1251 words - 5 pages

Boundary layers are thin regions next to the wall in the flow where viscous forces are important and affect the engineering process of producing materials. For example viscous forces play essential rules in glass fiber drawing, crystal growing, plastic extrusion, etc.[1] The final product quality depends on the rate of cooling in the process so the thickness of the thermal boundary layer have to be estimated. Blasius [2] studied the simplest boundary layer over a flat plate. He employed a similarity transformation that reduces the partial differential boundary layer equations to a nonlinear third-order ordinary differential equation before solving it analytically. The dynamics of the boundary layer flow over a stretching surface originated from the pioneering work of Crane [3]. Later on, various aspects of the problem have been investigated by Dutta et al. [4], Chen and Char [5], etc. Vajravelu [6] studied flow and heat transfer in a viscous fluid over a nonlinear stretching sheet with neglecting the viscous dissipation, then Cortell [7] presented his study about the flow and heat transfer on a nonlinear stretching sheet for two different types of thermal boundary conditions on the sheet, constant surface temperature and prescribed surface temperature. Nadeem et al. [8] studied the effects of heat transfer on the stagnation flow of a third-order fluid over a shrinking sheet. Recently, Prasad et al. [9] studied the mixed convection heat transfer over a non-linear stretching surface with variable fluid properties.

Due to recent studies, scientists realized that devices have to be cooled in a more effective way and the conventional fluids such as water are not appropriate anymore, so the idea of adding nanometer-sized particles to a fluid was presented. These tiny particles have high thermal conductivity, so the mixed fluids have better thermal properties [10-12]. The material of these nano scale particles is aluminum oxide (Al2O3), copper (Cu), copper oxide (CuO), gold (Au), silver (Ag), etc, which are suspending in base fluids such as water, oil, acetone and ethylene glycol, etc. Al2O3 and CuO are the most well-known nanoparticles used by many researchers in their works [13-17]. They claimed different results due to the size and shape and so the contact surface of the particles. In addition the base fluid characteristics were important as well. The main obstacle in this field was how to keep the particles suspended in static fluid which is discussed in [18]. Fortunately, the results were in a same trace that the thermal conductivity of the nanofluids is higher than the conventional fluids and this term is modeled mathematically in [19-24]. Lately Bachok et al. [25] mixed up the two mentioned concepts and presented his study about boundary layers flow [26] for nanofluids.

To the authors’ knowledge no analytical studies have thus far been communicated with regard to boundary layer flow and heat transfer of a nanofluid past a non-linearly...

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