Unsteady numerical simulation of flow and heat transfer in a uniformly Joule-heated rectangular pool

Based on the Joule heating nuclear waste treatment technology, a series of numerical simulation of fluid flow and heat transfer based on two-dimensional non-steady state model has been studied, the fluid is in a rectangular cavity with an aspect ratio of 2, the direct current contributes heat for heating the process medium by a pair of plate electrodes, the top wall is cooled with atmosphere and all the other walls are kept thermally insulated. For Pr = 1 fluid, the thermally driven stable convection and the electromagnetically driven stable flow can be observed respectively or both gravitationally and electromagnetically driven stable convection exhibit. The threshold Hartmann number for the first transition from an ax symmetric 2 cells steady flow to a steady non-asymmetric state 1 roll flow is 159.687, where the Nusselt number exhibits a minimum value. And the second transition from non-asymmetric state 1 roll flow to a steady asymmetric 2 rolls flow is fixed at Ha = 178.88. It is found that physically realizable periodic oscillation flow evolves for the low Pr fluid (Pr = 0.01), which can significantly affect the heat transfer. These transient characteristics of velocity and temperature fields are presented graphically.