Exact analytical solutions for micropolar magnetohydrodynamic flow: Insights into velocity slip and heat transfer characteristics

In this study, we investigate the laminar steady flow of a micropolar fluid along a permeable flexible surface subject to a uniform magnetic field acting normal to the surface, with wall transpiration and velocity slip at the surface. This analysis yields multiple exact solutions for the stretching/shrinking sheet, offering insights into the complex dynamics of the fluid-surface interaction. In addition, to enhance the realism of our model, we incorporate a power-law temperature distribution, providing a comprehensive understanding of the temperature profile in the context of the micropolar fluid flow. The multiplicity and existence of solutions in special cases are presented for both stretching and shrinking sheets. In particular, a unique solution is found for the stretching sheet in the cases of both suction and injection while dual solutions exist for the shrinking sheet over the range mu > mu( c) in suction, and no solution exist for the injection. For the skin friction, dual solutions appear in the region 0 <= alpha <= alpha (c), but single solution exists for a < 0. Furthermore, dual solutions are found for the heat transfer gradient in the regions - infinity <= alpha <= alpha (c) and mu( c) <= mu <= infinity . Moreover, this research contributes to the broader comprehension of fluid dynamics on flexible surfaces and their intricate thermal behaviors.