596 2016,28(4):596-602 DOI: 10.1016/S1001-6058(16)60663-7 Estimation of boundary-layer flow of a nanofluid past a stretching sheet: A revised model * Naeema ISHFAQ 1 , Zafar Hayat KHAN 2 , Waqar Ahmad KHAN 3 , Richard J. CULHAM 4 1. School of Mathematical Sciences, Peking University, Beijing 100871, China, E-mail: sanam_143_6@hotmail.com 2. Department of Mathematics, University of Malakand, Dir (Lower), Khyber Pakhtunkhwa, Pakistan 3. Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al Majma′ah, Saudi Arabia 4. Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada (Received October 6, 2014, Revised April 27, 2015) Abstract: The previous model for the boundary layer nanofluid flow past a stretching surface with a specified nanoparticle volume fraction on the surface is revisited. The major limitation of the previous model is the active control of the nanoparticle volume fraction on the surface. In a revised model proposed in this paper, the nanoparticle volume fraction on the surface is passively contro- lled, which accounts for the effects of both the Brownian motion and the thermophoresis under the boundary condition, whereas the Buongiorno’s model considers both effects in the governing equations. The assumption of zero nanoparticle flux on the surface makes the model physically more realistic. In the revised model, the dimensionless heat transfer rates are found to be higher whereas the dimensionless mass transfer rates are identically zero due to the passive boundary condition. It is also found that the Brownian motion parameter has a negligible effect on the Nusselt number. Key words: boundary layer flow, nanofluid, stretching sheet, Brownian motion, thermophoresis Introduction Buongiorno [1] developed a model for nanofluid that includes both the Brownian motion and thermo- phoresis effects. This model was employed by Kuznetsov and Nield [2] and Nield and Kuznetsov [3] to examine the influence of nanoparticles on the free convection past a vertical plate. They employed boun- dary conditions with respect to the nanoparticle fra- ction akin to the temperature. Later on, Khan and Pop [4] employed the same model to investigate the laminar flow generated by the stretching of a flat surface. They studied the effects of Brownian and thermophoresis * Project supported by the National Natural Science Foun- dation of China (Grant No. 11271023). Biography: Naeema ISHFAQ (1986-), Female, Ph. D. Candidate Corresponging author: Zafar Hayat KHAN, E-mail: zafarhayyatkhan@gmail.com parameters on the dimensionless heat and mass tran- sfer rates using the same approach as used in Refs.[2,3]. This means that the nanoparticle fraction on the wall can be specified arbitrarily, which is not realistic phy- sically. Most recently, Kuznetsov and Nield [5,6] deve- loped a physically realistic type of boundary condition which accounts for the effect of both Brownian and thermophoresis parameters. According to this new type of boundary condition, there is zero nanoparticle flux on the surface and the particle fraction values are adjusted accordingly. The model developed in Kuznetsov and Nield [5,6] was employed by Khan et al. [7,8] . Pal and Mandal [9] studied the magnetohydrody- namic boundary layer flow of an electrically condu- cting convective nanofluids induced by a non-linear vertical stretching/shrinking sheet with viscous dissi- pation, thermal radiation, and Ohmic heating. Their results reveal that by increasing the value of the Hartman number the velocity will decrease, whereas a reverse effect is found in the temperature profiles. Das [10] investigated numerically the boundary layer