CB-33 Analytical solution method to study magnetoconvection of micropolar fluid

This study introduces a new analytical solution approach to investigate the effects of magnetoconvection on the flow of micropolar fluid in a channel. The mathematical model comprises four coupled second-order ordinary differential equations governing fluid velocity, microrotation, magnetic field, and temperature, with boundary conditions imposed at the channel walls under both symmetric and asymmetric temperature distributions. Employing a series solution method, we derive explicit expressions for velocity, microrotation, temperature, and the magnetic field. Our analysis highlights notable differences between micropolar and Newtonian fluid behaviors, especially as the coupling number approaches unity and the micropolar parameter decreases. Moreover, we examine the induced magnetic field, often overlooked in previous studies, and demonstrate its sensitivity to the Hartmann number M, identifying a critical threshold beyond which its magnitude declines. The study also establishes the conditions under which reverse flow occurs near the heated or cooled wall, regulated by the buoyancy parameter λ; reverse flow is absent when buoyancy effects vanish (λ=0). Importantly, the application of an external magnetic field mitigates the reverse flow, underscoring its stabilizing impact on fluid motion. These findings provide valuable insights into the interaction between magnetic fields, heat conduction, and micropolar fluid dynamics, with promising implications for engineering and industrial applications involving magnetoconvection.