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

Abstract

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 parameters. The stretching sheet problem offers single solution, whereas for the shrinking sheet dual solutions are obtained in the region s∗ ≤ s < ∞ , and λ ≤ λ∗. 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 velocity 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 temperature and linearly growing wall temperature are derived for different special cases.