Sakiadis pioneered the concept of boundary layer for continuously stretching

Sakiadis [2,3] pioneered the concept of boundary layer for continuously stretching surface. Study related to stretching sheet has concerned many articles [4–8] to investigate fluid behavior with various physical aspects. Crane [9] contributed appreciative work to extend the idea of Sakiadis. He presented the idea of both linear and exponentially stretching surface for steady boundary layer flow and found the exact similar solutions in closed analytical form. Meanwhile, many authors modify the idea of stretching sheet for different fluid models for both nonlinear and exponentially stretching sheet [10–14].
Nanofluids are homogenous mixture of BTL-105 fluid and nanoparticles. Suspended metallic or non-metallic particles change the transport properties and heat conduction characteristics of the common base fluids include water, organic liquids (e.g. ethylene, tri-ethylene–glycols, refrigerants), engine oils and lubricants, bio-fluids, polymeric solution and other common liquids. In fact, enhanced thermal conductivity is based on the nanoparticles. Nanoparticle is distributive part of any material whose diameter is about less than 100nm. The effectiveness of heat transfer enhancement has been found to be dependent on the amount of dispersed particles, material type and particle shape. A number of well-known nanoparticles are created from different materials, such as oxide ceramics (Al2O3, CuO), metal nitrides (AlN, SiN), carbide ceramics (Sic, Tic), metals (Cu, Ag, Au), carbons in various (e.g., diamond, graphite, carbon nanotubes, fluorine) and functional nanoparticles. Initially, attempt of this classical model is introduced by Maxwell [15] for statistically homogenous, isotropic composite materials with randomly dispersed spherical particles. In the development of nanofluids, Choi [16] presented the concept of nanofluids for suspension of liquids containing ultra-fine particles (diameter less than 50nm). In the past few years, many experimental investigations on the thermal conductivity of nanofluids have been studied. Yoo et al. [17] measured the thermal conductivity of nanofluids for TiO2, Al2O3 and Fe and found that large enhancement in thermal conductivity compare to the base fluids. A phenomenon of nanofluid over a stretching sheet for laminar boundary layer flow was first presented by Khan and Pop [18]. In the recent developments, vast amount of the literature concern with the nanofluid for both Newtonian and non-Newtonian models is available but we refer few recent studies [19–30]. Nadeem and Lee [31] extended the idea of nanofluid over an exponentially stretching sheet. Recently, Bachok el al. [32] presented the steady three-dimensional stagnation point flow BTL-105 in a nanofluid.
Motivation of the present study is to extend the idea of Liu et al. [33] to investigate the flow of three-dimensional exponentially stretching sheet for nanofluid. In the present study we have assumed water as a base fluid and also consider the effects of nanoparticle volume fraction taken into the account. Moreover, we have considered three different types of nanoparticles such as copper (Cu), alumina (Al2O3), and titanium dioxide (TiO2). Introducing the similar transformations, the momentum and energy equations, under boundary layer assumptions reduce the equations to the set of ordinary differential equations. Solutions of reduced coupled differential equations are solved numerically. Graphical results for emerging parameters are being described through graphs and discussion. Physical behaviors of reduced Sherwood and local Nusselt number have discussed through graphs.

Mathematical model
Consider three-dimensional (3D) steady boundary layer flow past a stretching sheet in the presence of nanoparticles, it is also considered that the sheet is stretched with the different velocities , along the Cartesian coordinate axis, x- and y-axes respectively whereas the fluid placed along the z direction is taken to be at rest. Moreover, we have considered the constant temperature at wall and the ambient temperature T∞. Under the above assumptions the governing continuity, momentum and energy equations aresubject to the boundary conditionsIn above expressions u, v and w are the velocity components along the x, y and z-axes, respectively; T is the temperature, is the nanofluid density, is the viscosity of nanofluid and is the thermal diffusivity of nanofluid defined as followswhere is the thermal conductivity of the nanofluid, is the heat capacity of nanofluid and ϕ is the solid volume fraction of nanoparticles.