Stability Analysis of Unsteady Oriented Magneto‐Convective Porous Medium: Exploring Boundary‐Layer Flow Dynamics Through Regression Modeling

ABSTRACT Exploring flow stability in porous media, the consequence of magnetic fields on heat transfer (HT), the influence of inclination on flow, and optimizing industrial cooling systems are crucial. This study explores the stability of magneto‐convective flow in unsteady porous media, focusing on orientation effects and the impact of boundary layer (BL) conditions on flow behavior and heat transmission while developing regression models to predict these dynamics. We explore nonlinear, time‐varying partial differential equations (PDEs) that govern mass conservation, momentum, energy, and concentration, making relevant adjustments as required. A comprehensive numerical framework is developed to address these governing equations, employing a finite difference method (FDM) for spatial discretization and an implicit approach for time integration. Through stability analysis, we assess the flow behavior under diverse conditions, elucidating the critical parameters influencing flow stability and transitions. Furthermore, an extensive investigation is undertaken to establish a suitable steady‐state condition and to ensure uniform meshing throughout the process. Regression analysis is applied to elucidate the relationships between the key factors. This study examines the consequence of several physical factors on the distribution of velocity, temperature, and concentration within the system. The findings indicate that increasing the mass Grashof number significantly enhances buoyancy‐driven convection, while an inclined magnetic field profoundly modifies the flow dynamics and thermal profiles. The newly developed two linear regression models of multiple variables have 95.25% and 98.49% correlation coefficients for mean Nusselt number and shear stress, respectively. The study's originality lies in its detailed examination of how these parameters interact to impact inclined magnetic field convection flows. This comprehensive understanding may facilitate more accurate predictive models and enhancements in engineering design. It is significant for several industries, including petroleum and agricultural engineering, gas turbines, nuclear power facilities, heat exchangers, cooling systems, and chemical processing.