BOUNDARY LAYER FLOW OF SISKO FLUID WITH CONVECTIVE BOUNDARY CONDITIONS

Abstract

The study of boundary layer flows of non-Newtonian fluids has attracted much attention in the past because of its relevance in various industrial and engineering processes. Due to complexity of such fluids, several non-Newtonian fluid models have been proposed. With the growing importance of non-Newtonian fluids in modern technology and industries, the investigations of such fluids are desirable. A number of industrially important fluids including molten plastics, pulps, polymers, polymeric melts, foods and fossil fuels, which may saturate in underground beds, display non-Newtonian behaviors. These include shear thinning, shear thickening, viscoelasticity, yield stress etc. Sisko fluid model is one of the non-Newtonian fluid models that can be utilized to predict the shear-thinning as well as shear-thickening fluids. In spite of its wide occurrence in industry, only limited studies have been reported on the flow of Sisko fluids. In this work a mathematical model is developed to investigate the flow of Sisko fluid in the presence of convective boundary conditions. The governing nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations via similarity transformations. An analytical approach namely homotopy analysis method (HAM) is used to compute analytic solutions. Unlike perturbation methods, the HAM is independent of small/large physical parameters, and thus is valid no matter whether a non-linear problem contains small/large physical parameters or not. 4 More importantly, different from all perturbation and traditional non-perturbation methods, the HAM provides us a simple way to ensure the convergence of solution series, and therefore, the HAM is valid even for strongly nonlinear problems