Exact solutions of unsteady free convection flow past an oscillating plate with newtonian heating

Abstract

The motion of a viscous fluid caused by the oscillations of a vertical plate is important in many applied problems such as acoustic streaming around an oscillating body and an unsteady boundary layer with fluctuations. In boundary layer, free convection flow is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). This configuration occurs in convection flows set up when the bounding surfaces absorb heat by solar radiation. In this thesis, the unsteady free convection flow of an incompressible viscous fluid past an oscillating vertical plate with Newtonian heating is studied. The free convection flow with either heat or heat and mass transfer with radiation effect is considered. The problem of magnetohydrodynamic free convection flow in a porous medium is also studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutions for velocity, temperature and concentration are obtained using the Laplace transform technique. The corresponding expressions for skin friction, Nusselt number and Sherwood number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter, radiation parameter, Grashof number and phase angle. The results obtained show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction. However, the Nusselt number is decreased when the radiation parameter is increased. Also, the skin friction is decreased when the radiation parameter, phase angle and Grashof number are increased.