The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Hamilton–Crosser model

We previously developed a renovated Maxwell model for the effective thermal conductivity of nanofluids and determined that the solid/liquid interfacial layers play an important role in the enhanced thermal conductivity of nanofluids. However, this renovated Maxwell model is limited to suspensions with spherical particles. Here, we extend the Hamilton--Crosser model for suspensions of nonspherical particles to include the effect of a solid/liquid interface. The solid/liquid interface is described as a confocal ellipsoid with a solid particle. The new model for the three-phase suspensions is mathematically expressed in terms of the equivalent thermal conductivity and equivalent volume fraction of anisotropic complex ellipsoids, as well as an empirical shape factor. With a generalized empirical shape factor, the renovated Hamilton--Crosser model correctly predicts the magnitude of the thermal conductivity of nanotube-in-oil nanofluids. At present, this new model is not able to predict the nonlinear behavior of the nanofluid thermal conductivity.     

An experimental correlation approach for predicting thermal conductivity of water-EG based nanofluids of zinc oxide

In this study, the effects of temperature (20 °C<T<50 °C) and volume fracti°n (0<φ<4%) on the thermal conductivity of zinc oxide/ethylene glycol-water nanofluid have been presented. Nanofluid samples were prepared by a two-step method and thermal conductivity measurements were performed by a KD2 pro instrument. Results showed that the thermal conductivity increases uniformly with increasing solid volume fraction and temperature. The results also revealed that the thermal conductivity of nanofluids significantly increases with increasing solid volume fraction at higher temperatures. Moreover, it can be seen that for more concentrated samples, the effect of temperature was more tangible. Experimental thermal conductivity enhancement of the nanofluid in comparison with the Maxwell model indicated that Maxwell model was unable to predict the thermal conductivity of the present nanofluid. Therefore, a new correlation was presented for predicting the thermal conductivity of ZnO/EG-water nanofluid.     

Modified Maxwell model for predicting thermal conductivity of nanocomposites considering aggregation

The effect of nanoparticle aggregation on the thermal conductivity of nanocomposites or nanofluids is typically nonnegligible. A universal model(Maxwell model) including nanoparticle aggregation is modified in order to predict the thermal conductivity of nanocomposites more accurately. The predicted thermal conductivities of silica and titania nanoparticle powders are compared first with that measured by a hot-wire method and then with those in previous experimental works.The results show that there is good agreement between our model and experiments, and that nanoparticle aggregation in a nanocomposite enhances the thermal conductivity greatly and should not be ignored. Because it considers the effect of aggregation, our model is expected to yield precise predictions of the thermal conductivity of composites.     

水基ZnO纳米流体电导和热导性能研究

利用水热法生成了形状规则、粒径均匀的球形ZnO纳米颗粒, 并超声分散于水中, 制备得到稳定的水基ZnO纳米流体. 实验测量水基ZnO纳米流体在体积分数和温度变化时的电导率, 并测试室温下水基ZnO纳米流体在不同体积分数下的热导率. 实验结果表明, ZnO纳米颗粒的添加较大地提高了基液(纯水)的热导率和电导率, 水基ZnO纳米流体的电导率随纳米颗粒体积分数增加呈非线性增加关系, 而电导率随温度变化呈现出拟线性关系; 纳米流体的热导率与纳米颗粒体积分数增加呈近似线性增加关系. 本文在经典Maxwell热导模型和布朗动力学理论的基础上, 同时考虑了吸附层、团聚体和布朗运动等因素对热导率的影响, 提出了热导率修正模型.将修正模型预测值与实验值对比, 结果表明修正模型可以较为准确地计算出纳米流体的热导率. 关键词： 水热法 电导率 热导率 热导模型     

Comments on the effect of liquid layering on the thermal conductivity of nanofluids

This article provides critical examinations of two mathematical models that have been developed in recent years to describe the impact of nano-layering on the enhancement of the effective thermal conductivity of nanofluids. Discrepancy between the two models is found to be an artefact of an incorrect derivation used in one of the models. With correct formulation, both models predict effective thermal conductivity enhancements that are not significantly greater than those predicted by classical Maxwell theory. This study indicates that nano-layering by itself is unable to account for the effective thermal conductivity enhancements observed in nanofluids.     

The effect of particle size on the thermal conductivity of alumina nanofluids

We present new data for the thermal conductivity enhancement in seven nanofluids containing 8–282 nm diameter alumina nanoparticles in water or ethylene glycol. Our results show that the thermal conductivity enhancement in these nanofluids decreases as the particle size decreases below about 50 nm. This finding is consistent with a decrease in the thermal conductivity of alumina nanoparticles with decreasing particle size, which can be attributed to phonon scattering at the solid–liquid interface. The limiting value of the enhancement for nanofluids containing large particles is greater than that predicted by the Maxwell equation, but is predicted well by the volume fraction weighted geometric mean of the bulk thermal conductivities of the solid and liquid. This observation was used to develop a simple relationship for the thermal conductivity of alumina nanofluids in both water and ethylene glycol.     

The Role of Interfacial Layers in the Enhanced Thermal Conductivity of Nanofluids: A Renovated Maxwell Model

Nanofluids, a new class of solid/liquid suspensions, offer scientific challenges because their measured thermal conductivity is one order of magnitude greater than predictions. It has long been known that liquid molecules close to a solid surface form layered solid-like structures, but little is known about the connection between this nanolayer and the thermal properties of the suspensions. Here, we have modified the Maxwell equation for the effective thermal conductivity of solid/liquid suspensions to include the effect of this ordered nanolayer. Because this ordered nanolayer has a major impact on nanofluid thermal conductivity when the particle diameter is less than 10 nm, a new direction is indicated for development of next-generation coolants.     

Magnetohydrodynamic Stagnation Point Flow of a Maxwell Nanofluid with Variable Conductivity

This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell nanofluid.The Buongiorno's theory has been established to picture the inducement of Brownian and thermophrotic diffusions effects.Additionally,the aspect of heat sink/source is reported.The homotopic analysis method(HAM) has been worked out for the solution of nonlinear ODEs.The behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and discussed.The attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration fields.It is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion parameter.Moreover,for the confirmation of our study comparison tables are reported.     

The Effect of Zinc Oxide and Calcium Carbonate Nanoparticles on the Thermal Conductivity of Polypropylene

The thermal conductivity (TC) of compression-moulded polypropylene (PP) and PP filled with 5–15% zinc oxide (ZnO) or calcium carbonate (CaCO₃) nanoparticles, prepared by extrusion, was studied using a thermal conductivity analyzer (TCA). The effect of nanoparticle content and crystallinity on the thermal conductivity was investigated using conventional methods, including SEM, XRD, and DSC. The incorporation of nanoparticles improved the crystallinity and thermal conductivity simultaneously. The experimental TC values of the PP nanocomposites with different level of nanoparticles concentration showed a linear increase with an increase in crystallinity. The TC improvement in PP/ZnO nanocomposite was greater than that of PP/calcium carbonate nanocomposites. This fact can be attributed to the intrinsic, better thermal conductivity of the ZnO nanoparticles. Several models were used for prediction of the TC in the nanocomposites. In the PP/ZnO nanocomposites the TC values correlated well with the values predicted by the Series, Maxwell, Lewis and Nielson, Bruggeman, and De Loor models up to 10 wt%.     

Utilization of the magnetogranulometric analysis to estimate the thermal conductivity of magnetic fluids

In this study, the semi-empirical equation for the effective thermal conductivity of the Holotescu-Stoian model was applied to a set of four dilutions of a transformer oil based magnetic fluid with magnetite nanoparticles as magnetic phase, using the results obtained for the size distributions from the magnetogranulometry analysis, followed by a comparison with the measured values of the effective thermal conductivity obtained by the hot ball method. The link between the size distribution by number and by volume used in the magnetogranulometry analysis and the Holotescu-Stoian model adaptation to the lognormal distribution were presented. The comparison between the results given by the model and the corresponding experimental data showed that by using the approximated size distribution to calculate the effective thermal conductivity the analytical results much closer to the experimental ones are obtained, compared to those given by the Maxwell classical model.     

Thermal conductivity of the diamond-paraffin wax composite

The thermal conductivity of diamond-paraffin wax composites prepared by infiltration of a hydrocarbon binder with the thermal conductivity λ _m = 0.2 W m⁻¹ K⁻¹ into a dense bed of diamond particles (λ _f ∼ 1500 W m⁻¹ K⁻¹) with sizes of 400 and 180 μm has been investigated. The calculations using universally accepted models considering isolated inclusions in a matrix have demonstrated that the best agreement with the measured values of the thermal conductivity of the composite λ = 10–12 W m⁻¹ K⁻¹ is achieved with the use of the differential effective medium model, the Maxwell mean field scheme gives a very underestimated calculated value of λ, and the effective medium theory leads to a very overestimated value. An agreement between the calculation and the experiment can be provided by constructing thermal conductivity functions. The calculation of the thermal conductivity at the percolation threshold has shown that the experimental thermal conductivity of the composites is higher than this critical value. It has been established that, for the composites with closely packed diamond particles (the volume fraction is ∼0.63 for a monodisperse binder), the use of the isolated particle model (Hasselman-Johnson and differential effective medium models) for calculating the thermal conductivity is not quite correct, because the model does not take into account the percolation component of the thermal conductivity. In particular, this holds true for the calculation of the heat conductance of diamond-matrix interfaces in diamond-metal composites with a high thermal conductivity.     

Particle agglomeration and properties of nanofluids

The present study demonstrates the importance of actual agglomerated particle size in the nanofluid and its effect on the fluid properties. The current work deals with 5 to 100 nm nanoparticles dispersed in fluids that resulted in 200 to 800 nm agglomerates. Particle size distributions for a range of nanofluids are measured by dynamic light scattering (DLS). Wet scanning electron microscopy method is used to visualize agglomerated particles in the dispersed state and to confirm particle size measurements by DLS. Our results show that a combination of base fluid chemistry and nanoparticle type is very important to create stable nanofluids. Several nanofluids resulted in stable state without any stabilizers, but in the long term had agglomerations of 250 % over a 2 month period. The effects of agglomeration on the thermal and rheological properties are presented for several types of nanoparticle and base fluid chemistries. Despite using nanodiamond particles with high thermal conductivity and a very sensitive laser flash thermal conductivity measurement technique, no anomalous increases of thermal conductivity was measured. The thermal conductivity increases of nanofluid with the particle concentration are as those predicted by Maxwell and Bruggeman models. The level of agglomeration of nanoparticles hardly influenced the thermal conductivity of the nanofluid. The viscosity of nanofluids increased strongly as the concentration of particle is increased; it displays shear thinning and is a strong function of the level of agglomeration. The viscosity increase is significantly above of that predicted by the Einstein model even for very small concentration of nanoparticles.     

Thermophysical effects of carbon nanotubes on MHD flow over a stretching surface

This article is intended for investigating the effects of magnetohydrodynamics (MHD) and volume fraction of carbon nanotubes (CNTs) on the flow and heat transfer in two lateral directions over a stretching sheet. For this purpose, three types of base fluids specifically water, ethylene glycol and engine oil with single and multi-walled carbon nanotubes are used in the analysis. The convective boundary condition in the presence of CNTs is presented first time and not been explored so far. The transformed nonlinear differential equations are solved by the Runge–Kutta–Fehlberg method with a shooting technique. The dimensionless velocity and shear stress are obtained in both directions. The dimensionless heat transfer is determined on the surface. Three different models of thermal conductivity are comparable for both CNTs and it is found that the Xue [1] model gives the best approach to guess the superb thermal conductivity in comparison with the Maxwell [2] and Hamilton and Crosser [3] models. And finally, another finding suggests the engine oil provides the highest skin friction and heat transfer rates.     

MHD swirling flow and heat transfer in Maxwell fluid driven by two coaxially rotating disks with variable thermal conductivity

We develop a mathematical modeling for an electrically conducting non-Newtonian Maxwell fluid flow occurring between two coaxially parallel stretchable rotating disks at constant distant apart. The pressure and heat transfer analysis is carried out subject to the effects of axial magnetic field and temperature dependent thermal conductivity. The stretching and rotating rates of both disks are assumed different from each other. The two diverse phenomena, such as, when both disks are rotating with different angular velocities in the same as well as in the opposite directions are discussed. The similarity procedure adopted by von Kármán is utilized to reduce the governing momentum and energy equations into nonlinear ordinary differential equations. The solution of the governing problem is obtained numerically using bvp4c scheme in Matlab. The effects of active parameters including stretching rates, Deborah number, magnetic number, Prandtl number, thermal conductivity parameter and Reynolds number are examined for same as well as opposite rotation direction for radial, azimuthal, and axial flows, pressure and temperature fields. The classical flow pattern happening between the disks is significantly altered by the stretching action which is a main physical significances of this study. The azimuthal flow is observed higher for the same direction of disks rotation as compared to opposite disks rotation. The pressure field drops near the lower disk with increasing values of Reynolds number. The role of thermal conductivity parameter is quite useful to enhance the fluid temperature.     

Numerical simulation of Electrokinetically Driven Peristaltic Pumping of Silver-Water Nanofluids in an asymmetric microchannel

This article intends to focus on the theoretical and numerical investigation of the peristaltic pumping of water-based silver nanofluid in the presence of electroosmotic forces. The investigation is carried out in an asymmetric microchannel subject to the influence of mixed convection and viscous dissipation. No-slip boundary conditions for velocity, temperature, and nanoparticle volume fraction are imposed on channel walls. The lubrication approach is utilized to simplify the normalized constitutive equations. The distribution of electric potential in the electric double layer is characterized by Poisson-Boltzmann ionic distribution which is further linearized by Debye-Hückel approximation. Nanofluid properties are predicted by a combination of the Buongiorno two-phase mixture model and homogeneous flow model. Additionally, the effective thermal conductivity and dynamic viscosity of silver-water nanofluid are characterized by the Corcione model. Silver nanoparticles of 20nm diameter are utilized in this suspension. The transformed set of nonlinear and coupled equations is numerically executed for axial velocity, temperature, and nanoparticle volume fraction by employing the mathematical software Maple 17. Pumping and trapping phenomena are also investigated. A comparison between the thermal conductivity of nanofluid predicted by the Corcione model and the Maxwell model is further presented. The influence of various flow parameters is outlined through graphical results. It has been observed that the thermal conductivity of silver-water nanofluid enhances with increasing nanoparticle volume fraction and temperature but decreases for larger sized nanoparticles. Moreover, the heat transfer rate rises significantly when smaller silver nanoparticles are suspended in water. Furthermore, the temperature of nanofluid is directly related to the Debye length parameter and the Helmholtz- Smoluchowski velocity parameter.     

Dynamical Conductivity of the Dilute Lorentz Gas with Spherically Symmetric Scatterers

The dynamical conductivity of the Lorentz gas with spherically symmetric potentials is studied to lowest order in the density of scatterers. The frequency-dependent friction coefficient is calculated from the Fourier transform of the force–force time-correlation function determined by the dynamics of a single scattering process. The corresponding dynamical conductivity varies with frequency on the scale of the inverse collision time. As an example, the conductivity is calculated for a scattering potential of the Maxwell type.     

Electrical Conductivity of Nonideal Plasma

The electrical conductivity of fully ionized moderately nonideal plasmas with coulomb interaction parameters 0.1 < ? ? 1 where ? = Ze2n1/3/KT is the ratio of coulomb and thermal energies is calculated for displaced Maxwell and Fermi electron distributions, respectively. The electrons are scattered by an effective coulomb potential ?(r) = Zer-1 exp (-r/?) which considers binary (0 < r < ?) and many-body (? < r < ?) interactions. The shielding distance is given by ? = ?(4?n/3Z)-1/3 with ? = ?0?-N ~ 1 for classical plasmas and ? = ?(4?n/3Z)-1/3 with ? = ?0?-N?-M ~ 1 for quantum plasmas, where ? = Ze2n1/3/h2 m-1n2/3 is the ratio of coulomb interaction and quantum potential energies of the electrons. It is shown that the resulting conductivity formulas are applicable to densities up to four orders of magnitude higher than those of the ideal conductivity theory, which breaks down at higher densities because the Debye radius loses its physical meaning as a shielding length and upper impact parameter.     

Electrical Conductivity of Nonideal Quasi-Metallic Plasmas

Electrical conductivity formulas are derived from first principles for fully ionized nonideal plasmas. The theory is applicable to an electron-ion system with a 1) Maxwell electron distribution with an arbitrary interaction parameter ? = Ze2n1/3/KT (ratio of the mean coulomb interaction and thermal energies) and 2) Fermi electron distribution with an interaction parameter ? = Ze2n1/3h?2m-1 n2/3 (ratio of the coulomb interaction and Fermi energies). The momentum relaxation time of the electrons in the plasma is calculated based on plane electron wave functions interacting with the continuum oscillations (plasma waves) through a shielded coulomb potential Us(r) = esee exp (-r/?s)/r, which takes into account both electron-ion interactions (s = i) and electron-electron interactions (s = e). It is shown that the resulting conductivity formulas are applicable to higher densities, for which the ideal plasma conductivity theory breaks down because the Debye radius loses its physical meaning as a shielding length and upper impact parameter. The conductivity obtained for classical plasma is of the form ?c = ?c*(KT)3/2/m1/2e2 and agrees with the ideal plasma conductivity formula with respect to the temperature and density dependence for ?/Z ? 0, but its magnitude is significantly reduced as ?/Z increases. For quantum plasmas, the conductivity obtained is of the form ?Q = ?Q*h3n/m2Ze2, which shows that the degenerate plasma behaves like a low-temperature metal.