Asymptotic Analysis of Magnetohydrodynamic Boundary-Layer Flow for an Upper-Convected Maxwell Fluid

Abstract

The magnetohydrodynamic (MHD) boundary-layer flow of an upper-convected Maxwell (UCM) fluid is investigated using asymptotic analysis. The governing nonlinear partial differential equations are first reduced to ordinary differential equations via boundary-layer approximations and similarity transformations. An asymptotic solution satisfying the prescribed boundary conditions is then constructed using the homotopy renormalization method based on Taylor expansion. The analytical results show that the Hartmann number modifies the velocity distribution via the Lorentz force, introducing electromagnetic damping into the momentum balance and affecting the boundary-layer structure. Increasing the Deborah number enhances the elastic contribution from the upper-convected Maxwell model, influencing near-wall shear behavior and nonlinear coupling. In the asymptotic limit of vanishing Deborah number, the governing equation reduces to the classical Newtonian MHD boundary-layer formulation. To validate our analytical results, we develop a numerical scheme based on interpolation wavelet collocation to solve the original partial differential equations directly. Comparisons reveal excellent agreement between the asymptotic and numerical solutions throughout the flow domain. The parameter ranges correspond to moderate magnetic interaction and weak-to-moderate viscoelastic effects relevant to polymer extrusion, electrically conducting coating flows, and liquid-metal cooling under magnetic fields. The asymptotic expressions provide insight into the coupled effects of inertia, elasticity, and electromagnetic forces.