Hiemenz flow with heat transfer in a slip condition micropolar fluid model: Exact solutions

The impingement of Hiemenz stagnation-point flow and a flexible surface which has linear stretching/shrinking is studied. The flow is governed by the wall's velocity, gyration velocity, transpiration and velocity slip pa-rameters. The stretching sheet problem offers single solution, whereas for the shrinking sheet dual solutions are obtained in the region s* < s < infinity , and lambda < lambda*. The stretching/shrinking strength parameter (c) under different values produces numerous exact solutions. The existence of critical numbers explains the increasing or decreasing nature of solutions. Dual solutions are found for skin friction, couple stress friction and temperature gradient. In the process of boundary layer, increasing suction or injection decreases velocity. The effect of ve-locity slip indicates a decrease in linear wall velocity. It was found that the number and formation of solutions are dependent on a parameter measuring correlation of the external flow strength to the surface stretching/shrinking parameter which is a key player in determining exact solutions. Exact solutions for the uniform surface tem-perature and linearly growing wall temperature are derived for different special cases.

Automated summary

This study investigates the interaction of Hiemenz stagnation-point flow with a flexible surface that exhibits linear stretching/shrinking. The flow is controlled by parameters such as wall velocity, gyration velocity, transpiration, and velocity slip. Different values of the stretching/shrinking strength parameter (c) yield multiple exact solutions. Dual solutions are found for skin friction, couple stress friction, and temperature gradient. The number and formation of solutions are dependent on a parameter measuring the correlation between the external flow strength and the surface stretching/shrinking parameter. Exact solutions are derived for different special cases involving uniform surface temperature and linearly growing wall temperature.