Mathematical modeling and numerical computations of unsteady generalized Newtonian fluid flow with convective heat transfer

Abstract

In this article, the boundary layer flow and heat analysis are addressed for the unsteady 3D flow of Sisko fluid over a bidirectional time-dependent stretching sheet. The governing nonlinear partial differential equations involving momentum and temperature are transformed to nonlinear ordinary differential equations while using the suitable transformations. The modeled equations are then solved numerically using the shooting technique with RK-45 Fehlberg method. Additionally, to validate the accuracy of the present results, we have provided a comparison between two different techniques, namely shooting technique and bvp4c Matlab package and also presented a comparative study with previous published work and perceived an excellent agreement. Significant behaviors are observed while portraying the velocity and temperature profiles. The results are illustrated for both cases and it is perceived from the graphs that the velocity and temperature profiles raise with the augmentation of unsteady parameter for the shear thinning fluid while the reverse trend is observed for the shear thickening fluid. It is noticed from the graphs that the temperature profile decreases for both cases including pseudoplastic $$(0<n<1)$$ and dilatant $$(n>1)$$ , while the rate of heat transfer raises for both cases.