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The current numerical study comprises the MHD lid-driven flow of bi-viscosity fluid inside the I-shaped cavity with variable heated short side walls, uniformly heated bottom and the rest of the walls are supposed to be adiabatic. Physical problems are formulated mathematically by exhausting the Navier-stokes and energy balance equation with the help of bi-viscosity model. In governing equations, pressure terms are eliminated by using the Penalty method, and then Galerkin weighted-residual procedure with finite element technique is used to solve them. The obtained results establish that the fluid flow velocity and heat transfer rate have been increased by increasing the bi-viscosity parameter (β) and Reynolds number (Re), respectively. The intensity of streamlines and circulation cells increases with an increasing Grashof number, due to enhanced convective flow. Furthermore, the magnitude of Nusselt number along the bottom lid (Nub) decreases by 25.92% with an increase in the value of Ha from 0 to 60. The applications of the under-considered problem can be found in numerous heat transfer phenomena, such as in heat exchangers, solar collectors, polymer suspensions, cooling processes of devices, production of food, manufacturing float glass, chemical catalytic reactors, and high-performance boilers.
Javed et al. (Wed,) studied this question.