Natural Convection Of Nanofluid Research Articles

Heatline analysis on natural convection for nanofluids confined within square cavities with various thermal boundary conditions

Natural convection of nanofluids in presence of hot and cold side walls (case 1) or uniform or non-uniform heating of bottom wall with cold side walls (case 2) have been investigated based on visualization of heat flow via heatfunctions or heatlines. Galerkin finite element method has been employed to solve momentum and energy balance as well as post processing streamfunctions and heatfunctions. Various nanofluids are considered as Copper–Water, TiO2–Water and Alumina–Water. Enhancement of heat transfer with respect to base fluid (water) has been observed for all ranges of Rayleigh number (Ra). Dominance of viscous force or buoyancy force are found to play significant roles to characterize the heat transfer rates and temperature patterns which are also established based on heatlines. In general, convective closed loop heatlines are present even at low Rayleigh number (Ra=103) within base fluid, but all nanofluids exhibit dominant conductive heat transport as the flow is also found to be weak due to dominance of viscous force for case 1. On the other hand, convective heat transport at the core of a circulation cell, typically represented by closed loop heatlines, is more intense for nanofluids compared to base fluid (water) for case 2 at Ra=105. It is also found that heatlines with larger heatfunctions values for nanofluids coincide with heatlines with smaller heatfunction values for water at walls. Consequently, Nusselt number which is also correlated with heatfunctions show larger values of nanofluids for all ranges of Ra. Average Nusselt numbers show that larger enhancement of heat transfer rates for all nanofluids at Ra=105 and Alumina–Water and Copper–Water exhibit larger enhancement of heat transfer rates.

Natural convection in nanofluids: Are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement?

Natural convection heat transfer and fluid flow of CuO–Water nanofluids is studied using the Rayleigh–Bénard problem. A two component non-homogenous equilibrium model is used for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. Variable thermal conductivity and variable viscosity are taken into account in this work. Finite volume method is used to solve governing equations. Results are presented by streamlines, isotherms, nanoparticle distribution, local and mean Nusselt numbers and nanoparticle profiles at top and bottom side. Comparison of two cases as absence of Brownian and thermophoresis effects and presence of Brownian and thermophoresis effects showed that higher heat transfer is formed with the presence of Brownian and thermophoresis effect. In general, by considering the role of thermophoresis and Brownian motion, an enhancement in heat transfer is observed at any volume fraction of nanoparticles. However, the enhancement is more pronounced at low volume fraction of nanoparticles and the heat transfer decreases by increasing nanoparticle volume fraction. On the other hand, by neglecting the role of thermophoresis and Brownian motion, deterioration in heat transfer is observed and this deterioration elevates by increasing the volume fraction of nanoparticles.

Nanofluid multi-phase convective heat transfer in closed domain: Simulation with lattice Boltzmann method

The lattice Boltzmann method is applied to simulate the thermal field and flow field of nanofluid natural convection in a square cavity. The heat transfer characteristics of nanofluid are compared with that of water to explore nanofluid heat transfer mechanism. The flow field shows different characters at different Rayleigh number and the average Nusselt number is obtained changing with Rayleigh number.

Natural Convection of Nanofluids in a Square Enclosure with a Protruding Heater

This paper reports a numerical study on natural convection from a protruding heater located at the bottom of a square cavity filled with a copper-water nanofluid. The vertical walls of the cavity are cooled isothermally; the horizontal ones are adiabatic, and the heater is attached to the bottom wall. The heat source is assumed either to be isothermal or to have a constant heat flux. The effective viscosity and thermal conductivity of the nanofluid are modeled according to Brinkman and Patel, respectively. Numerical solutions of the full-governing equations, based on the lattice Boltzmann method, are obtained for a wide range of the governing parameters: the Rayleigh number, Ra; the Prandtl number, Pr; the geometrical parameters specifying the heater; the volume fraction of nanoparticles, Φ. For a particular geometry, it has been found that, for a given Ra, heat transfer is enhanced with increasing Φ, independently of the thermal boundary condition applied on the heater.

Analytical and numerical study of buoyancy-driven convection in a vertical enclosure filled with nanofluids

This paper presents an analytical and numerical study of natural convection of nanofluids contained in a rectangular enclosure subject to uniform heat flux along the vertical sides. Governing parameters of the problem under study are the thermal Rayleigh number Ra, the Prandtl number Pr, the aspect ratio of the cavity A and the solid volume fraction of nanoparticles, Φ. Three types of nanoparticles are taken into consideration: Cu, Al2O3 and TiO2. Various models are used for calculating the effective viscosity and thermal conductivity of nanofluids. In the first part of the analytical study, a scale analysis is made for the boundary layer regime situation. In the second part, an analytical solution based on the parallel flow approximation is reported for tall enclosures (A ≫ 1). In the boundary layer regime a good agreement is obtained between the predictions of the scale analysis and those of the analytical solution. Solutions for the flow fields, temperature distributions and Nusselt numbers are obtained explicitly in terms of the governing parameters of the problem. A numerical study of the same phenomenon, obtained by solving the complete system of the governing equations, is also conducted. A good agreement is found between the analytical predictions and the numerical simulations.

Rayleigh-Bénard convection in nanofluids: Effect of temperature dependent properties

In this work, heat transfer enhancement using CuO-water nanofluids in natural convection using the Rayleigh-Bénard convection problem is investigated. The main focus of the current study is on the effects of variable thermal conductivity and variable viscosity of nanofluids on heat transfer enhancement in natural convection. The results are presented over a wide range of Rayleigh numbers (Ra = 10 3–10 6) and volume fractions of nanoparticles (0 ≤ φ ≤ 9%). For Ra > 10 3, and using the variable properties of nanofluid, the average Nusselt number was reduced by increasing the volume fraction of nanoparticles. However, for Ra = 10 3, the average Nusselt number was enhanced by increasing the volume fraction of nanoparticles. To study the significance of effects of temperature dependence of viscosity and thermal conductivity of nanofluid, the results obtained by using variable properties of nanofluid are compared with those based on constant property simulations and it was found that the temperature influence is small compared to the influence of high viscosity brought by the presence of high concentration of nanoparticles. The variable thermal conductivity and variable viscosity models were compared to both the Maxwell-Garnett (MG) model and the Brinkman model. It was found that for Ra > 10 3 the average Nusselt number was much more sensitive to the viscosity models than to the thermal conductivity models.

Natural convection of nanofluids in a shallow rectangular enclosure heated from the side

AbstractThis article reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with nanofluids. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure while the two horizontal ones are assumed insulated. Three types of nanoparticles are taken into consideration: Cu, Al2O3and TiO2. Various models are used for calculating the effective viscosity and thermal conductivity of nanofluids. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number Pr, the aspect ratio of the cavity,Aand the solid volume fraction of nanoparticles, Φ. In the first part of the analytical study a scale analysis of the present problem is made. In the second part analytical solutions are obtained, in the limit of an infinite layer ($A\gg 1$), for the stream function and temperature fields. The analytical model relies on the assumption of a parallel flow approximation in the core region of the cavity and an integral form of the energy equation in the end regions. In the high Rayleigh number regime a good agreement is obtained between the predictions of the scale analysis and those of the analytical solution. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations based on the lattice Boltzmann method.Cet article présente une étude analytique et numérique de la convection naturelle dans une cavité rectangulaire peu profonde remplie de nanofluides. Les conditions aux limites de Neumann pour la température sont appliquées sur les parois verticales de l'enceinte tandis que les deux parois horizontales sont supposées isolées. Trois types de nanoparticules sont pris en considération: Cu, Al2O3et TiO2. Divers modèles sont utilisés pour le calcul de la viscosité et la conductivité thermique effective du nanofluide. Les paramètres régissant le problème sont le nombre de Rayleigh thermique, Ra, le nombre de Prandtl Pr, le facteur de forme de la cavité, A et la fraction volumique de nanoparticules solides, phi. Dans la première partie de l'étude analytique une analyse d'échelle du problème est réalisée. Dans la deuxième partie les solutions analytiques sont obtenues, dans la limite d'une couche infinie, pour la fonction de courant et les champs de température. Le modèle de la solution repose sur l'hypothèse de l'écoulement parallèle dans la région centrale de la cavité et sur un bilan de conservation d'énergie dans les extrémités. Pour des nombres de Rayleigh assez élevés un bon accord est obtenu entre les prédictions de l'analyse d'échelle et ceux de la solution analytique. Des solutions numériques des équations complètes sont obtenues pour une large gamme des paramètres de contrôle. Un bon accord est observé entre le modèle analytique et les simulations numériques basées sur la méthode de Lattice Boltzmann. © 2011 Canadian Society for Chemical Engineering

비정상열선법을 이용한 나노유체 열전도도 측정 시 자연대류 개시점에 대한 연구

We perform a numerical study to determine the time of onset of natural convection in a transient hot wire (THW) device for measuring the thermal conductivity of nanofluids. The samples used in this simulation are water-based Al2O3 nanofluids with volume fractions of 1%, 4%, and 10%, and the properties are calculated by theoretical models and experimental correlations. The THW apparatus using coated wire is modeled by the control-volume-based finite difference method, and the start of natural convection is determined by observing the temperature rise of the wire under a gravity field. The onset time is 11.5 s for water and 41.6 s for water-based Al2O3 nanofluids predicted by Maxwell thermal conductivity model with a 10% volume fraction. We confirm that the onset time of natural convection of nanofluids in the cylinder increases with the nanoparticle volume fraction. We suggest a correlation for predicting the onset time on the basis of the numerical results. Finally, it is shown that the measurement error due to natural convection is negligible if the measurement using the transient hot wire method is completed before the onset of natural convection in the base fluid.

Numerical Analysis of Al2O3/Water Nanofluids Natural Convection in a Wavy Walled Cavity

In the present work, heat transfer enhancement of Al2O3-water nanofluids in natural convection applied to differentially heated wavy cavities is investigated numerically. The governing equations are written in stream function-vorticity form and solved by using the finite volume technique. The effective thermal conductivity and viscosity of the nanofluid are approximated by the Maxwell–Garnetts and Brinkman models, respectively. The solutions are presented by streamlines, isotherms, local and mean Nusselt numbers, and velocity profiles for different Rayleigh numbers (103 ≤ Ra ≤ 105), amplitude of wavy wall (0.85 ≤ a ≤ 1.1), and different volume fraction of nanofluids (ϕ = 0.05 and 0.1). It is observed that the addition of a nanoparticle of Al2O3 into the base fluid increases the mean Nusselt number. It is also more effective on flow field than that of temperature distribution. The geometry parameter or surface waviness can be decided to heat transfer regime even for the same Rayleigh number.

Natural convection of nanofluids in a shallow cavity heated from below

This paper reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with nanofluids. Neumann boundary conditions for temperature are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed insulated. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number Pr, the aspect ratio of the cavity, A and the solid volume fraction of nanoparticles, Φ . For convection in an infinite layer ( A ≫ 1 ) , analytical solutions for the stream function and temperature are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical convection of nanofluids is predicted explicitly by the present model. Furthermore, a linear stability analysis of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat transfer is presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations.

Combined thermophoresis, Brownian motion and Dufour effects on natural convection of nanofluids

The objective of the present work is to investigate theoretically the basics of natural convection heat transfer of nanofluids. On this regard thermophoresis of nanoparticles and the Dufour effect on natural convective heat transfer on nanofluids are investigated simultaneously. Positive thermophoresis implies that nanoparticles move from a hot wall to a cold wall and the Dufour effect implies that heat transfer will induce by volume fraction gradients. By using simple formulation the combined effects of Brownian motion and thermophoresis are considered to get the volume fraction distribution and its difference between hot and cold walls. Having volume fraction gradient of nanofluid, the implication of Dufour effect on the variation of heat transfer and Nusselt number of natural convection is computed. For approximate conditions closed form expression is derived to estimate Nusselt number of natural convection heat transfer for different volume fractions based on the pure water (base fluid) Nusselt number. This expression is used to predict natural convective Nusselt number for three kinds of nanofluids related to three experimental measurements of other investigators and also compared to the most recent theoretical developments. Good agreements are observed between experimental results and the present estimation due to the Dufour effect and similar trends are found by comparing with theoretical computations.

Experimental Studies of Natural Convection Heat Transfer of Al2O3/DI Water Nanoparticle Suspensions (Nanofluids)

The natural convection heat transfer characteristics of [Formula: see text] nanofluids comprised of 47 nm, [Formula: see text] and water, with volume fractions ranging from 0.5% through 6%, has been investigated through a set of experimental measurements. The temperature of the heated surface and the Nusselt number of different volume fractions of [Formula: see text] nanofluids natural convection tests clearly demonstrated a deviation from that of pure base fluids (distilled water). In the investigation, a deterioration of the natural convection heat transfer coefficient was observed with increases of the volume fraction of the nanoparticles in the nanofluids. The deterioration phenomenon was further investigated through a visualization study on a 850 nm diameter polystyrene particle/water suspension in a bottom heating rectangular enclosure. The influence of particle movements on the heat transfer and natural flow of the polystyrene particle/DI water suspension were filmed, and the temperature changes on the heating and cooling surfaces were recorded. The results were analyzed in an effort to explain the causes of the natural convection heat transfer deterioration of the 47 nm [Formula: see text] nanofluids observed in the experiments. The visualization results confirmed the natural convective heat transfer deterioration, and further explained the causes of the deterioration of the nanofluids natural convective heat transfer.

Nanofluids natural convection heat transfer in horizontal annulus

The effect of using nanoparticles on natural convection heat transfer in horizontal cylindrical annuli was investigated numerically using finite volume technique together with SIMPLE algorithm for Do/Di = 2 and 1.25. Aluminium oxide (Al2O3) nanoparticles in water as base fluid were used in the current investigation. Laminar conditions up to Rayleigh number Ra of 109 were investigated for 0%, 1% and 4% nanoparticle concentrations. The results indicated that nanoparticles can increase heat transfer in the conduction dominated regime while it decreases it in the convection dominated regime.

Instability of Nanofluids in Natural Convection

Abstract Instability of natural convection in nanofluids is investigated in this work. As a result of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be much lower, by one to two orders of magnitude, as compared to that for regular fluids. The highly promoted turbulence, in the presence of nanoparticles for as little as 1% in volume fraction, significantly enhances heat transfer in nanofluids, which may be much more pronounced than the enhancement of the effective thermal conductivity alone. Seven dominating groups are extracted from the nondimensional analysis. By extending the method of eigenfunction expansions in conjunction with the method of weighted residuals, closed-form solutions are derived for the Rayleigh number to justify such remarkable change by the nanoparticles at the onset of instability.

Thermal instability of nanofluids in natural convection

Thermal (Bénard) instability in nanofluids is investigated in this work. Emphasizing the combined behaviors of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be lower by one to two orders of magnitude than that for regular fluids. The highly promoted turbulence increases the energy bearing capacity of nanofluids, which could result in higher overall heat transfer coefficient than the increase of the effective thermal conductivity alone. The dominating groups are extracted from the nondimensional analysis. Close form solutions for the Rayleigh number are derived from the method of eigenfunction expansions and the weighted residual method.

A note on heat transfer modelling of Newtonian nanofluids in laminar free convection

The natural convection heat transfer of Newtonian nanofluids in a laminar external boundary-layer is investigated from the integral formalism approach. In particular, this study deals with γ-Al 2O 3/water nanofluids whose Newtonian behaviour was experimentally confirmed for particle volume fractions less than 4% [N. Putra, W. Roetzel, S.K. Das, Natural convection of nano-fluids, Heat and Mass Transfer 39 (2003) 775–784; S.Z. Heris, S.Gh. Etemad, M.N. Esfahany, Experimental investigation of oxide nanofluids laminar flow convective heat transfer, Int. Comm. Heat Mass Transfer 33 (2006) 529–535; R. Prasher, D. Song, J. Wang, Measurements of nanofluid viscosity and its implications for thermal applications, Appl. Phys. Lett. 89 (2006) 133108]. Based on a macroscopic modelling and under the assumption of constant thermophysical nanofluid properties, it is shown that special care has to be exercised in drawing generalized conclusions about the heat transfer enhancement with the use of nanofluids. It has been found that natural convection heat transfer is not solely characterized by the nanofluid effective thermal conductivity and that the sensitivity to the viscosity model used seems undeniable and plays a key role in the heat transfer behaviour.

Natural convection of nano-fluids

Fluids with nano size solid particles suspended in them have been given the name nano-fluid which in recent studies have shown tremendous promise as heat transfer fluids. However, before suggesting such fluids for applications a thorough knowledge of physical mechanism of heat transfer in such fluids is wanted. The present study deals with one such aspect of natural convection of nano fluids inside horizontal cylinder heated from one end and cooled from the other. An apparently paradoxical behaviour of heat transfer deterioration was observed in the experimental study. Nature of this deterioration and its dependence on parameters such as particle concentration, material of the particles and geometry of the containing cavity have been investigated. The fluid shows characters distinct from that of common slurries.