The combined analysis of phonon and electron heat transfer mechanism on thermal conductivity for nanofluids

The paper features the mathematical model representing the analytical calculation of phonon and electron heat transfer analysis of thermal conductivity for nanofluids. The mathematical model was developed on the basis of statistical nanomechanics. We have made the detailed analysis of the influence of temperature dependence on thermal conductivity for nanofluids. On this basis are taken into account the influences such as formation of nanolayer around nanoparticles, the Brown motion of solid nanoparticles and influence of diffusive-ballistic heat transport.The analytical results obtained by statistical mechanics are compared with the experimental data and they show relatively good agreement.     

A Review of Thermal Conductivity Models for Nanofluids

Nanofluids, as new heat transfer fluids, are at the center of attention of researchers, while their measured thermal conductivities are more than for conventional heat transfer fluids. Unfortunately, conventional theoretical and empirical models cannot explain the enhancement of the thermal conductivity of nanofluids. Therefore, it is important to understand the fundamental mechanisms as well as the important parameters that influence the heat transfer in nanofluids. Nanofluids’ thermal conductivity enhancement consists of four major mechanisms: Brownian motion of the nanoparticle, nanolayer, clustering, and the nature of heat transport in the nanoparticles. Important factors that affect the thermal conductivity modeling of nanofluids are particle volume fraction, temperature, particles size, pH, and the size and property of nanolayer. In this paper, each mechanism is explained and proposed models are critically reviewed. It is concluded that there is a lack of a reliable hybrid model that includes all mechanisms and influenced parameters for thermal conductivity of nanofluids. Furthermore, more work needs to be conducted on the nature of heat transfer in nanofluids. A reliable database and experimental data are also needed on the properties of nanoparticles.     

Study on forced convective heat transfer of non-newtonian nanofluids

This paper is concerned with the forced convective heat transfer of dilute liquid suspensions of nanoparticles (nanofluids) flowing through a straight pipe under laminar conditions. Stable nanofluids are formulated by using the high shear mixing and ultrasonication methods. They are then characterised for their size, surface charge, thermal and rheological properties and tested for their convective heat transfer behaviour. Mathematical modelling is performed to simulate the convective heat transfer of nanofluids using a single phase flow model and considering nanofluids as both Newtonian and non-Newtonian fluid. Both experiments and mathematical modelling show that nanofluids can substantially enhance the convective heat transfer. Analyses of the results suggest that the non-Newtonian character of nanofluids influences the overall enhancement, especially for nanofluids with an obvious non-Newtonian character.     

A critical review of convective heat transfer of nanofluids

A nanofluid is a suspension of ultrafine particles in a conventional base fluid which tremendously enhances the heat transfer characteristics of the original fluid. Furthermore, nanofluids are expected to be ideally suited in practical applications as their use incurs little or no penalty in pressure drop because the nanoparticles are ultrafine, therefore, appearing to behave more like a single-phase fluid than a solid–liquid mixture. About a decade ago, several published articles focused on measuring and determining the effective thermal conductivity of nanofluids, some also evaluated the effective viscosity. There are only a few published articles on deriving the forced convective heat transfer of nanofluids. The purpose of this article is to summarize the published subjects respect to the forced convective heat transfer of the nanofluids both of experimental and numerical investigation.     

Determination of nanolayer thickness for a nanofluid

Recent core–shell–medium models as a modification of the traditional effective medium theories for explaining the enhanced thermal conductivity of nanofluids are semi-empirical. Generally, the resulting thickness and conductivity of the nanolayer both have to be chosen to match the measured thermal conductivity of the nanofluid. Here, we attempt to find a more systematic procedure to determine the nanolayer thickness and the thermal conductivity profile within the nanolayer. An expression for the nanolayer thickness is derived by manipulation of the three basic heat conduction regions. Comparison of the estimated thermal conductance with known experimental data and thermal diffusion length are made.     

A critical synthesis of thermophysical characteristics of nanofluids

A critical synthesis of the variants within the thermophysical properties of nanofluids is presented in this work. The experimental results for the effective thermal conductivity and viscosity reported by several authors are in disagreement. Theoretical and experimental studies are essential to clarify the discrepancies in the results and in proper understanding of heat transfer enhancement characteristics of nanofluids. At room temperature, it is illustrated that the results of the effective thermal conductivity and viscosity of nanofluids can be estimated using the classical equations at low volume fractions. However, the classical models fail to estimate the effective thermal conductivity and viscosity of nanofluids at various temperatures. This study shows that it is not clear which analytical model should be used to describe the thermal conductivity of nanofluids. Additional theoretical and experimental research studies are required to clarify the mechanisms responsible for heat transfer enhancement in nanofluids. Correlations for effective thermal conductivity and viscosity are synthesized and developed in this study in terms of pertinent physical parameters based on the reported experimental data.     

Effect of thermophysical properties models on the predicting of the convective heat transfer coefficient for low concentration nanofluid

The term of nanofluid refers to a solid–liquid mixture with a continuous phase which is a nanometer sized nanoparticle dispersed in conventional base fluids. In order to study the heat transfer behavior of the nanofluids, precise values of thermal and physical properties such as specific heat, viscosity and thermal conductivity of the nanofluids are required. There are a few well-known correlations for predicting the thermal and physical properties of nanofluids which are often cited by researchers to calculate the convective heat transfer behaviors of the nanofluids. Each researcher has used different models of the thermophysical properties in their works. This article aims to summarize the various models for predicting the thermophysical properties of nanofluids which have been commonly cited by a number of researchers and use them to calculate the experimental convective heat transfer coefficient of the nanofluid flowing in a double-tube counter flow heat exchanger. The effects of these models on the predicted value of the convective heat transfer of nanofluid with low nanoparticle concentration are discussed in detail.     

Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity

In this paper, thermal characteristics of natural convection in a rectangular cavity heated from below with water-based nanofluids containing alumina (Al₂O₃ nanofluids) are theoretically investigated with Jang and Choi’s model for predicting the effective thermal conductivity of nanofluids and various models for the effective viscosity. To validate theoretical results, we compare theoretical results with experimental results presented by Putra et al. It is shown that the experimental results are put between a theoretical line derived from Jang and Choi’s model and Einstein’s model and a theoretical line from Jang and Choi’s model and Pak and Cho’s correlation. In addition, the effects of the volume fraction, the size of nanoparticles, and the average temperature of nanofluids on natural convective instability and heat transfer characteristics of water-based Al₂O₃ nanofluids in a rectangular cavity heated from below are theoretically presented. Based on the results, this paper shows that water-based Al₂O₃ nanofluids is more stable than base fluid in a rectangular cavity heated from below as the volume fraction of nanoparticles increases, the size of nanoparticles decreases, or the average temperature of nanofluids increases. Finally, we theoretically show that the ratio of heat transfer coefficient of nanofluids to that of base fluid is decreased as the size of nanoparticles increases, or the average temperature of nanofluids is decreased.     

Review of convective heat transfer enhancement with nanofluids

Nanofluids are considered to offer important advantages over conventional heat transfer fluids. Over a decade ago, researchers focused on measuring and modeling the effective thermal conductivity and viscosity of nanofluids. Recently important theoretical and experimental research works on convective heat transfer appeared in the open literatures on the enhancement of heat transfer using suspensions of nanometer-sized solid particle materials, metallic or nonmetallic in base heat transfer fluids. The purpose of this review article is to summarize the important published articles on the enhancement of the forced convection heat transfer with nanofluids.     

Numerical Investigation on Conjugate Heat Transfer Performance of Microchannel Using Sphericity-Based Gold and Carbon Nanoparticles

Numerical study has been carried out on the laminar forced convection flow of nanofluids in a wide rectangular microchannel. The flow and heat transfer characteristics of gold and of single-walled carbon (SWCNT) nanofluids are investigated in order to find an efficient and cost-effective heat transfer fluid. The effects of nanoparticle volume concentration and of spherical and cylindrical particulate sizes on the conjugate heat transfer performance of the microchannel are reported. The effective thermal conductivity of a nanofluid is evaluated on the basis of particle sphericity by considering the volume and surface area of the nanoparticles. The average convective heat transfer coefficient increases with increase in Reynolds number and volume concentration. Moreover, sphericity-based thermal conductivity evaluation showed that increasing the length of the SWCNT nanoparticle has significant effect on the heat transfer performance, concluding that axial heat conduction dominates the radial heat conduction within the nanoparticle. The carbon nanofluid is identified as an optimized heat transfer fluid with better heat transfer characteristics in comparison with the gold nanofluid. It also reduces the cost of the working fluid. The variations in the interface temperature between solid and fluid regions are reported for nanofluids with different concentrations at different Reynolds numbers. The diameter and length of the SWCNT nanoparticle show a significant effect on heat transfer characteristics.     

A combined model for the effective thermal conductivity of nanofluids

This paper presents a combined static and dynamic mechanisms-based model for predicting the effective thermal conductivity of nanofluids. The model includes the effects of particle size, nanolayer, Brownian motion, and particle surface chemistry and interaction potential which are the static and dynamic mechanisms responsible for the enhanced effective thermal conductivity of nanofluids. Present model shows reasonably good agreement with the experimental results of several types of nanofluids and gives better predictions compared to the existing models.     

Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids

Heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids is investigated for various pertinent parameters. A model is developed to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion. The transport equations are solved numerically using the finite-volume approach along with the alternating direct implicit procedure. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. The effect of suspended ultrafine metallic nanoparticles on the fluid flow and heat transfer processes within the enclosure is analyzed and effective thermal conductivity enhancement maps are developed for various controlling parameters. In addition, an analysis of variants based on the thermophysical properties of nanofluid is developed and presented. It is shown that the variances within different models have substantial effects on the results. Finally, a heat transfer correlation of the average Nusselt number for various Grashof numbers and volume fractions is presented.     

The Interfacial Layer and the Thermal Conductivity of Nanofluid

Nanofluids are a class of colloidal dispersion of nanosized particles which are found to exhibit anomalous heat conducting properties compared to other conventional heat transfer fluids. Among various factors responsible for this anomaly, the role of nanolayer thickness is found to be quite important. This article includes its effect by suggesting a new exponential form for the profile of thermal conductivity in the interfacial layer. The effect of nanoparticle size, the volume fraction, and the ratio of thermal conductivity of the nanoparticle to the base fluid form part of the discussion. The presented scheme predicts well the enhancement of thermal conductivity of two nanofluids, alumina/EG and CuO/water, used as an example. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 288–296, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21084     

Laminar heat transfer of gas in a parallel‐plate microchannel with one wall temperature constant and the other adiabatic

Based on “wall‐adjacent layer” effect, the convective heat transfer for developed laminar flow of gas through parallel‐plate microchannel with one wall temperature constant and the other adiabatic was analyzed theoretically. Considering the change in thermal conductivity and viscosity of gas in the region adjacent to the solid wall, mathematical models were built and the dimensionless temperature distribution and the corresponding heat transfer characteristics were simulated numerically. The results indicate that the laminar heat transfer coefficient is less than that of the larger passages, while the dimensionless temperature is greater than that of the larger passages. Compared with the monotonous boundary conditions, the varied heat transfer coefficient amplitude of mixed boundary condition is lower. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 58–64, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10075     

Mathematical correlations on factors affecting the thermal conductivity and dynamic viscosity of nanorefrigerants

The past decade has seen the rapid development of nanofluids science in many aspects. In recent years, refrigerant-based nanofluids have been introduced as nanorefrigerants due to their significant effects over heat transfer performance. Recently important theoretical and experimental research works on convective heat transfer appeared in the open literatures on the enhancement of heat transfer using suspensions of nanometer-sized solid particle materials, metallic or nonmetallic in base heat transfer fluids. Suitable models from existing studies have been used to determine the thermal conductivity and viscosity of the nanorefrigerants for the nanoparticle concentrations of 1 to 5 vol.%. In this study, the thermal conductivity of Al₂O₃/R-134a nanorefrigerant increased with the augmentation of particle concentration and temperature however, decreased with particle size intensification. In addition, the results of viscosity of the nanorefrigerant show a significant increment with the increase of volume fractions. Therefore, optimal particle volume fraction is important to be considered in producing nanorefrigerants that can enhance the performance of refrigeration systems.     

Heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the sidewalls

The heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the vertical walls, are investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than a conventional solid–liquid mixture, which implies that all the convective heat transfer correlations available for single-phase flows can be extended to nanoparticle suspensions, provided that the thermophysical properties appearing in them are the nanofluid effective properties calculated at the reference temperature. In this connection, two empirical equations, based on a wide variety of experimental data reported in the literature, are developed for the evaluation of the nanofluid effective thermal conductivity and dynamic viscosity, whereas the other effective properties are evaluated by the conventional mixing theory. The heat transfer enhancement across the differentially heated enclosure that derives from the dispersion of nano-sized solid particles into a host liquid is calculated for different operating conditions, nanoparticle diameters, combinations of suspended nanoparticles and base liquid, and cavity aspect ratios. The fundamental result obtained is the existence of an optimal particle loading for maximum heat transfer. Specifically, for any assigned combination of solid and liquid phases, the optimal volume fraction is found to increase slightly with decreasing the nanoparticle size, and to increase much more remarkably with increasing both the nanofluid average temperature and the slenderness of the enclosure.     

Numerical studies on heat and fluid flow of nanofluid in a partially heated vertical annulus

A numerical investigation on natural convective heat transfer of nanofluid (Al₂O₃+water) inside a partially heated vertical annulus of high aspect ratio (352) has been carried out. The computational fluid dynamics solver Ansys Fluent is used for simulation and results are presented for various volume fraction of nanoparticles (0‐0.04) at different heat flux values (3‐12 kW/m²). Two well‐known correlations for evaluating thermal conductivity and viscosity have been used. Thus different combinations of the available correlations have been set to form four models (I, II, III, and IV). Therefore, a detailed analysis has been executed to identify effects of thermophysical properties on heat transfer and fluid flow of nanofluids using different models. The results show enhancement in heat transfer coefficient with volume fraction of nanoparticles. Highest enhancement achieved is found to be 14.17% based on model III, while the minimum is around 7.27% based on model II. Dispersion of nanoparticles in base fluid declines the Nusselt number and Reynolds number with different rates depending on various models. A generalized correlation is proposed for Nusselt number of nanofluids in the annulus in terms of volume fraction of nanoparticles, Rayleigh number, Reynolds number, and Prandtl number.     

Experimental and theoretical studies of thermal conductivity,viscosity and heat transfer coefficient of titania and alumina nanofluids

Thermal conductivity, viscosity and heat transfer coefficient of water-based alumina and titania nanofluids have been investigated. The thermal conductivity of alumina nanofluids follow the prediction of Maxwell model, whilst that of titania nanofluids is slightly lower than model prediction because of high concentration of stabilisers. None of investigated nanofluids show anomalously high thermal conductivity enhancement frequently reported in literature. The viscosity of alumina and titania nanofluids was higher than the prediction of Einstein–Batchelor model due to aggregation. Heat transfer coefficients measured in nanofluids flowing through the straight pipes are in a very good agreement with heat transfer coefficients predicted from classical correlation developed for simple fluids. Experimental heat transfer coefficients in both nanofluids as well as corresponding wall temperatures agree within ±10% with the values obtained from numerical simulations employing homogeneous flow model with effective thermo-physical properties of nanofluids. These results clearly shows that titania and alumina nano-fluids do not show unusual enhancement of thermal conductivity nor heat transfer coefficients in pipe flow frequently reported in literature.     

A Review on the Mechanisms of Heat Transport in Nanofluids

Due to superior thermal properties and many potential applications, nanofluids have recently attracted the attention of the research community. Though the experiments in nanofluids have revealed the spectacular heat transfer enhancement in them, there are many inconsistencies in the reported experimental values and controversies in the mechanisms proposed for heat transport in nanofluids. This indicates that it is crucial to be aware of the different mechanisms contributing to superior thermal properties of nanofluids and discuss the existing controversies in them. Therefore, in this article, we provide an overview of the various possible mechanisms reported in the literature that contribute to enhanced thermal conductivity of nanofluids. The other factors affecting the nanofluids thermal conductivity and the mathematical models for estimating nanofluids thermal conductivity with their limitations are also discussed.     

Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime

We have measured the pressure drop and convective heat transfer coefficient of water-based Al₂O₃ nanofluids flowing through a uniformly heated circular tube in the fully developed laminar flow regime. The experimental results show that the data for nanofluid friction factor show a good agreement with analytical predictions from the Darcy’s equation for single-phase flow. However, the convective heat transfer coefficient of the nanofluids increases by up to 8% at a concentration of 0.3 vol% compared with that of pure water and this enhancement cannot be predicted by the Shah equation. Furthermore, the experimental results show that the convective heat transfer coefficient enhancement exceeds, by a large margin, the thermal conductivity enhancement. Therefore, we have discussed the various effects of thermal conductivities under static and dynamic conditions, energy transfer by nanoparticle dispersion, nanoparticle migration due to viscosity gradient, non-uniform shear rate, Brownian diffusion and thermophoresis on the remarkable enhancement of the convective heat transfer coefficient of nanofluids. Based on scale analysis and numerical solutions, we have shown, for the first time, the flattening of velocity profile, induced from large gradients in bulk properties such as nanoparticle concentration, thermal conductivity and viscosity. We propose that this flattening of velocity profile is a possible mechanism for the convective heat transfer coefficient enhancement exceeding the thermal conductivity enhancement.