Convective Heat Transfer in Boundary Layer Flows of Sisko Fluid

Abstract

The main theme of this thesis is to make a solid contribution for a meaningful research study of the boundary layer flows of a non-Newtonian fluid. The research focuses on the flow and convective heat transfer of the Sisko fluid, which is a subclass of a generalized Newtonian fluid. One of the main aims of this work is the mathematical modeling of the governing boundary layer equations for the steady three-dimensional flow over a flat surface and infinite rotating disk. To gain a better insight about the behavior of these flows, numerical and/or analytical solutions are needed. We also focus on the development of solutions for different circumstances. Each problem after being successfully modeled, and with comprehensive results obtained, are meaningfully interpreted.

The problems concerns convective heat transfer which include two-dimensional flow in the planer and axisymmetric over non-linear stretching sheets, flow past a wedge geometry, flow near a stagnation point with nonlinear stretching sheet and with nonlinear radiation effects, three dimensional flow due to a bidirectional stretching surface and flow due to an infinite rotating disk. The transformed boundary layer equations are solved numerically by the implicit finite difference method with Keller box. Further, simple shooting and multiple shooting techniques using adaptive Runge Kutta method with Broyden's/Newton’s method in the flow domain are also utilized. In addition, exact solutions of the resulting nonlinear differential equations are also provided in some special cases. In some cases, the obtained numerical results are compared with the analytic solutions obtained by using the homotopy analytic method (HAM) to check the veracity of our results. The presented numerical results are also validated by comparing xiii

them with previously published pertinent literature. The excellent correspondence inspires the confidence in the veracity of our numerical results.

The numerical data for the velocity and temperature fields is graphically presented and the effects of the relevant non-dimensional parameters such as the power-law index, stretching parameter, wall temperature parameter, material parameter of Sisko fluid, Prandtl number, Eckert number, wedge angle parameter, buoyancy parameter, velocity ratio parameter, temperature ratio parameter, radiation parameter, skin friction coefficient and local Nusselt number have been observed by encompassing a broader range. A profound observation is that the temperature profile and the corresponding thermal boundary layer thickness reduce with increasing values of the material parameter of the Sisko fluid. However, it is noted that the material parameter affects the temperature field marginally. In addition, effects of the material parameter on temperature field are more prominent for lower Prandtl number.