Analysis of dimensional and non-dimensional models for simulating magnetohydrodynamic convective flow in a lid-driven chamber

This numerical study compares the results of different dimensional and non-dimensional models of magnetohydrodynamic (MHD) convective flow with Joule heating for various working fluids in a differentially heated lid-driven square domain. The left side of the cavity is at a higher temperature than the right side, whereas the top and bottom walls are insulated. The right wall of the cavity slides downward at a constant velocity, creating a clockwise aiding convective flow, while the remaining walls remain motionless. A vertical magnetic field is imposed on the bottom side of the cavity to introduce MHD flow of the working fluid. The cavity is filled with one of six working fluids: mercury, air, water, ammonia, Freon-134a, or propane. The mathematical model of the proposed problem consists of mass continuity, momentum conservation, and thermal energy equations, which can be expressed in pressure-velocity formulation. Using dimensional analysis, a total of 49 alternative non-dimensional models have been introduced. Both dimensional and non-dimensional models with appropriate boundary conditions are solved using the Galerkin finite element method. Parametric simulation is performed for varying Grashof, Reynolds, Prandtl, and Hartmann numbers. The impact of different working fluids is extensively compared under fixed operating conditions. It is found that all dimensionless models agree with the dimensional model under similar governing and geometric conditions, in terms of the mean Nusselt number, mean fluid temperature, mean drag coefficient, performance evaluation criterion, total entropy generation, and ecological coefficient of performance. Additionally, the highest Prandtl number maximizes the ecological thermal effectiveness of the proposed system.