Heat and mass transfer mechanisms in nanofluids boundary layers J. Serna University Center of Defence at the Spanish Air Force Academy, MDE-UPCT, Calle Coronel López Pena, s/n, 30720 Santiago de la Ribera, Murcia, Spain article info Article history: Received 21 March 2015 Received in revised form 21 August 2015 Accepted 21 August 2015 Keywords: Nanofluids Boundary layer Heat transfer Selfsimilarity abstract Steady two-dimensional nanofluids boundary layers are studied with focus on heat and mass transfer properties. The study is conducted by numerical analysis of the nonlinear boundary layer equations in a self-similar form for the case of constant wall temperature. The density, specific heat, viscosity, conduc- tivity, and thermal diffusion dependence on the solid-phase volumetric fraction are considered, as well as the brownian diffusion dependence on temperature. Under the assumption of dilute mixtures, the zeroth order solution is calculated as an approach to the particles distribution in the boundary layer and it is compared with the results obtained from the full equations solutions. The effects of the Schmidt number, the wall temperature, and the particle bulk volumetric fraction on the Nusselt number, the Sherwood number, and the skin-friction coefficient are elucidated and compared to the values obtained for the pure fluid and for uniform mixtures. An increase in the heat transfer performances with respect to the case of the base fluid is found for most of the cases. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Due to the promising potential for heat transfer applications, nanofluids have received a great attention worldwide in recent days [1]. These fluids are obtained by mixing nanometer-scale solid particles in a base liquid, and their applications include, among others, thermal waste heat management of new power weapons [2], increase of performances of solar collectors [3,4], or nuclear safety issues [5]. Regarding these points, the main effect of the addition of nanoparticles is the increase of the thermal conductiv- ity much more than the Maxwell’s theory [6] predicts. Addition- ally, the fact that nanofluids are highly stable [7] make them attractive as a solution for cooling applications. Notwithstanding the big effort made, models for heat transfer in nanofluids are nowadays under continuous revision, both to the particle size level [8] as to the continuous formulation of the nanofluid behavior [9,10]. In certain modern works, dating from approximately seven years ago, nanofluids are modeled as a uniform, homogenous mix- ture [11–16]. In these studies, the effect of the nanoparticles is con- sidered only for the calculation of the average properties of the fluid for a constant, bulk volumetric fraction. This methodology is supported by the large values of Lewis and Schmidt numbers found in nanofluids [17]. Nevertheless, in recent years, the effect of the solid-phase distribution has began to be studied in order to get a deeper knowledge of nanofluids behavior [18–20]. Most of these works are based on the four nonlinear equations Buongiorno’s model [17]. Regarding boundary layer studies, the uniform mixture model is found up to recent dates, researches in [21–25] considered only the momentum and energy equations, without taking into account the particles’ dynamics. In these works, the particles presence is reduced to a modification of the transport coefficients and, conse- quently, the effective Reynolds and Prandtl numbers, that differ from those related to the base fluid. Kuznetsov’s work [26] is a pioneering study in modeling the conservation equation for the solid phase for natural convective boundary layer flows. In this work, the thermal and brownian diffusion coefficients are consid- ered constant. The same model is used by RamReddy [27] to study a mixed convection boundary layer with focus in the Soret effect. As a result of RamReddy’s work, the Soret effect is seemed to enhance the skin friction, and heat and mass transfer perfor- mances. Avramenko [18], based on Lie group analysis, performed a selfsimilar study of convective boundary layers. Considering con- stant thermal and brownian diffusion factors as in previous works, the effect of the Schmidt number on boundary layers thickness and heat and mass transfer is studied. This work concludes that the local distribution of the particles has no appreciable effect. Notwithstanding, the mixed convection boundary layer study in [3] established that thermophoresis and brownian motion play a key role on both the heat transfer and the nanoparticles distribu- tion. These phenomena result in the presence of additional nonlin- ear terms in the equations. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.08.072 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved. E-mail address: jose.serna@cud.upct.es International Journal of Heat and Mass Transfer 92 (2016) 173–183 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt