Effects of Viscous Dissipation on the Thermal Boundary Layer of Pseudoplastic Power-Law Non-Newtonian Fluids Using Discretization Method and the Boubaker Polynomials Expansion Scheme

Karem Boubaker,Xinxin Zhang,Liancun Zheng,Ali H Bhrawy,Botong Li

doi:10.5402/2012/181286

Abstract

Heat transfer of pseudoplastic power-law non-Newtonian fluids aligned with a semi-infinite plate is studied. Unlike in most classical works, the effects of viscous dissipation which is coupled with the temperature-dependent thermal diffusivity are considered in the energy equation. The discretization method is used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. The solutions are presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of power-law index and the Zheng number on the dynamics are analyzed. The associated heat-transfer characteristics are also tabulated in some domains of the said parameters.

Highlights

Since 1960, a considerable attention has been devoted to predict the drag force behavior and energy transport characteristics of the non-Newtonian fluid flows
A variety of constitutive equations have been proposed to describe the flow and heat transfer non-Newtonian characteristics, among them the empirical Ostwaald-de Waele model, which is known as the so-called power-law model, gained much acceptance
Gorla et al and Ece and Buyuk [18, 19] performed a boundary-layer analysis for the free convection flow over a vertical flat plate embedded in a porous medium saturated by a power-law non-Newtonian fluid and gave the similarity solution to the classical boundary layer equations of the power-law wall plume problem

Summary

Introduction

Since 1960, a considerable attention has been devoted to predict the drag force behavior and energy transport characteristics of the non-Newtonian fluid flows. The effect of magnetic field is found to decrease the velocity distribution and to increase the skin-friction coefficient It seems that, in all the works cited above, the power law kinematic viscosity was applied only on the momentum equations and the thermal conductivity is still treated as constant. Pop et al [16, 17] proposed a model which states that the thermal conductivity of non-Newtonian fluids was power-law-dependent on the velocity gradient Based on this consumption, Gorla et al and Ece and Buyuk [18, 19] performed a boundary-layer analysis for the free convection flow over a vertical flat plate embedded in a porous medium saturated by a power-law non-Newtonian fluid and gave the similarity solution to the classical boundary layer equations of the power-law wall plume problem. We first formulate a thermal boundary layer equation for the power-law non-Newtonian fluids with a new variable thermal conductivity and provide similarity solutions

Formalization of the Nonlinear Boundary Value Problem

Discretization Method Solution

BPES Solution

Numerical Results

Conclusions