Influence of Variable Lorentz Force-Dependent Viscosity on Mixed Double Diffusion in Inclined Finned Rectangular Containers: RSM Optimization and ANN Prediction

This study examines the effect of a non-uniform magnetized field (variable Lorentz force) and mixed double diffusion within inclined rectangular containers. A wire carrying an electric current, located at a specific point near the lower edge, generates the variable Lorentz force. The dynamic viscosity of the ferrofluids (blood-Fe3O4) is supposed to change as a function of the non-uniform Lorentz force. The flow domain includes two heated fins of variable lengths, with the upper wall moving at a constant velocity. Key effects considered in this analysis include viscous dissipation and an exponential chemical reaction. The governing equations are derived based on ferrohydrodynamic (FHD) principles, transformed into dimensionless forms, and numerically solved using the control volume method (CVM) with a semi-implicit approach for pressure distributions. Additionally, advanced techniques such as response surface method (RSM) and artificial neural networks (ANN) are utilized to enhance and predict the heat transfer rate under varying control parameters. The results indicate that lower Rayleigh numbers lead to forced convection dominance, while lower Reynolds numbers result in wave-like heat transfer behavior characteristic of buoyancy-driven flow. Modifying the fin lengths was found to obstruct overall flow but enhance the temperature and concentration gradients. Furthermore, at a fixed fin length ( $$\:H=0.5$$ ), increasing the Reynolds number to 1000 enhances the heat transfer rate by up to 61%.