487 WA Khan 1 Pop/temational Joumal of Heat ad Tre 53(010)477-43 a2.4 /Nb=0.1,0.3,0.5 b28 Pr=10 e=10 2.6 Nb=0.1.0.4.0. 1.8 Pr=1 2.4 Le=10 0.1 0.2 0.3 0.4 0.5 0.2 0.3 0.4 tion rates a 2 b4.6 Le=5 Le=25 1.8 Pr=10 4Pr=10 .6 14 Nb=0.1.0.2.0.3 Nb=0.2.0.3.0.4 0.5 02 0.4 0. 02 0.4 0. Fig 9.Effect of Nb and Le numbers on dimensionless concentration rates. number is a decreasing function.while the reduced Sherwood is and N easing ch value s of the parameter IS EM.Spar Acknowledgments References The Pr aC子e为 200112 1988)5 9 间S然ao之oi2 eohnc,mn ae动设Sa器份 Fluid Flow26(2005)530-546. number is a decreasing function, while the reduced Sherwood number is an increasing function of each values of the parameters Pr, Le, Nb and Nt considered. In the future, the study can be ex￾tended to different types of nanofluids as Cu, Al2O3 and TiO2. Acknowledgments The authors wish to express their very sincerely thanks to the reviewers for their valuable comments and suggestions. References [1] H.S. Takhar, A.J. Chamkha, G. Nath, Unsteady three-dimensional MHD￾boundary-layer flow due to the impulsive motion of a stretching surface, Acta Mech. 146 (2001) 59–71. [2] J. Vleggaar, Laminar boundary layer behaviour on continuous accelerating surface, Chem. Eng. Sci. 32 (1977) 1517–1525. [3] L.J. Crane, Flow past a stretching plate, J. Appl. Math. Phys. (ZAMP) 21 (1970) 645–647. [4] K.N. Lakshmisha, S. Venkateswaran, G. Nath, Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface, ASME J. Heat Transfer 110 (1988) 590–595. [5] C.Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids 27 (1984) 1915–1917. [6] H.I. Andersson, B.S. Dandapat, Flow of a power-law fluid over a stretching sheet, SAACM 1 (1991) 339–347. [7] E. Magyari, B. Keller, Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls, Eur. J. Mech. B Fluids 19 (2000) 109–122. [8] E.M. Sparrow, J.P. Abraham, Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid, Int. J. Heat Mass Transfer 48 (2005) 3047–3056. [9] J.P. Abraham, E.M. Sparrow, Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface, Int. J. Heat Fluid Flow 26 (2005) 289–295. [10] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer 52 (2009) 3187– 3196. [11] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD 66, 1995, pp. 99–105. [12] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke, Anomalously thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett. 79 (2001) 2252–2254. [13] K. Khanafer, K. Vafai, M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer 46 (2003) 3639–3653. [14] H.U. Kang, S.H. Kim, J.M. Oh, Estimation of thermal conductivity of nanofluid using experimental effective particle volume, Exp. Heat Transfer 19 (2006) 181–191. [15] S.E.B. Maiga, S.J. Palm, C.T. Nguyen, G. Roy, N. Galanis, Heat transfer enhancement by using nanofluids in forced convection flow, Int. J. Heat Fluid Flow 26 (2005) 530–546. Nt Shx/Re1/2 x 0.1 0.2 0.3 0.4 0.5 3.8 4 4.2 4.4 4.6 Nb = 0.2, 0.3, 0.4 Le = 25 Pr = 10 Nt Shx/Re1/2 x 0.1 0.2 0.3 0.4 0.5 1 1.2 1.4 1.6 1.8 2 Le = 5 Pr = 10 Nb=0.1, 0.2, 0.3 a b Fig. 9. Effect of Nb and Le numbers on dimensionless concentration rates. Nt Shx/Re1/2 0.1 0.2 0.3 0.4 0.5 2.4 2.6 2.8 Pr = 10 Le = 10 Nb=0.1, 0.4, 0.5 Nt Shx/Re1/2 0.1 0.2 0.3 0.4 0.5 1.6 1.8 2 2.2 2.4 Nb=0.1, 0.3, 0.5 Pr = 1 Le = 10 a b Fig. 8. Effects of Nb and Pr number on dimensionless concentration rates. 2482 W.A. Khan, I. Pop / International Journal of Heat and Mass Transfer 53 (2010) 2477–2483