Modeling of micropolar nanofluid flow over flat surface with slip velocity and heat transfer: Exact multiple solutions
Waqar Khan Usafzai, Emad H. Aly, Marwa M. Tharwat, Amr M. Mahros
Abstract
This study presents new exact solutions for the flow of a non–Newtonian micropolar fluid in a water–based nanofluid, which is initiated by a bidirectional moving permeable surface. The surface is either stretching or shrinking linearly along its length, and experiences velocity slip under constant wall temperature or linearly growing wall temperature. By using a similarity reduction of the micropolar nanofluid equations, a coupled system of ordinary differential equations is obtained, which is governed by various parameters such as the moving parameter, mass transpirations, velocity slip, material parameter, and nanofluid concentration parameter. Explicit exact solutions are derived for both the general flow and the gyration velocity fields. The effects of these parameters on the fluid flow and temperature distributions are demonstrated through graphical analysis. The study finds that single solution exist for the stretching sheet case, and dual solutions appear in the region s⩾sc, where sc=1.4943 for the shrinking sheet. One of the two components of the dual solutions exhibits algebraic decay for large war flux values. It is also found that when either a=0, or velocity slip is very large, their thermal solutions coincide and are entirely dependent on mass transpiration.