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The aim of the current study is to mainly investigate the complex interaction of Lorentz force with the micropolar fluids inside a lid-driven square cavity. We used a numerical method to solve the challenging nonlinear partial differential equations that arise from the mathematical modeling of the fluid flow in the presence of a magnetic field. This is because such complex problems do not have analytical solutions or are very hard to find. The dimensionless form of the governing partial differential equation is solved using the Stream-Vorticity formulation. Unlike most of the previous studies, a uniform magnetic field throughout the flow domain was not assumed, which is more realistic. We introduce a confined magnetic field in the shape of multiple horizontal and vertical strips. With the help of our self-developed computer codes in MATLAB language, we intend to understand the way where these parameters affect the flow and thermal properties of the nanofluids. It is found that the confined Lorentz force causes the spinning of micropolar particles, which creates the intricate structure of vortices inside the flow regime. Further, the Nusselt number (Nu) and the skin friction (CfRe) have opposite trends with the Reynolds number and the magnetic field strength. The Nu is significantly influenced by the microrotation parameter while CfRe is not. Both Nu and CfRe are slightly increased by the magnetic field. The Nusselt number is much more sensitive to the Reynolds number than the skin friction. For example, when the Reynolds number increases from 1 to 20, the Nusselt number rises from 0.94 to 7.48, while the skin friction only changes from 45.24 to 44.97. Similarly, the Nusselt number is more affected by the magnetic strip width than the skin friction. A small increase of 0.1 in the magnetic strip width leads to a nearly 5% increase in the Nusselt number, but only a 0.5% increase in the skin friction. This shows that the heat transfer is more influenced by the magnetic strip width than the fluid friction.
Ahmad et al. (Mon,) studied this question.