The aim of this study is to analyze the heat transfer rate under inclined buoyancy force for nano and dusty fluids by incorporating key parameters such as the Prandtl number, volume fraction, fluid interaction parameter for temperature, and fluid-particle interaction parameter for velocity in the presence of magnetohydrodynamics (MHD) effects. The investigation focuses on understanding how these parameters influence velocity and heat transfer behavior in a porous medium. Nano and dusty fluids are crucial for thermal systems, environmental regulation, and materials processing. Unlike previous studies, this work examines their combined effects and employs response surface methodology (RSM) for optimization. The governing nonlinear ordinary differential equations are derived via similarity transformations and solved using bvp4c in MATLAB. RSM is employed to analyze parametric effects and determine optimal conditions for heat transfer enhancement. Higher Local Grashof number increases flow rate but decreases heat transfer rate. MHD and porosity effects significantly impact velocity and temperature. Dust-fluid interactions affect boundary layer behavior and heat transfer rates. Dusty fluid interactions influence boundary layer thickness and heat transfer. Findings are applicable in heat exchangers, electronics cooling, and industrial furnaces. The study offers a foundation for hybrid nanofluids, time-dependent flows, and fractional modeling in future research.

This study investigates three-dimensional magnetohydrodynamic convection in a cubic cavity with a symmetrical ellipsoidal obstacle in two different scenarios, under the combined effect of internal heat source and magnetic field strength. The significance of this research is based on understanding the interlinking of geometric orientation, buoyancy, and magnetic damping on the dynamics of the flow and thermal transfer phenomena. The approach taken is based on finite element simulations using COMSOL Multiphysics (version 6.3), coupled with a surrogate model of XGBoost to predict the Nusselt numbers for each of the configurations. The results show that the increase of the heat source parameter promotes the circulation driven by buoyancy and heat transport, while the increase of the Hartmann number suppresses fluid motion by the Lorentz force, leading to the reduction of heat transport. The orientation of the symmetrical ellipsoid has a major influence on the asymmetry of the flow and the properties of mixing. The extraordinary agreement between the numerical results and the predicted results is a validation of the accuracy of the proposed analytical framework. These insights have important implications for practical applications in energy systems, electronic cooling, and magnetically controlled heat processes.