The effect of different types of nanoparticles on the heat transfer from a continuously moving stretching surface in a concurrent, parallel free stream has been studied. The stretching surface is assumed to have powerlaw velocity and temperature. The governing equations are converted into a dimensionless system of equations using nonsimilarity variables. Resulting equations are solved numerically for various values of flow parameters. The effect of physical quantities on the temperature profiles is discussed in detail.
The thermal management of continuously moving surfaces in a quiescent or flowing fluid plays a major role in determining the quality of final products and production rates during many manufacturing processes such as extrusion of metal or polymer sheets, wire drawing, glass fiber production, continuous casting, and paper production. Since the pioneering work of Sakiadis [
It is well known that conventional heat transfer fluids used in the abovementioned studies have low thermal properties. Rapid developments in modern manufacturing techniques allow for the production of nanosized metallic or nonmetallic particles in the range between 1 and 100 nm which are used as additives inside the base fluids such as water, oil, and ethylene glycol for improving heat transfer. This new type of liquidsolid mixture is termed nanofluid. Starting from studies of Masuda et al. [
The aim of this work is to investigate the effect of different types of nanoparticles (namely, copper (Cu) and Alumina (Al_{2}O_{3})) on the heat transfer from a continuously moving stretching surface in a concurrent, parallel free stream. The stretching surface is assumed to have powerlaw velocity and temperature. The governing equations are made dimensionless using nonsimilarity variables. Local nonsimilarity solutions are obtained for the temperature distributions. The results are given in tabular and graphical forms. The effects of the problem parameters are discussed in detail.
The geometry of the present problem and its coordinate system are shown in Figure
Flow geometry.
The continuous stretching surface is assumed to have powerlaw wall temperature. The positive
Thermophysical properties of nanoparticules and base fluid.
Substances 



Pr 

Water  0.613  997.1  4179  6.2 
Cu  401  8933  385  — 
Al_{2}O_{3}  40  3970  765  — 
In order to obtain nonsimilar solutions, one may introduce
The associated boundary conditions are
It is worth mentioning that the terms on the right hand sides of (
Substituting (
Differentiating (
The
In contrast to the local similarity method, the nonsimilar terms on the righthand side of the boundary layer equations are retained. As a consequence of this, it is expected that the results obtained from the local nonsimilarity method are more accurate than those of the local similarity method. The set of coupled equations (
The primary physical quantity of interest is the local Nusselt number which represents the surface heat transfer rate.
The local heat flux at the surface is defined as
Substituting (
The transformed local nonsimilar equations (
Numerical comparison of
Pr  Soundalgekar and Murty  Chen  Present results  








0.7  0.3508  0.8028  0.3509  0.8029  0.3508  0.8028 
2  0.6831  1.4683  0.6832  1.4683  0.6833  1.4683 
10  1.6808  3.4515  1.6802  3.4517  1.6803  3.4516 
Figure
Variation of dimensionless temperature for different values of
Figure
Variation of dimensionless temperature for different values of parameter
Figure
Variation of dimensionless temperature for different values of parameter
Figure
Variation of dimensionless temperature for different values of
Tables
WaterCu nanofluid (Pr = 6.2,











1.0000  1.0426  1.0426  1.1896  1.1896 
0.01  1.0403  1.0360  1.0778  1.1780  1.2255 
0.05  1.2128  1.0037  1.2173  1.1289  1.3691 
0.1  1.4582  0.9557  1.3936  1.0646  1.5524 
WaterAl_{2}O_{3} nanofluid (Pr = 6.2,










0.0  1.0000  1.0426  1.0426  1.1896  1.1896 
0.01  1.0386  1.0288  1.0688  1.1719  1.2171 
0.05  1.2037  0.9749  1.1735  1.1045  1.3295 
0.1  1.4371  0.9108  1.3089  1.0261  1.4746 
This paper deals with the effects of different types of nanoparticles on the heat transfer from a continuously moving stretching surface in a concurrent, parallel free stream. The governing equations are derived using the boundary layer approximation and reduced to local nonsimilar ones. Resulting equations are solved numerically. Dimensionless temperature profiles are shown graphically for various problem parameters. It is found that the heat transfer rate increases with the increase of suspended nanoparticle volume fraction. The highest heat transfer enhancement is obtained when Cu nanoparticles are used. It is also concluded that the thermal boundary layer thickness for Al_{2}O_{3}water nanofluid is higher than that of Cuwater nanofluid.