Lie symmetry approach to investigate the flow and heat transfer over a stretching sheet with slip velocity and variable heat flux

This study investigates the unsteady flow dynamics of a thin viscous fluid film over a heated variable horizontal stretching sheet, incorporating slip velocity and variable heat flux conditions. Using the Lie symmetry approach, new similarity transformations are derived by constructing a general linear combination of the admitted symmetries, leading to a reduced system of nonlinear ordinary differential equations containing arbitrary constant coefficients. It has been shown that the existence of these arbitrary coefficients enables control over the flow dynamics and heat transfer. The inclusion of slip and variable heat flux modifies the underlying Lie algebra, yielding novel solution structures compared to existing models. The reduced ordinary differential equation system is analytically treated via the homotopy perturbation method, revealing the influence of physical and control parameters on velocity and temperature fields. Shooting technique coupled with Runge–Kutta has also been implemented for a numerical validation of all the deduced analytical solutions. Graphical illustrations of these solutions reflect the modulation of flow and heat transfer characteristics enabled by the arbitrary Lie control parameters.