Analytical Resolution of Magnetic Field Effects on Flow Reversal in Channel Mixed Convection

Abstract This study presents an analytical investigation of magnetohydrodynamic (MHD) mixed convection in inclined channels, addressing fundamental gaps in predicting flow reversal phenomena. Novel exact closed-form solutions are developed for the strongly coupled nonlinear equations governing this complex flow, overcoming mathematical challenges from magnetic field effects. The model establishes a comprehensive framework for four distinct flow regimes: stable unidirectional flow (Region I), localized top-wall reversal (Region II), bottom-wall reversal (Region III), and dual-wall reversal (Region IV). The analysis systematically reveals how critical governing parameters, particularly the magnetic interaction parameter (M), combined with buoyancy intensity, flow inertia, and channel inclination, dynamically reconfigure reversal boundaries and alter flow transition thresholds. Beyond quantitative changes, the analysis demonstrates how variations in these parameters fundamentally transform the topology of reversal domains, with magnetic effects exerting primary control over regime transitions. The results provide new insight into reversal mechanisms, showing how Lorentz forces modify velocity profiles, suppress secondary flows, and reshape thermal distributions. This work introduces a complete analytical mapping of flow reversal behavior in magnetized inclined channels, offering valuable understanding for thermal management system design.