Adaptive Shooting Analysis of Magnetized Micropolar Flow in Transpiration-Controlled Riga Channels with Radiative and Cross-Diffusion Effects

Abstract

Electromagnetically controlled transport in microstructured fluids is of considerable interest in advanced thermofluidic and microfluidic technologies, particularly when heat and mass transfer are strongly coupled. This study investigates steady micropolar fluid flow and coupled thermo-solutal transport in a transpiration-controlled channel driven by an upper Riga plate. The mathematical model accounts for non-uniform Riga-induced Lorentz forcing, thermal radiation, Joule dissipation, and Soret–Dufour cross-diffusion effects, leading to a highly nonlinear system of coupled boundary-value equations. The novelty of the work lies in examining the combined influence of these mechanisms within a confined micropolar channel configuration, which has received limited attention in the existing literature. The governing equations are transformed into a dimensionless form and solved using a fourth-order Hybrid Block Runge–Kutta shooting scheme with analytical initialization. The results demonstrate that micropolar material parameters suppress the velocity, microrotation, and concentration fields while enhancing the temperature distribution. Stronger electromagnetic forcing generated by the Riga plate and larger modified Hartmann effects significantly attenuate the flow and microrotation characteristics. Moreover, Dufour and Soret cross-diffusion mechanisms substantially modify thermal and concentration transport, whereas increasing thermal and mass Peclet numbers enhance local heat and mass transfer rates. These findings provide new insight into the control of coupled momentum, thermal, and species transport in electromagnetically actuated micropolar channel flows and offer useful guidance for the design of advanced thermal-management and microfluidic systems.