Unsteady Mixed Convection Three‐Dimensional Hiemenz Stagnation Point Flow

ABSTRACT

This research explores the detailed examination of unsteady mixed convection 3D Hiemenz stagnation‐point flows over a vertical flat wall immersed in viscous, incompressible fluid. Through the application of similarity solutions, the governing nonlinear coupled partial differential equations are converted into nonlinear coupled ordinary differential equations. The analysis involves the derivation of the similarity solution, incorporating , , and , which represent shear to strain rate ratio, mixed convection parameter, and the unsteady parameter, respectively. These equations are subsequently solved using Runge–Kutta method with the shooting technique. Numerical solutions are obtained for typical values of , , and (which is a function of ) with particular focus on identifying the critical values and , especially in relation to opposing flow. Asymptotic results are derived for large values of , , and . Dual solutions are found to exist for opposing flows, and the critical values of and of are observed in opposing flows, leading, which to two solution branches through saddle node bifurcation at and . A stability analysis of the unsteady flow solutions was performed for various values of mixed convection parameter and unsteadiness parameter , revealing that the lower solution branches are unstable, while the upper solution branches are stable.