08-02-2013, 02:36 PM
Numerical investigation of slip flow and convective surface effects on MHD boundary layer flow of a nanofluid past a stretching sheet
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Abstract
The steady two-dimensional boundary layer flow of nanofluid past stretching surface in the presence of slip flow and convective surface is investigated numerically. The effects of Brownian motion, thermophoresis, non-uniform heat source (or sink) and magnetic field are included in the nanofluid model. A similarity transformation is used to reduce the governing equations and the boundary condition into non-linear ordinary differential equations with appropriate boundary conditions. The resulting differential equations with the appropriate boundary conditions are solved by an efficient shooting algorithm with fourth order Runge–Kutta technique. Numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction profiles as well as the local Nusselt and local Sherwood numbers are discussed for various values of physical parameters. Comparisons of the present paper with the existing results in the literature are made and a good agreement was found and this supports the validity and the accuracy of our numerical computations.
Introduction
The study of the magnetohydrodynamics (MHD) flow for electrically conducting fluid past a heated surface has attracted many researchers in view of its important applications in many engineering problems such as plasma studies, petroleum industries, magnetohydrodynamic power generators, cooling of nuclear reactors, the boundary layer control in aerodynamics, and crystal growth. Many investigators have studied the effect of the magnetic field over a stretching surface and a semi-infinite plate with or without heat and mass transfer (Chakrabarti and Gupta, 1977; Andersson, 1992; Chiam, 1993; Vajravelu and Hadjinicolaou, 1997; Pop and Na, 1998; Kumari and Nath, 1999; Takhar et al., 2003; Chamkha, 2003; Liu, 2005; Mukhopadhyay et al., 2005; Kandaswamy et al., 2005; Afify, 2009; Sankar et al., 2011; Das, 2012; Afify and Elgazery, 2012; Prasanta and Oleg, 2012). Recently, Ferdows et al. (2013) investigated the combined effects of thermal radiation and convective surface boundary condition on steady magnetohydrodynamic free convective heat and mass transfer flow past a moving permeable stretching sheet.
Conclusions
In the present paper, we have studied numerically as well as physically of steady MHD boundary-layer flow of a nanofluid past a stretching surface in the presence of non-uniform heat source (or sink) with the effects of slip flow and convective boundary conditions. The governing partial differential equations were converted into ordinary differential equations by using a suitable similarity transformation, which are solved numerically by using an efficient shooting algorithm with fourth order Runge–Kutta technique.
Mathematical formulation
Consider steady two-dimensional boundary layer flow of a nanofluid past a stretching sheet with a linear velocity variation with the distance x i.e. where a, is a constant and x is the coordinate measured along the stretching surface, as shown in Fig. 1. A steady uniform stress leading to equal and opposite forces is applied along the x-axis so that the sheet is stretched keeping the origin fixed. The flow is considered to be laminar, Newtonian, incompressible and electrically conducting fluid. The impressed electrical field is assumed to be zero and both the induced magnetic and electric fields of the flow are negligible in comparison with the applied magnetic field which corresponds to very small magnetic Reynolds number.