Applications of Spectral Relaxation Method on Nonlinear Ordinary Differential Equations Governing some types of fluid flow

Abstract

In this thesis we solve systems of nonlinear ordinary differential equations by applying the spectral relaxation method (SRM).The SRM is an efficient numerical method that gives accurate results. First we give a historical idea and details of the SRM method. Then we present a study of a boundary layer flow with a convective surface boundary condition. The system of equations governing the thermo-hydrodynamic boundary layer flow is solved using the spectral relaxation method. The effects of the governing fluid parameters on the velocity, temperature and concentration profiles are also studied .Dufour and Soret effects on incompressible Newtonian fluid flow over a vertical down-pointing cone, are investigated studied numerically by using the spectral relaxation method. Results presented in this study are compared with those of previously published literature for selected values of the governing physical parameters. We also analysed the residual error and we investigate the accuracy of the method, and then we compare the result against solutions obtained from published literature.