Convective heat transfer analysis for magnetohydrodynamics Reiner–Philippoff nanofluid flow over a curved stretching surface: non-similar solution

Purpose The primary purpose of this research is to investigate the flow and heat transfer characteristics of non-Newtonian nanofluids, specifically Reiner–Philippoff (R-Ph) fluids, across a radially magnetized, curved, stretched surface. By considering factors such as Brownian motion, thermophoresis and viscous dissipation, the study aims to enhance the understanding of heat transfer mechanisms in various engineering and industrial applications, thereby contributing to improved thermal management strategies. Design/methodology/approach This study employs the local non-similarity method to analyze the flow and thermal behavior of R-Ph nanofluids over a radially magnetized, curved, stretched surface. The governing system is simplified using suitable transformations, and a local non-similarity approach is applied to treat non-dimensional partial differential equations as ordinary differential equations. The resulting system is numerically solved by employing the Bvp4c algorithm via MATLAB. Various dimensionless parameters, such as thermophoresis and magnetic numbers, are systematically varied to evaluate their impact on the velocity, concentration and temperature profiles of the nanofluid. Findings The results indicate that the concentration profile of the nanofluid improves with increasing thermophoresis and magnetic numbers, while it decreases with higher Schmidt and Bingham numbers. The velocity of the nanofluid decreases with larger magnetic numbers and curvature parameters but increases with the R-Ph fluid and Bingham numbers. Additionally, the temperature profile shows a decreasing trend for higher curvature and Bingham numbers while rising with higher Brinkman and magnetic numbers. The Sherwood number increases with Schmidt number, thermophoresis and Brownian motion parameters. Originality/value This study provides a novel analysis of R-Ph nanofluids in the context of curved stretching surfaces under magnetic fields, contributing to the understanding of non-Newtonian fluid dynamics. The use of the local non-similarity method to transform and solve the governing equations offers a fresh perspective on heat transfer phenomena. The findings have significant implications for various fields, including engineering, electronics and biomedical applications, by enhancing thermal efficiency and performance in systems utilizing nanofluids.