Boundary Layer Flow and Heat Transfer in A Special Third-Grade Fluid Over a Shrinking Sheet with Magnetic Field and Radiation

Abstract

This study investigates the boundary layer flow and heat transfer behavior of a special third-grade fluid over a shrinking sheet in the presence of a magnetic field and thermal radiation. The governing nonlinear partial differential equations are reduced to a system of coupled ordinary differential equations through Lie group analysis and appropriate similarity transformations. The resulting system is solved numerically using MATLAB’s boundary value solver to obtain similarity solutions. The results reveal the existence of dual solutions within certain ranges of the shrinking parameter. A stability analysis based on the smallest eigenvalue is carried out to determine the physically relevant solution, indicating that only the upper branch solution is stable. The effects of key physical parameters on velocity and temperature distributions, as well as on engineering quantities such as the skin-friction coefficient and Nusselt number, are examined in detail. The findings provide useful physical insight into the behavior of non-Newtonian fluids, with potential applications in polymer processing, thermal management systems, and biomedical engineering.