Numerical investigation of magnetohydrodynamic effect on fluid flow and heat transfer in cavities

Abstract

An elaborate theoretical study on Magnetohydrodynamic (MHD) effect on fluid flow and heat transfer in two-dimensional square and rectangular cavities with different configurations has been presented in this thesis. The numerical results have been provided in graphical form showing effects of various relevant non-dimensional parameters. The validity of the calculated results has been shown with the available numerical results of the similar study. A semi-empirical relation has been introduced from the correlation of the available experimental data without MHD effect. The relevant governing equations have been solved by using finite element method of Galerkin’s weighted residual approach. The investigation has been done for three types of cavity configurations. They are natural convection flow in a square enclosure with a heated circular obstacle, mixed convection flow in a lid driven cavity heated from sinusoidal shaped bottom surface and double-diffusive natural convection in an inclined cavity with a partially heated bottom surface. In each of the above cases the effect of magnetic field is considered. In this study, the effects of different non-dimensional parameters e.g. Rayleigh number, Reynolds number, Prandtl number, Soret number, Dufour number, Schmidt number, Hartmann number and Joule heating have been considered. In addition to these parameters, the effects of other parameters such as angle of orientation of magnetic field, diameter of the heated obstacle, cavity aspect ratio, wave amplitude and number of waves and inclination angle of the cavity have also been included in the study. The graphical representation in the form of streamlines, isotherms, average temperature, average velocity and average Nusselt number have been made in general. Additionally the iso-concentration, average Sherwood number and average concentration have been presented for the double-diffusive natural convection. The present study reveals that MHD effect makes significant change in the fluid flow and temperature in general. It is further observed that due to MHD effect heat transfer rate decreases remarkably in each of the three configurations. In the case of natural convection heat transfer there appears profound effect of the size of the heated obstacle. There is an appreciable effect of wavy bottom surface on the heat transfer in case of mixed convection. It is also observed that there is a considerable effect of inclination angle of the cavity on temperature, velocity and concentration in case of double diffusive heat transfer. Finally a semi-empirical relation has been developed from the correlation of the experimental results of a two dimensional square cavity for natural convection heat transfer without MHD effect. This expression provides a relationship among the average Nusselt number, Rayleigh number and Prandtl number.