Multi-parameter perturbation analysis of a second grade fluid flow past an oscillating infinite plate.

Abstract

In this dissertation we consider the two dimensional flow of an incompressible and electrically conducting second grade fluid past a vertical porous plate with constant suction. The flow is permeated by a uniform transverse magnetic field. The aim of this study is to use the multi-parameter perturbation technique to study the effects of Eckert numbers on the flow of a pulsatile second grade fluid along a vertical plate. We further aim to investigate the effects of other fluid and physical parameters such as the Prandtl numbers, Hartmann numbers, viscoelastic parameter, angular frequency and suction velocity on boundary layer velocity, temperature, skin friction and the rate of heat transfer. Similarity transformations are used to reduce the governing partial differential equations to ordinary differential equations. We used perturbation methods to solve the coupled ordinary differential equations for zero Eckert number and the multiparameter perturbation technique to solve the coupled ordinary differential equations for small viscoelastic parameters and Eckert numbers. It is found that increasing the Eckert number or the viscoelastic parameter enhances the boundary layer velocity while reducing the temperature, the rate of heat transfer and the skin-friction. The results for the boundary layer velocity and the temperature are presented graphically and discussed. The results for the rate of heat transfer in terms of the Nusselt number and the skin friction are tabulated and discussed. A good agreement is found between these results and other published research. The comparison between the results for zero Eckert numbers and small Eckert numbers is also presented graphically and discussed.