A Spectral Relaxation Approach for Magneto Hydrodynamic Boundary Layer Flow and Heat Transfer Analysis

Abstract

The present thesis discusses the convective heat transfer analysis of viscous incompressible fluids over a stretching surface (cylindrical surface) by taking transverse magnetic field into account. The fluids under investigation are Newtonian/non-Newtonian, Casson fluid model, Tangent Hyperbolic fluid model, Powell-Eyring fluid and mixed with nanoparticles. By employing the similarity transformations, the governing equations along with the appropriate boundary conditions are altered through non-dimensional variables into a set of coupled non-linear ordinary differential equations with boundary conditions. Further, the transformed ordinary differential equations are numerically solved by using novel spectral relaxation methodand#8223; along with the successive over relaxation methodand#8223;. The proposed algorithm is convergent and efficient numerical method which can be used as an alternative to solve non-linear boundary value problems. The investigations are performed to illustrate the influence of various flow controlling parameters like ratio parameter, magnetic parameter, exponent parameter, thermal radiation parameter, Brownian motion, thermophoresis, thermal radiation parameter and Prandtl number on axial and transverse velocities, and temperature distributions of fluid flow etc. The obtained numerical results for the present study are verified with the available (numerical) solutions in literature. A good agreement exists between the results of the present work and the available results. The obtained numerical solutions are presented graphically for velocity, temperature and concentration profiles. Also, skin friction coefficients are tabulated for comparison. Finally, it has been shown that there is significant improvement in the rate of convergence in conjunction with the successive over relaxation method. The thesis has been divided into six chapters where each chapter represents a specific objective. newline