Falkner-Skan Flow of a Maxwell Fluid with Heat Transfer and Magnetic Field

M Qasim,S Noreen

doi:10.1155/2013/692827

Abstract

This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic fi eld with heat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method (HAM). Effects of the involved parameters, namely, the Deborah number, Hartman number, and the Prandtl number, are examined carefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted.

Highlights

The Falkner-Skan problem under various aspects has attracted the attention of several researchers [1]
Such fluids cannot be studied by employing a single constitutive relationship. This is due to diverse properties of non-Newtonian fluids in nature. These non-Newtonian fluid models are discussed in view of three main categories, namely, the differential, the rate, and the integral types
The Maxwell fluid allows for the relaxation effects which cannot be predicted in differential type fluids, namely, second, third, and fourth grades

Summary

Introduction

The Falkner-Skan problem under various aspects has attracted the attention of several researchers [1]. There are several materials which do not obey the Newton’s law of viscosity, for example, biological products like blood and vaccines, foodstuffs like honey, ketchup, butter, and mayonnaise, certain paints, cosmetic products, pharmaceutical chemicals and so forth These fluids are characterized as the non-Newtonian fluids. The Falkner-Skan wedge flow of a non-Newtonian fluid was firstly investigated by Rajagopal et al [12]. To the best of our knowledge, no one investigated the Falkner-Skan flow problem for rate type fluids. In [10], Yao has examined the Falkner-Skan wedge flow He established series solution for the velocity and temperature by using homotopy analysis method [16,17,18,19,20,21,22,23,24,25]. The variations of embedded parameters have been discussed

Problem Development

Homotopy Analysis Solutions

Convergence of the Homotopy Solutions

Results and Discussion