Magnetohydrodynamics heat transfer rate under inclined buoyancy force for nano and dusty fluids: Response surface optimization for the thermal transport

Abstract 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.