Convective behaviour of a uniformly Joule-heated liquid pool in a rectangular cavity

A two-dimensional mathematical model has been developed to study the interaction between gravitational body force and self-induced electromagnetic body force in a Joule-heated liquid pool in a rectangular cavity, with an aspect ratio of 2. The Joule heating of the liquid pool in the cavity is accomplished by passing a large alternating current employing a pair of plate electrodes immersed in the liquid. The electrode surfaces are assumed to be isopotential and rest of the boundaries is treated as electrically insulated. The upper boundary of the liquid pool is an isothermal boundary while the rest of the boundaries are assumed to be thermally insulated. The present study investigates the convective behaviour of different liquids under Joule heating. Numerical simulations have been carried out employing Boussinesq fluids for Rayleigh numbers up to 2.5×105 and Hartmann numbers up to 4×107. This study shows that the heat transfer in the uniformly Joule-heated liquid is governed by the gravitational body force when Ha2Pr/Ra<120 and by the self-induced electromagnetic body force when Ha2Pr/Ra>100. It also indicates that the thermal field is strongly dependent on Pr in electromagnetically driven flows while Pr has negligible effect on temperature field in thermally driven flows for 103⩾Pr⩾10. Heat transfer correlations for thermally driven flows, electromagnetically driven flows and combined flows are also presented.