Abstract
In this study, the steady stagnation point flow and heat transfer of three different types of nanofluid over a linearly shrinking/stretching sheet is investigated numerically. A similarity transformation is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The effects of the governing parameters on the nanofluid flow and heat transfer characteristics are analyzed and discussed. Numerical results for the local Nusselt number, skin friction coefficient, velocity profiles and temperature profiles are presented for different values of the solid volume fraction (&phi) and for three different types of nanoparticles (Cu, Al<sub>2</sub>O<sub>3</sub> and TiO<sub>2</sub>) in stretching or shrinking cases. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for Cu-water nanofluid compared to the Al<sub>2</sub>O<sub>3</sub>-water and TiO<sub>2</sub>-water nanofluids. Furthermore, it was seen that the effect of the solid volume fraction of nanoparticles on the heat transfer and fluid flow characteristics is more important compared to the type of the nanoparticles.
Highlights
The viscous flow and heat transfer in the boundary layer region due to a stretching sheet has several theoretical and technical applications in industries such as the aerodynamics, food processing, extrusion and glass fiber production. Crane (1970) was the first to consider the steady boundary layer flow of a viscous fluid which is incompressible due to a linearly stretching plate
We have studied how the nanoparticle volume fraction parameter φ, influence the boundary layer flow and heat transfer characteristics in a nanofluid toward the shrinking/stretching sheet using three different types of nanoparticles: copper Cu, alumina Al2O3 and titania TiO2
It is found that the heat transfer rates and skin friction coefficient increase as the nanoparticle volume fraction φ increases
Summary
The viscous flow and heat transfer in the boundary layer region due to a stretching sheet has several theoretical and technical applications in industries such as the aerodynamics, food processing, extrusion and glass fiber production. Crane (1970) was the first to consider the steady boundary layer flow of a viscous fluid which is incompressible due to a linearly stretching plate. Crane (1970) was the first to consider the steady boundary layer flow of a viscous fluid which is incompressible due to a linearly stretching plate. Chiam (1994) extended the works of Hiemenz (1911) and Crane (1970) by study the stagnation-point flow over a stretching sheet. The viscous flow and heat transfer in the boundary layer region due to a shrinking sheet attracted the attention of researchers for its interesting physical character, for example, on a rising, shrinking balloon. The boundary layer flow caused by a shrinking sheet is quite different from the stretching case. The unsteady case of recent problem is investigated by Fan et al (2010) with assumptions that the sheet is shrunk impulsively from rest and simultaneously the surface temperature is suddenly increased from that of surrounding fluid
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