Utilizing Response Surface Methodology (RSM) on Magnetohydrodynamic Ternary Nanofluid Flow Over a Radiated Nonlinearly Permeable Shrinking Sheet for Heat Transfer Optimization

Abstract A nonlinear permeable shrinking sheet refers to a boundary where the permeability changes nonlinearly, and the sheet itself is contracting or shrinking over time. Meanwhile, magnetohydrodynamics (MHD) models electrically conducting fluids as a single continuous medium. Hence, this research integrates magnetohydrodynamics (MHD) models electrically conducting fluids as a single continuous medium. The distribution of three nanoparticles—aluminum oxide (Al 2 O 3 ), titanium dioxide (TiO 2 ), and silver (Ag)—in water (H 2 O) is considered to represent the ternary nanofluid model. Two analyses are performed: (i) numerical analysis—to describe the mathematical model; and (ii) statistical analysis—to optimize the heat transfer rate using Response Surface Methodology (RSM). The numerical results are obtained through bvp4c scheme in MATLAB after applying similarity transformation to reduce the governing equations. The findings show dual solutions due to the shrinking parameter, while ternary nanoparticles enhance heat transfer more than mono- or hybrid nanofluids. The nonlinearity parameter increases temperature profiles, whereas heat generation decreases them. Further, Response Surface Methodology (RSM) is applied to optimize the highest heat transfer rate by identifying three optimal parameter values for nonlinearity, radiation, and heat generation. With a suggested desirability of 99.98%, the optimization approach suggests that minimizing nonlinearity while maximizing radiation and heat generation parameters leads to the highest heat transfer rate. Potential applications of this work can consider systems with thermal management such as high-temperature furnaces, or high-performance coatings for aerospace surfaces that exposed to radiative and electromagnetic effects.