Heat Transfer—Asian Research, 45 (6), 2016 Natural Convection Flow of a Nanoluid along a Vertical Plate with Streamwise Temperature Variations A.M. Rashad, 1 Ali J. Chamkha, 2 and S.M.M. EL-Kabeir 1,3 1 Department of Mathematics, Aswan University, Faculty of Science, 81528, Aswan, Egypt 2 Manufacturing Engineering Department, The Public Authority for Applied Education and Training, Shuweikh 70654, Kuwait 3 Department of Mathematics, Salman bin Abdulaziz University, College of Science and Humanity Studies, Al-Kharj, Saudi Arabia This work is devoted to study the natural convection boundary-layer low of nanoluids along a vertical lat plate with the effect of sinusoidal surface temperature variations. The model utilized for the nanoluid incorporates the effects of Brownian motion and thermophoresis. An appropriate set of dimensionless variables is used to transform the governing equations of the problem into a nonsimilar form. The obtained nonsimilar equations have the property that they reduce to various special cases previously considered in the open literature. An adequate and eficient implicit, tri-diagonal inite difference method is employed for the numerical solution of the obtained equations. Comparison with previously published work is performed and the results are found to be in excellent agreement. A representative set of numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction, as well as the surface shear stress, rates of heat and nanoparticle volume fraction have been presented graphically and discussed to show interesting features of the so- lutions. C⃝ 2014 Wiley Periodicals, Inc. Heat Trans Asian Res, 45(6): 499–514, 2016; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21173 Key words: Brownian motion, nanoluids, thermophoresis, natural convec- tion, sinusoidal surface temperature 1. Introduction It is known now that nanoluids are a new class of nanotechnology-based heat transfer luids engineered by dispersing nanometer scale solid particles with typical length scales on the order of 1 nm to 100 nm in traditional heat transfer luids. Choi [1] was the irst who reported the term of nanoluids to describe this new class of luid. The base luids used are usually water, ethylene gly- col, toluene, and oil. The choice of base luid–particle combination depends on the application for which the nanoluid is intended. Recent studies on nanoluid reported that nanoparticles changed the luid characteristics because thermal conductivity of these particles was higher than convectional luids. Nanoparticles are of great scientiic interest as they are effectively a bridge between bulk materials and atomic or molecular structures. The common nanoparticles that have been used are aluminum, copper, iron, and titanium or their oxides. Several beneits of the industrial applications C⃝ 2014 Wiley Periodicals, Inc. 499