Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
Laminar boundary layer flow and heat transfer of Newtonian nanofluid over a stretching sheet with the sheet velocity distribution of the form (Uw=CXβ) and the wall temperature distribution of the form (Tw= T∞+ axr) for the steady magnetohydrodynamic(MHD) is studied numerically. The governing momentum and energy equations are transformed to the local non-similarity equations using the appropriate transformations. The set of ODEs are solved using Keller–Box implicit finite-difference method. The effects of several parameters, such as magnetic parameter, volume fraction of different nanoparticles (Ag, Cu, CuO, Al2O3 and TiO2), velocity parameter, Prandtl number and temperature parameter on the velocity and temperature distributions, local Nusselt number and skin friction coefficient are examined. The analysis reveals that the temperature profile increases with increasing magnetic parameter and volume fraction of nanofluid. Furthermore, it is found that the thermal boundary layer increases and momentum boundary layer decreases with the use of water based nanofluids as compared to pure water. At constant volume fraction of nanoparticles, it is also illustrated that the role of magnetic parameter on dimensionless temperature becomes more effective in lower value.
 U.S. Choi: Enhancing thermal conductivity of fluids with nanoparticle Developments and Applications of Non-Newtonian Flows 231 (1995) 99-105.
 S. Choi, Z. Zhang, W. Yu, F. Lockwood, E. Grulke: Anomalously thermal conductivity enhancement in nanotube suspensions, Journal of Applied Physics Letters 79 (2001) 2252–2254.
 S. Z. Heris, M. N. Esfahany, S. Gh. Etemad: Experimental Investigation of Convective Heat Transfer of Al2O3/Water Nanofluid in Circular Tube, International Journal of Heat and Fluid Flow 28 (2006) 203–210.
 M. Hojjat, S. Etemad, R. Bagheri: Laminar heat transfer of non-Newtonian nanofluids in a circular tube, Korean Journal of Chemical Engineering 27 (2010) 1391–1396.
 B.C. Pak, Y. Cho: Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer 11 (1998) 151-170.
 Y. Xuan, Q. Li: Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer 125 (2003) 151-155.
 A. Ahuja: Augmentation of heat transport in laminar flow of polystyrene suspensions, Journal of Applied Physics 46 (1975) 3408-3425.
 J. Buongiorno: Convective transport in nanofluids, Journal of Heat Transfer 128 (2006) 240-250.
 MA Fadzilah, R Nazar, M. Arifin, I. Pop: MHD boundary-layer flow and heat transfer over a stretching sheet with induced magnetic field. Journal of Heat Mass Transfer 47 (2011) 155–162.
 A. Ishak, R. Naza, I. Pop: MHD boundary-layer flow due to a moving extensible surface, Journal of Engineering Mathematics 62 (2008) 23–33.
 A.V. Kuznetsov, D.A Nield: Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences 49 (2010) 243-247.
 N. Bachok, A.Ishak, I.Pop: Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, International Journal of Thermal Sciences 49 (2010) 1663-1668.
 W.Ibrahim, B. Shanker: Unsteady MHD boundarylayer flow and heat transfer due to stretching sheet in the presence of heat source or sink, International Journal of Computers & Fluids 70 (2012) 21-28.
 A. Ishak, R. Naza, I. Pop: Heat transfer over a stretching surface with variable heat flux in microplar fluids. Physics Letters A 5 (2008) 559–61.
 A. Noghrehabadi, R. Pourrajab, M. Ghalambaz: Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature, International Journal of Thermal Sciences 54 (2012) 253-261
 M. Narayana, P. Sibanda: Laminar flow of a nanoliquid film over an unsteady stretching sheet, International Journal of Heat and Mass Transfer 55 (2012) 7552-7560.
 A. Aziz, W.A. Khan: Natural convective boundary layer flow of a nanofluid past a convectively heated vertical plate, International Journal of Thermal Sciences 52 (2012) 83-90.
 L. Zheng, C. Zhang, X. Zhang, J. Zhang: Flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium, Journal of the Franklin Institute 350 (2013) 990–1007.
 P. Rana, R. Bhargava: Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study, Communications in Nonlinear Science and Numerical Simulation 17 (2012) 212–226.
 A. Mahdy: Unsteady mixed convection boundary layer flow and heat transfer of nanofluids due to stretching sheet, Nuclear Engineering and Design 249 (2012) 248– 255.
 K.V. Prasad, P.S. Pal Dulal, Datti: MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 2178–2189.
 H. Xu, S. Liao: Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet, Computers and Mathematics with Applications 57 (2009) 1425_1431.
 N. Masoumi, N. Sohrabi, A.A. Behzadmehr: New model for calculating the effective viscosity of nanofluids, Journal of Physics D: Applied Physics 42 (2009) 055501–055506.
 C.H. Chon, K.D. Kihm, S.P. Lee, S.U. Choi: Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, Journal of Applied Physics Letters 87 (2005) 153107–153110.
 H.A. Mintsa, G. Roy, C.T. Nguyen, D. Doucet: temperature dependent thermal conductivity data for water-based nanofluids, International Journal of Thermal Sciences 48 (2009) 363–371.
 C.T Nguyen., F. s Desgrange, G. Roy, T. Galanis, S. Boucher, H.A.n Mintsa: Temperature and particlesize dependent viscosity data for waterbased nanofluids–hysteresis phenomenon, International Journal of Heat Fluid Flow 28 (2009) 1492–1506.
 Kh. Khanafer, K. Vafai: A critical synthesis of thermophysical characteristics of nanofluids, International Journal of Heat Mass Transfer 54 (2011) 4410–4428.
 D.A.G. Bruggeman: Berechnung verschiedener physikalischer konstanten von heterogenen substanzen, I. Dielektrizitatskonstanten und leitfahigkeiten der mischkorper aus isotropen substanzen, Annals of Physics 24 (1935) 636– 679.
 J.C. Maxwell Garnett: Colours in metal glasses and in metallic films, Philos. Trans. R. Soc. Lond. A203 (1904). 385–420.
 H.C. Brinkman: The viscosity of concentrated suspensions and solutions. Journal of Chemical Physics 20 (1952) 571–581.
 S.E.B. Maiga, S.J. Palm, C.T.Nguyen, G. Roy, N. Galanis: Heat transfer enhancement by using nanofluids in forced convection flow, International Journal of Heat and Fluid Flow 26 (2005) 530–546.
 E. Abu-Nada: Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step, International Journal of Heat Fluid Flow 29 (2008) 242–249.
 A. Akbarinia, A. Behzadmehr: Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes, Journal of Applied Thermal Engineering 27 (2007) 1327–1337.
 T. Cebeci, J. Cousteix: Modeling and Computation of Boundary-Layer Flows, Second Edition, Horizons Publishing Inc., Long Beach, California-Springer-Verlag, (2005).
 A. Ishak, R. Nazar, I. Pop: Boundary layer flow and heat transfer over an unsteady stretching vertical surface Meccanica 44 (2009) 369–375.
 M.E.Ali: Heat transfer characteristics of a continuous stretching surface, Journal of Heat Mass Transfer 29 (1904) 227–234.
 L.J. Grubka, K.M. Bobba: Heat transfer characteristics of a continuous, stretching surface with variabletemperature, ASME Journal of Heat Transfer 107 (1985) 248–250.