Mixed convection three-dimensional Hiemenz stagnation point flow

This study delves into the intricate analysis of the steady mixed convection three-dimensional Hiemenz stagnation-point flows over a vertical flat wall immersed in viscous and incompressible fluid. The analysis considers the derivation of a similarity solution, incorporating $\gamma$, indicative of the shear to strain rate ratio, and $\lambda$ representing a mixed convection parameter. Numerical solutions are derived meticulously for typical values of $\delta$ (which is function of $\gamma$) and $\lambda$ with particular towards discerning critical values ${\lambda }_c$ especially concerning opposing flow. Asymptotic results are obtained for large values of $\lambda$ and $\delta$. It is observed that dual solutions are present for opposing flows. It is noticed that the critical values ${\lambda }_c$ of $\lambda$ are found in opposing flow, which produce two solution branches by making saddle node bifurcation at ${\lambda }_c$. A stability analysis of the steady flow solutions was carried out for different values of mixed convection parameter $\lambda$ and it reveals that, the lower solution branches are unstable while the upper solution branches are stable.