Numerical Study of Carreau Fluid Flow with Infinite Shear Rate Viscosity

Abstract

A wider survey of the literature confesses that a significant attention has been given to the boundary layer flows and heat transfer analysis over the stretchin g sur face s. In most 01" these cases the fluids under consideration are Newtonian fluids. However, to the best of our knowledge very few studies have been reported on the boundary layer flows of non-Newtonian fluids. Particularly, boundary layer flow with heat and mass transfer of the Carreau fluid in the presence of infinite shear rate viscosity over the stretching surface is not being addressed properly. The study of boundary layer flows with heat and mass transfer over stretching surface is such a class ic problem in fluid dynamics that it has been structured to a great extent over the years. The main aim of the research presented in this thesis is to explore and analyze the boundary layer flow of Carreau viscosity model in the presence of infinite shear rate viscosity. Additionally, the heat and mass transfer characteristics are also explored. For this purpose, boundary layer equations for steady two and three dimensional flows of Carreau fluid model in the presence of infinite shear rate viscosity have been derived. In general the boundary layer equations of non-Newtonian fluid models arc highly nonlinear and compli cated. This complexity becomes more difficult when we consider the flow over complex geometries with various boundary conditions. To obtain the solutions of such problems we have employed the two different numerical schemes namely Runge-Kutta Fhelberg method along with shooing technique and Matlab built-in routine bvp4c. The obtained numerical results of velocity, temperature and concentration fields are presented graphically for various physical parameters. Generally the results disclose a minor dependence of the velocity, temperature and co ncentration distributions on the viscosity ratio parameter. It is interesting to note that the graphs of velocity and temperature disclose quite the opposite trends with uplifting viscosity ratio parameter for both shear thinning and thickening fluids. Additionally, the momentum and thermal boundary layers thickness become thick in shear thinning fluid with the increase of viscosity ratio parameter. However, quite the opposite is true for shear thickening fluid . It is further found that the temperature and concentration di sclose the same trends with enhancing viscosity ratio parameter. Furthermore, graphical and tabular results are presented to verify the numerical analysis.