Spectral Quasi linearistion method for solving Nonlinear odes Governing some types of fluid flow

Abstract

In this thesis we study the spectral quasi-linearisation method (SQLM) and its applications on di erent types of nonlinear systems of ordinary di erential equations. In chapter1 and chapter2 we present a literature review and details of the method of solution respectively. In chapter 3, we present a study of the convective heat transfer over inverted cone. The system of equations which governed the ow has been converted into a one equation then, we solve it using the spectral quasi-linearisation method. Also the e ects of the power-law index parameter on the velocity, temperature pro les are determined. In chapter 4, we investigate the problem of nano- uid ow over a wavy surface with non-controllable nanoparticle ux at the boundary. We solve the governing di erential equations numerically by using the SQLM. The results presented in this study were shown graphically and in tabular form. The e ects of the governing parameters namely the Local Rayleigh number, the buoyancy ratio, the Brownian motion parameter, the thermophoresis parameter and the local Lewis number are determined. The analysis of residual error and accuracy of the method are carried out.