Ferro-Fluid Flow and Heat Transfer over Unsteady Stretching Sheet in the Presence of a Nonuniform Magnetic Field

Ferrofluids have extensive applications in various fields such as electronic packaging, mechanical and thermal engineering, aerospace, and biotechnology due to their unique properties. This study investigates the magneto-thermomechanical interaction between a viscous, incompressible ferrofluid and a heated, stretching sheet in the presence of a nonuniform magnetic field. The focus is on the laminar flow and heat transfer within the boundary layer of a magnetohydrodynamic (MHD) fluid resulting from an unsteady stretching sheet with extended heat flux. The governing partial differential equations are transformed into a system of coupled, nonlinear ordinary differential equations using dimensionless transformations. The Homotopy Perturbation Method (HPM) is employed to solve this system. The study examines the effects of magneto-thermomechanical interactions on the velocity and temperature boundary layer profiles, as well as their impact on heat transfer and wall skin friction. The results show that an increase in the ferrohydrodynamic interaction parameter (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}) leads to higher velocity and temperature magnitudes, while a decrease in the magnetization parameter (M) results in increased velocity within the thermal boundary layer. Additionally, the magnetic doublet parameter significantly affects the velocity profile, and an increase in the thermal radiation parameter (R) slightly decreases the temperature. These findings are validated through comparison with previously published works, demonstrating a high level of agreement. The study contributes to the understanding of the complex interplay between magnetic fields, temperature, and fluid mechanics in ferrofluids and establishes the effectiveness of the Homotopy Perturbation Method (HPM) for analyzing nonlinear magnetohydrodynamic ferrofluid flows.