Heat and Mass Transfer in the Boundary Layer of Unsteady Viscous Nanofluid along a Vertical Stretching Sheet

Eshetu Haile,B Shankar

doi:10.1155/2014/345153

Abstract

Heat and mass transfer in the boundary-layer flow of unsteady viscous nanofluid along a vertical stretching sheet in the presence of magnetic field, thermal radiation, heat generation, and chemical reaction are presented in this paper. The sheet is situated in the xz-plane and y is normal to the surface directing towards the positive y-axis. The sheet is continuously stretching in the positive x-axis and the external magnetic field is applied to the system parallel to the positive y-axis. With the help of similarity transformations, the partial differential equations are transformed into a couple of nonlinear ordinary differential equations. The new problem is then solved numerically by a finite-difference scheme known as the Keller-box method. Effects of the necessary parameters in the flow field are explicitly studied and briefly explained graphically and in tabular form. For the selected values of the pertinent parameters appearing in the governing equations, numerical results of velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number are obtained. The results are compared to the works of others (from previously published journals) and they are found in excellent agreement.

Highlights

The flow over a stretching surface is an important problem in many engineering processes with applications in industries such as extrusion, melt-spinning, hot rolling, wire drawing, glass-fiber production, manufacture of plastic and rubber sheets, and cooling of a large metallic plate in a bath, which may be an electrolyte
(ii) The velocity profile decreases with an increase in the buoyancy ratio number, magnetic parameter, suction parameter, and Prandtl number whereas it increases with the increment of free convection, radiation, Brownian motion, thermophoresis, and heat source parameters
(iv) Nanoparticles volume fraction is enhanced by Prandtl number, thermophoresis parameter, magnetic parameter, and buoyancy ratio number whereas Lewis number, heat source parameter, Brownian motion parameter, radiation parameter, chemical reaction parameter, suction parameter, and free convection parameter reduce the concentration profile

Summary

Introduction

The flow over a stretching surface is an important problem in many engineering processes with applications in industries such as extrusion, melt-spinning, hot rolling, wire drawing, glass-fiber production, manufacture of plastic and rubber sheets, and cooling of a large metallic plate in a bath, which may be an electrolyte. Khan et al [14] studied the unsteady free convection boundary layer flow of a nanofluid along a stretching sheet with thermal radiation and viscous dissipation effects in the presence of a magnetic field. Flow over a wedge with a porous medium in the presence of ohmic heating, and viscous dissipation were studied [25] These days, because of the numerous applications of nanofluids in science and technology, a comprehensive study on heat and mass transfer in the boundary layer of unsteady viscous nanofluid in the presence of different fluid properties is indispensable. The paper entitled “Heat and mass transfer in the boundary layer of unsteady viscous nanofluid along a vertical stretching sheet” in the presence of thermal radiation, viscous dissipation, and chemical reaction is considered. Effects of the pertinent parameters involved in the governing equations on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are briefly explained

Formulation of the Problem

Numerical Solution

Results and Discussion

Conclusion

A: Unsteady parameter B: Magnetic field strength C