Conjugate transfer of heat and mass in unsteady flow of a micropolar fluid with wall couple stress

Abstract

This is an attempt to investigate the unsteady flow of a micropolar fluid with free convection caused due to temperature and concentration differences. Micropolar fluid is taken over a vertical plate oscillating in its own plane. Wall couple stress is engaged at the bounding plate together with isothermal temperature and constant mass diffusion. Problem is modelled in terms of coupled partial differential equations together with some physical conditions and then written in non-dimensional form. Exact solutions are determined using the Laplace transform method. For convenience, they are expressed in simplified form using exponential functions and complementary error functions. Using computational software MATHCAD, analytical results of velocity, temperature, microrotation and concentration are plotted in graphs and discussed for various embedded parameters. Results of skin friction, wall couple stress, rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) are also evaluated. Present results of micropolar fluid are graphically compared with published results of Newtonian fluid. It is found that micropolar fluid velocity is smaller than Newtonian fluid.