. A uniformly heated circular cylinder is placed at the centre of the cavity as a heat source. To find the effects of Rayleigh number (Ra) on the thermal fields and fluid flow in presence of magnetic field and a heated circular cylinder as heat source by visualization and line graphs is the objective of this study. Numerical results are presented in graphical and tabular form. The study is conducted for different values of Rayleigh number, some fixed Hartmann numbers (Ha) and heat flux (q). In the conclusion it has been observed that the temperature field and fluid flow pattern are functions of the parameters Rayleigh number and Hartmann number.