Analysis of nonlinear axisymmetric flow and thermal transport in cross fluids using a semi-analytical approach

This study presents a semi-analytical investigation of nonlinear axisymmetric flow and heat transfer of a Cross fluid over a radially stretching sheet, a configuration of considerable importance in thermofluid and polymer-processing applications. The governing nonlinear momentum and energy equations are formulated by incorporating viscoelastic and shear-thinning effects characteristic of Cross non-Newtonian fluids. An innovative application of the Rajendran–Joy method is developed to derive accurate approximate analytical solutions for the coupled transport equations. The effects of the power-law index, local Weissenberg number, and Prandtl number on velocity and temperature distributions are systematically analyzed. Variations in the local skin-friction coefficient and heat-transfer rate are also examined to elucidate the underlying transport mechanisms. The obtained analytical solutions are validated through numerical simulations performed in Matlab and by comparison with previously published results, demonstrating excellent agreement. The study highlights the efficiency, robustness, and predictive capability of the proposed methodology for solving highly nonlinear thermofluid transport problems.