Boundary layer flow of nanofluid over an exponentially stretching surface
© Nadeem and Lee; licensee Springer. 2012
Received: 26 July 2011
Accepted: 30 January 2012
Published: 30 January 2012
The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter α, Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt.
Keywordsnanofluid porous stretching surface boundary layer flow series solutions exponential stretching
During the last many years, the study of boundary layer flow and heat transfer over a stretching surface has achieved a lot of success because of its large number of applications in industry and technology. Few of these applications are materials manufactured by polymer extrusion, drawing of copper wires, continuous stretching of plastic films, artificial fibers, hot rolling, wire drawing, glass fiber, metal extrusion and metal spinning etc. After the pioneering work by Sakiadis , a large amount of literature is available on boundary layer flow of Newtonian and non-Newtonian fluids over linear and nonlinear stretching surfaces [2–10]. However, only a limited attention has been paid to the study of exponential stretching surface. Mention may be made to the works of Magyari and Keller , Sanjayanand and Khan , Khan and Sanjayanand , Bidin and Nazar  and Nadeem et al. [15, 16].
More recently, the study of convective heat transfer in nanofluids has achieved great success in various industrial processes. A large number of experimental and theoretical studies have been carried out by numerous researchers on thermal conductivity of nanofluids [17–22]. The theory of nanofluids has presented several fundamental properties with the large enhancement in thermal conductivity as compared to the base fluid .
In this study, we have discussed the boundary layer flow of nanofluid over an exponentially stretching surface with suction and injection. To the best of our knowledge, the nanofluid over an exponentially stretching surface has not been discussed so far. However, the present paper is only a theoretical idea, which is not checked experimentally. The governing highly nonlinear partial differential equation of motion, energy and nanoparticle volume fraction has been simplified by using suitable similarity transformations and then solved analytically with the help of HAM [24–39]. The convergence of HAM solution has been discussed by plotting h-curve. The effects of pertinent parameters of nanofluid have been discussed through graphs.
2 Formulation of the problem
where (u, v) are the velocity components in (x, y) directions, ρ f is the fluid density of base fluid, ν is the kinematic viscosity, T is the temperature, C is the nanoparticle volume fraction, (ρc) p is the effective heat capacity of nanoparticles, (ρc) f is the heat capacity of the fluid, α = k/(ρc) f is the thermal diffusivity of the fluid, D B is the Brownian diffusion coefficient and D T is the thermophoretic diffusion coefficient.
in which U0 is the reference velocity, β(x) is the suction and injection velocity when β(x) > 0 and β(x) < 0, respectively, T w and T∞ are the temperatures of the sheet and the ambient fluid, C w , C∞ are the nanoparticles volume fraction of the plate and the fluid, respectively.
where Re x = U w x/ν is the local Renolds number.
3 Solution by homotopy analysis method
in which , , , are the constants and the numerical data of above solutions are shown through graphs in the following section.
4 Results and discussion
This research was supported by WCU (World Class University) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology R31-2008-000-10049-0.
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