An improved model for thermal conductivity of nanofluids with effects of particle size and Brownian motion

Abstract

Based on the generalized distribution of the temperature field, an improved model for the thermal conductivity of nanofluid has been derived. The impact of particle size and Brownian motion is modeled through the effective volume fraction, based on particle radius. In the special case, the generalized relationship reduces to the classical Maxwell model. On the other hand, the effect of Brownian movement is equivalent to increasing the effective volume fraction of nanoparticles. The effective radius of the nanoparticle is proposed, where the switching time and the equivalent volume fraction depend on the Brownian velocity of the nanoparticles. Considering the above two effects, an effective model is obtained. Comparison of thermal conductivity for Al 2 O 3 -water nanofluid is made between the present model and several theoretical models. Theoretical predictions on CuO-water nanofluid, ZnOTiO 2 hybrid nanofluids and MWCNTs nanofluid are also verified against experimental data.

Conjugate heat transfer performance of stepped lid-driven cavity with Al2O3/water nanofluid under forced and mixed convection

“…8, it is observed Fig. 7 Average Nusselt number at different Reynolds number for forced and mixed convection types of pure water in forward step at different Grashof numbers that Patel et al [14] model results in 20.56% higher thermal conductivity value for 3 vol.% Al 2 O 3 /water nanofluid in comparison with the lowest thermal conductivity value of Dong and Chen [16] obtained in the present study. The use of micro-convection phenomena based thermal conductivity models will result in higher values of thermal conductivity when compared with other models.…”

“…That are, conduction through fluid, conduction through solid and advection because of the Brownian motion of the particles as well as aggregation. The classical thermal conductivity models of Maxwell [6], Bruggeman [7], Hamilton and Crosser [8], as well as Lu and Lin [9], Chon et al [10], Chandrasekar et al [11], Dong and Chen [16] exhibits similar thermal conductivity values. From Fig.…”

“…Reference [6][7][8][9][10][11][12] represents the thermal conductivity models without consideration of Brownian motion. Whereas, Reference [13][14][15][16] represents the thermal conductivity models considering both the Brownian motion and aggregation effects. From Fig.…”

“…He concluded that Brownian motion is mainly responsible for nanofluid thermal conductivity enhancement. Incorporation of Brownian motion into the thermal conductivity model along with particle size was carried out by Dong and Chen [16]. Goudarzi et al [17] numerically investigated migration of nanoparticles under Brownian diffusion and concludes it as an important enhancing phenomenon in heat transfer.…”

“…The effective thermal conductivity of Al 2 O 3 /water nanofluid evaluated by considering the brownian motion of nanoparticles with Patel et al[14] results in 20.56% higher value for 3 vol.% Al 2 O 3 /water nanofluid in comparison with the lowest thermal conductivity value of Dong and Chen[16] obtained in the present study showing the importance and considering requirement of brownian motion in nanofluid heat transfer.• At Re = 500, 3 vol.% Al 2 O 3 /water nanofluid enhances the heat transfer performance by 23.63% in comparison with that of pure water for mixed convection with Gr = 20,000 in forward step.…”