Study of heat transfer in steady flows of Carreau fluids near a stretching cylinder using numerical solutions

Abstract

This thesis describes boundary layer formations near a stretching cylinder placed in a shearthinning fluid. An important Carreau fluid model is adopted to account for shear-thinning effects in the flow field. The thesis aims at discovering the significance of shear-thinning characteristic in the flow and thermal fields. Firstly, heat flow near an axially stretching cylinder immersed in Carreau fluid is formulated. Previous studies concerning Carreau fluid flow driven by a stretching cylinder are discussed with a view to point out some crucial errors concerning mathematical modeling. For computational results, a widely employed MATLAB package bvp4c is utilized, which is based on a collocation scheme. New numerical results of the resulting six parameter problem are worked out, which are utilized to assess the contribution of surface curvature on the flow fields in the presence of shear-thinning effect. In addition, plots of wall shear rates are elucidated for varying choices of parameters. Secondly, Mathematical modeling of flow around a stagnation-point on a vertical stretching cylinder is placed in a shear-thinning fluid is investigated. Buoyant force term arising due to the vertical boundary is formulated under the well-known Oberbeck-Boussinesq approximation. Numerical results are acquired using shooting technique via 5th order Runge-Kutta integration approach and additionally MATLAB built-in function bvp4c is applied to attest the solutions. Graphical illustrations are included to predict the contribution of buoyant force term on the underlying flow characteristics in the existence of non-Newtonian effect.