It is also found in the study of Wang and Majumdar

[12] that the insertion of nanoparticle increases the viscosity of the fluid. There are various theoretical relations predicting the thermal conductivity and viscosity of nanofluids, but these empirical relations do not satisfy the experimental data up to a satisfying range. Chon et al. [13] found an empirical correlation for the thermal conductivity of Stem Cells inhibitor nanofluids within the particle size range of 11 to 150 nm and temperature range of 21°C to 71°C. They reported that the Brownian motion of nanoparticles constitutes a key mechanism of the thermal conductivity enhancement with increasing temperature and decreasing nanoparticle sizes. However, this empirical formula was valid only for water-Al2O3 nanofluid. Very recently, Corcione [14] analyzed the experimental data of thermal conductivity

and viscosity of nanofluids, AZD1480 mouse which were obtained by various researchers for different types of nanoparticles dispersed in different base fluids, and found an empirical correlating selleck chemicals equation for the prediction of effective thermal conductivity and dynamic viscosity of nanofluids. With the advances in thermal properties and viscosity of nanofluids, various researchers studied the convective flow numerically as well as experimentally. Ho et al. [15] studied the natural convection of nanofluid having a particle concentration within the range of 0% to 4% in a square enclosure and analyzed the effects caused by uncertainties of viscosity and thermal conductivity. This study was limited to Al2O3-water nanofluid only. A detailed study of the natural convection of water-based nanofluids in an inclined enclosure

has been done by Elif [16]. In this study, he investigated heat transfer enhancement using five different types of nanoparticles dispersed in water. To model the problem, he used a renovated Maxwell model containing the effect of interfacial layers in the enhanced thermal conductivity of nanofluids, given by Yu and Choi [17]. Abu-Nada and Oztop Venetoclax in vivo [18] investigated the effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. All these authors reported that the heat transfer rate increases with the increase in nanoparticle concentration in the base fluid. However, in these studies, the effect of temperature and Brownian motion was not considered in the formulation of the problem. Abu-Nada [19] investigated the natural convection heat transfer in horizontal cylindrical annulus filled with Al2O3-water nanofluid taking the effect of variable viscosity and thermal conductivity. In the study, the effective thermal conductivity was calculated by the model of Chon et al. [13], and to formulate the dynamic viscosity of the Al2O3-water nanofluid, the author used the experimental data and found the empirical correlation for the dynamic viscosity as a function of temperature and particle concentration. Ho et al.