Unsteady micropolar boundary layer flow and convective heat transfer

Abstract

Most industrial fluids such as polymers, liquid crystals and colloids contain suspensions of rigid particles that undergo rotation. However, the classical Navier- Stokes theory normally associated with Newtonian fluids is inadequate to describe such fluids as it does not take into account the effects of these microstructures. In this research, the unsteady boundary layer forced and mixed convection of micropolar fluids are considered where the unsteadiness is due to an impulsive motion of the free stream. Both small and large time solutions as well as the occurrence of flow separation, followed by flow reversal are taken into account. The two-dimensional flow along the entire surface of a cylinder and a sphere is solved numerically using the Keller’s box scheme in a three dimensional grid where the discretization is made either on a net cube, or a zig-zag grid in the case of flow reversal. The numerical results show that as the micropolar material parameter increases, the thickness of both velocity and microrotation boundary layers, as well as the peak value of the skin friction coefficient along the body surface, also increase. Meanwhile, the value of the Nusselt number, in the case of micropolar fluids, is lower near the forward stagnation point and higher near the rear stagnation point compared to Newtonian fluids. It is also found that the separation time is brought forward in both cases of weak and strong concentration of microelements in the assisting mixed convective flows. However, in the opposing case, the separation time is delayed for a flow past a cylinder, while for a flow past a sphere, only the weak concentration of microelements can give similar results.