Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid

Nor Azizah Yacob,Kuppalapalle Vajravelu,Ioan Pop,Anuar Ishak

doi:10.1186/1556-276x-6-314

Abstract

The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.

Highlights

Blasius [1] was the first who studied the steady boundary layer flow over a fixed flat plate with uniform free stream
In contrast to the Blasius problem, Sakiadis [7] introduced the boundary layer flow induced by a moving plate in a quiescent ambient fluid
The objective of this study is to extend the study of Magyari and Weidman [41] to a stretching/shrinking surface with a convective boundary condition immersed in a nanofluid, that is, to study the steady boundary layer shear flow over a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid

Summary

Introduction

Blasius [1] was the first who studied the steady boundary layer flow over a fixed flat plate with uniform free stream. In contrast to the Blasius problem, Sakiadis [7] introduced the boundary layer flow induced by a moving plate in a quiescent ambient fluid. Tsou et al [8] studied the flow and temperature fields in the boundary layer on a continuous moving surface, both analytically and experimentally and verified the results obtained in [7]. Crane [9] extended this concept to a stretching plate in a quiescent fluid with a stretching velocity that varies with the distance from a fixed point and presented an exact analytic solution. Different from the above studies, Miklavčič and Wang [10] examined the flow due to a shrinking sheet where the velocity moves toward a fixed point. Fang [11] studied the boundary layer flow over a

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