Instability of mixed convection flow in a differentially heated channel under a transverse magnetic field with internal heating

Abstract

This paper reports the linear stability of laminar magnetohydrodynamic (MHD) mixed convection flow in a differentially heated channel under a transverse magnetic field with the internal heating. Three different electrically conducting fluids, such as liquid mercury, water-based electrolytes, and Flibe (a molten salt mixture of lithium fluoride and beryllium fluoride), are considered to examine the present study. A spectral collocation method is used to solve the governing equations. The impact of the magnetic field and strength of the internal heating on the instability mechanism is examined. The results show that the MHD fully developed flow stabilizes on increasing the strength of the magnetic field, whereas it destabilizes on increasing the strength of the heat source parameter. The stability of flow also decreases by increasing the Reynolds number. The flow of liquid mercury is more stable in comparison with water-based electrolytes and the Flibe case. The kinetic energy balance shows that the high strength of the magnetic field leads to a significant reduction of the energy amplification of the disturbances. In contrast, the strength of the internal heating acts in a reverse way. Three different types: shear, thermal-shear, and thermal-buoyant, instabilities are observed as a function of Hartmann number for liquid mercury. The type of instability for water-based electrolytes and Flibe is only thermal buoyant. The disturbance flow moves toward the cold wall of the channel on increasing the strength of the magnetic field for all considered fluids, whereas it shifts to the entire channel on increasing the strength of the heat source parameter.