On the Solution of the Spectral Quasi-linearization Method of Selected Problems in Fluid Mechanics

Abstract

In this thesis, we study the application of the spectral quasi-linearization method (SQLM) to different types of highly nonlinear ordinary differential equations which governed some fluid flow. Approximate numerical solutions are obtained. The residual error analysis is used to determine the speed of convergence, convergence rate and accuracy of the method. The main theme in this study is the application of recent semi-numerical method in the solution of nonlinear boundary value problems, particularly those arise in the study of fluid flow problems. First we gave a historical idea and details of the method of the solution. Second, we present a study of Oldroyd-B fluid flow over a moving surface. The highly nonlinear governing equations are solved using a novel spectral Quasi-linearization method (SQLM). This method combines a non-perturbation technique with the Chebyshev spectral collection method to produce an algorithm with accelerated and assured convergence. A parametric study addressing the effects of various flow parameters on the fluid properties, the skin friction coefficient is given. Also, an investigation of heat transfer in Oldroyd-B fluid flow over a moving surface is presented. The ordinary differential equations are solved numerically using the SQLM. Verification of the accuracy and correctness of the results is achieved by comparing our results with those in the literature review. The effects of the governing parameters on the flow characteristic are investigated. The result for the skin friction is presented in tabular form. We then, explore the use of a nonperturbation spectral quasi-linearization method to solve the coupled highly nonlinear system of differential equations due to a laminar flow with convective surface boundary conditions. The effects of Dufour, Soret and heat convective parameters are investigated. The velocity and temperature distributions as well as the skin-friction and heat transfer coefficients have been obtained and discussed for various physical parametric values