Spectral Relaxation Method for Solving Boundary Layer Equations

Abstract

The heat transfer characteristics of the working fluid in several devices play important role in the overall efficiency of the system. Some fluids with poor heat transfer characteristics affects the performance of these devices. The performance of these devices may be drastically improved by using nanofluid in place of the traditional working fluids. Due to this reason, now a days, the nanofluids are being used in several industrial and domestic appliances such as chillers and refrigerator, cooling electronics devices etc. The aim of the present thesis is to investigate the flow of a nanofluid over a stretching sheet under the influence of a transverse magnetic field using spectral relaxation method. The governing equations modelling such flows are highly non-linear partial differential equations which were reduced to non-linear ordinary differential equations using suitable transformations and then the approximate solution was obtained by spectral relaxation method. Chapter 1 is introductory. In this chapter a brief account of the nanofluid and its applications, magnetohydrodynamic flows and its applications, heat transfer, boundary layer, governing equations, boundary conditions, the non-dimensional parameters and the spectral relaxation method is presented . In chapter 2, the fluid flow problem arising during the flow of a viscous incompressible and electrically conducting fluid over a stretching sheet under the influence of an external magnetic field, internal heat generation, and homogeneous-heterogeneous reactions is revisited using the spectral relaxation method. The same problem was earlier solved by using bvp4c routine of MATLAB. The present results were compared with existing results and were found to be an excellent agreement. Chapter 3 presents a review of the flow of a viscous incompressible and electrically conducting nanofluid over a stretching sheet under the influence of a transverse magnetic field, non linear thermal convection, viscous and Joule heating, and homogeneousheterogeneous reactions. The problem which was earlier solved by using successive linearisation method, is now dealt with the spectral relaxation method.