Mathematical Study for Stagnation Point Flows of Newtonian and Non-Newtonian Fluids

Abstract

Non-Newtonian °uids feature in an extensive range of industrial and technological applica- tions including polymer processing, biotechnology, lubrication of aerospace and automotive vehicles and Nuclear thermo-hydraulics. Moreover, oblique stagnation point °ows have at- tracted some attention in recent years as they generalize the models used by engineers to include all possible angle of impingement of industrial °ows on solid surfaces. Motivated by simulating non-Newtonian multi-physical transport phenomena, the present thesis is devoted to the mathematical modeling, computation and subsequent physical analysis for non-orthogonal stagnation °ow of various type of °uid models namely Casson °uid model, Je®rey °uid model and Oldroyd-B °uid model which is a generalization of the upper con- vected Maxwell model. The governing equations for mass, linear momentum, heat (en- ergy) and concentration are modeled and then transformed by using applicable similarity conversions. The emerging strongly coupled nonlinear non-dimensional boundary value problems are solved with robust well-tested Runge-Kutta Fehlberg numerical quadrature and a shooting technique with tolerance level of 10¡5 and Keller box method, validation with Adomian decomposition method is also included. Comparison with the previous ex- isting published literature is also made and a very good agreement between the results is observed for limiting case. An extensive parametric study has been conducted to evaluate heat, momentum and concentration characteristics for the aforementioned °uid models. Mathematical modeling of these non-Newtonian models is presented with various physical e®ects such as mixed convection, thermal radiation, MHD, homogeneous-heterogeneous reactions and incorporation of nano°uids and micro-organisms. Results for physical quan- tities such as local skin friction, local Nusselt number and Sherwood number are depicted through graphs and tabular form. The obtained graphical results are discussed physically in a lucid manner. The result provides interesting insights into certain nuclear reactor x transport phenomena and furthermore a benchmark for more general CFD simulations. The present work retain signi¯cant validity in actual coating °ows and generalizes the conventional orthogonal case to the industrially relevant scenario of oblique °ow.