Stagnation Point Flow of a Nanofluid toward an Exponentially Stretching Sheet with Nonuniform Heat Generation/Absorption

A Malvandi,G Domairry,F Hedayati

doi:10.1155/2013/764827

Abstract

This paper deals with the steady two-dimensional stagnation point flow of nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via similarity variables and solved analytically via HAM. Effects of governing parameters such as heat generation/absorption λ, stretching parameter ε, thermophoresis , Lewis number Le, Brownian motion , and Prandtl number Pr on heat transfer and concentration rates are investigated. The obtained results indicate that in contrast with heat transfer rate, concentration rate is very sensitive to the abovementioned parameters. Also, in the case of heat generation , despite concentration rate, heat transfer rate decreases. Moreover, increasing in stretching parameter leads to a gentle rise in both heat transfer and concentration rates.

Highlights

Many researchers have paid much attention to viscous fluid motion near the stagnation region of a solid body, where “body” corresponds to either fixed or moving surfaces in a fluid
This paper deals with the analytical study of boundary layer stagnation point flow of nanofluid toward an exponentially stretching surface with nonuniform heat generation/absorption which is the extension of Hassani and coworkers’ study [47] and the mentioned Nadeem and Lees’ one [20]
A rise in Nt at lower values of Lewis number (Le) leads to a drop in concentration rate, while for higher

Summary

Introduction

Many researchers have paid much attention to viscous fluid motion near the stagnation region of a solid body, where “body” corresponds to either fixed or moving surfaces in a fluid. Buongiorno developed an alternative model to explain the abnormal convective heat transfer enhancement in nanofluids and eliminate the shortcomings of the homogenous and dispersion models. He considers seven slip mechanisms, including inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus, fluid drainage, and gravity, and claimed that, of these seven, only Brownian diffusion and thermophoresis are important slip mechanisms in nanofluids. This paper deals with the analytical study of boundary layer stagnation point flow of nanofluid toward an exponentially stretching surface with nonuniform heat generation/absorption which is the extension of Hassani and coworkers’ study [47] and the mentioned Nadeem and Lees’ one [20]. It is hoped that the obtained results will present useful information for applications, and serve as a complement to the previous studies

Governing Equations

Analytical Solution by Homotopy Analysis Method

Result and Discussion

Conclusion