Effect of nanofluid variable properties on mixed convection in a square cavity Saeed Mazrouei Sebdani a , Mostafa Mahmoodi a, * , Seyed Mohammad Hashemi b a Department of Mechanical Engineering, University of Kashan, Kashan, Iran b Department of Mechanical Engineering, KN Toosi University of Technology, Tehran, Iran article info Article history: Received 9 May 2011 Received in revised form 3 September 2011 Accepted 3 September 2011 Available online 1 October 2011 Keywords: Nanofluid Variable properties Mixed convection Cavity Finite volume method abstract The problem of mixed convection fluid flow and heat transfer of Al 2 O 3 ewater nanofluid with temper- ature and nanoparticles concentration dependent thermal conductivity and effective viscosity inside a square cavity has been investigated numerically. The geometry of the present work was a square cavity with a heat source on the bottom wall, insulated top wall and moving downward cold side walls. The effects of increase in shear force while the buoyancy force was constant and effects of increase in buoyancy force when the shear force was kept constant were investigated. When the heat source was located in the middle of bottom wall, when the Rayleigh number was kept constant, the effect of addition of nanoparticles on enhancement of heat transfer increased with increase in Reynolds number. For a constant Reynolds number and for high Rayleigh numbers, the rate of heat transfer decreased with increase in nanoparticle volume fraction. Moreover it was found that the rate of this decrease increased with increase in Rayleigh number. Also the obtained results showed that when the heat source moved toward the side wall, the rate of heat transfer increased. The results obtained using variable thermal conductivity and variable viscosity models were compared to the results obtained by the Maxwell- Garnett model and the Brinkman model. The results showed that significant differences existed between the calculated overall heat transfers for the two different combinations of formulas. Moreover the difference increased with increase in nanoparticles volume fraction. Ó 2011 Elsevier Masson SAS. All rights reserved. 1. Introduction Nanofluid, which is a mixture of nano-sized particles suspended in a base fluid, has a higher thermal conductivity than the base fluid. This higher thermal conductivity enhances rate of heat transfer in industrial applications. Many researchers have investi- gated different aspects of nanofluids [1]. There are a number of recent studies on the mixed convection heat transfer in cavities filled with nanofluids. Tiwari et al. [2] used the finite volume method to investigate flow and heat transfer in a square cavity with insulated top and bottom walls and differen- tially-heated moving side walls. The cavity was filled with the Copperewater nanofluid. Conducting a parametric study, they investigated effects of the Richardson number and volume fraction of the nanoparticles on the heat transfer inside the cavity and observed that for the Richardson number equal to unity the average Nusselt number increased substantially with increase in the volume fraction of the nanoparticles. In a review paper Morshed et al. [3] addressed various investigations of nanofluids such as experimental and analytical studies on the effective thermal conductivity, effective thermal diffusivity, and convective heat transfer. They concluded that the existing classical models could not predict viscosity and effective thermal diffusivity of the nano- fluids. In another study, Ho et al. [4] investigated influences of uncertainties due to adapting different models for the effective thermal conductivity and the dynamic viscosity of aluminaewater nanofluid on the natural convection heat transfer in a square cavity. Their results showed that the heat transfer across the cavity could be either enhanced or mitigated with respect to that of the base fluid depending on the model used for the thermal conductivity and the viscosity of the nanofluid. Using the control volume method, Muthtamilselvan et al. [5] investigated the mixed convection heat transfer in a lid-driven rectangular enclosure filled with the Copperewater nanofluid. The enclosure’s side walls were insulated while its horizontal walls were kept at constant temperatures, with the top wall moving at a constant velocity. They observed that both the aspect ratio of the cavity as well as the nanoparticles volume fraction affected the fluid flow and heat transfer inside the enclosure. Talebi et al. [6] used the finite volume method to study mixed convection heat transfer in a lid-driven cavity filled with Copperewater nanofluid. The vertical walls of the cavity were differentially heated while its top and bottom walls * Corresponding author. E-mail address: mmahmoodi46@gmail.com (M. Mahmoodi). Contents lists available at SciVerse ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts 1290-0729/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.09.003 International Journal of Thermal Sciences 52 (2012) 112e126