方腔内Cu/Al2O3水混合纳米流体自然对流的格子Boltzmann模拟

纳米流体作为一种较高的导热介质, 广泛应用于各个传热领域. 鉴于纳米颗粒导热系数和成本之间的矛盾, 本文提出了一种混合纳米流体. 为了研究混合纳米流体颗粒间相互作用机理和自然对流换热特性, 在考虑颗粒间相互作用力的基础上, 利用多尺度技术推导了纳米流体流场和温度场的格子Boltzmann方程, 通过耦合流动和温度场的演化方程, 建立了Cu/Al₂O₃水混合纳米流体的格子Boltzmann模型, 研究了混合纳米流体颗粒间的相互作用机理和纳米颗粒在腔体内的分布. 发现在颗粒间相互作用力中, 布朗力远远大于其他作用力, 温差驱动力和布朗力对纳米颗粒的分布影响最大. 分析了纳米颗粒组分、瑞利数对自然对流换热的影响, 对比了混合纳米流体(Cu/Al₂O₃-水)与单一金属颗粒纳米流体(Al₂O₃-水)的自然对流换热特性, 发现混合纳米流体具有更强的换热特性.     

含不同形状内热源的圆管内纳米流体自然对流及换热数值研究

采用格子玻尔兹曼方法对有三种恒温热源(圆形、三角形、方形)参与的圆管内纳米流体(铜-水)自然对流进行数值研究.主要研究瑞利(Ra)数,纳米颗粒体积分数以及热源几何形状等控制参数对纳米流体的流动与传热的影响.结果发现纳米颗粒体积分数的增加有利于强化传热,且在Ra数较小时,平均努塞尔(Nu)数增加的幅度要优于Ra数较大的情...     

Lattice Boltzmann method for nanofluid flow in a porous cavity with heat sources and magnetic field

In this article, Lattice Boltzmann method (LBM) has been applied to investigate the influences of magnetic field and heat sources on water based nanofluid natural convection inside a porous cavity with three square heat sources. Koo–Kleinstreuer–Li (KKL) model is applied to study Brownian motion impact on nanofluid flow. Effects of Rayleigh number (Ra), Darcy number (Da), nanofluid volume fraction (ϕ), and Hartmann number (Ha) on heat transfer characteristics are analyzed. From the obtained results we observe a decrease in the temperature gradient with increasing Ha; while quite the opposite effect is true with increasing Da and Ra. In the absence of magnetic field, for higher values of Darcy and Rayleigh numbers, thermal plumes are generated and the temperature gradient is enhanced. Moreover, small eddies are generated near the vertical centerline. However, in the presence of magnetic field, the number of thermal plumes decreases.     

Non-Darcy free convection of Fe3O4-water nanoliquid in a complex shaped enclosure under impact of uniform Lorentz force

Effect of Lorentz forces on natural convection in a complex shaped cavity filled with nanoliquid immersed in porous medium is investigated by means of Control volume based finite element method (CVFEM). Non Darcy model is taken into account for porous media. The working fluid is Fe₃O₄ –water and its viscosity considered as function of magnetic field. Figures are illustrated for different values of Darcy number (Da), Fe₃O₄ -water volume fraction (?), Rayleigh (Ra) and Hartmann (Ha) numbers. Results depict that enhancing in Lorentz forces results in reduce in nanofluid motion and increase the thickness of thermal boundary. Convective heat transfer enhances with rise of Darcy number.     

Numerical modeling of nanofluid flow and heat transfer in a quartered gearwheel-shaped heat exchanger using FVM

The numerical modeling of natural convection fluid flow and heat transfer in a quarter of gearwheel-shaped heat exchanger is carried out. The heat exchanger is included with internal active square bodies. These bodies have hot and cold temperatures with different thermal arrangements. Three different thermal arrangements are considered and showed with Case A, Case B and Case C. The CuO-water nanofluid is selected as operating fluid. The Koo-Kleinstreuer-Li (KKL) correlation is utilized to estimate the dynamic viscosity and thermal conductivity. In addition, the shapes of nanoparticles are taken account in the analysis. The Rayleigh number, nanoparticle concentration and thermal arrangements of internal active bodies are the governing parameters. The impacts of these parameters on the fluid flow, heat transfer rate, local and total entropy generation and heatlines are studied, comprehensively. The results show that the heat transfer rate enhances with increasing of Rayleigh number and nanoparticle concentration. Moreover, the thermal arrangement of internal active bodies has considerable effect on the heat transfer between heat sources and heat sinks. On the other hand, the total entropy generation enhances and decreases with increasing of Rayleigh number and nanoparticle concentration, respectively.     

Transient electrohydrodynamic convective flow and heat transfer of MWCNT - Dielectric nanofluid in a heated enclosure

A computational research was performed to analyze the electrohydrodynamic (EHD) convective heat transfer in a differentially heated dielectric-MWCNT nanofluid layer. The study was conducted on a square enclosure subjected to a temperature gradient between these two vertical walls as well as a potential difference between these horizontal walls. The enclosure was filled with MWCNT oil-based nanofluid; the MWCNT nanoparticles were dispersed in a perfectly insulating thermal oil with a volume fraction of hardly exceeded 0.4%. The governing equations were derived with the assumption of homogeneous nanofluid and were solved with employing finite volume method. Based on the obtained results, it was found that the increase of Rayleigh number, electric Rayleigh number and nanoparticle concentration enhanced the heat transfer. For high thermal and electric Rayleigh number values, the flow and heat transfer became time dependent and accordingly a frequency study was also performed. It was found that the inclusion of an electric field with the addition of nanoparticles led to a significant heat transfer enhancement of about 43%.     

Laminar free convection heat transfer between vertical isothermal plates

The paper represents results on numerical investigation of flow and heat transfer between two isothermal vertical plates under laminar natural convection. A system of complete Navier–Stokes equations is solved for a two-dimensional gas flow between the plates along with additional rectangular regions (connected to inlet and outlet sections), whose characteristic sizes are much greater than the spacing between the plates. The calculations were performed over very wide ranges of Rayleigh number Ra = 10 ÷ 10⁵ and a relative channel length AR = L/w = 1 ÷ 500. The influence of the input parameters on the gas-dynamic and thermal structure of thermogravitational convection, the local and mean heat transfer, and also the gas flow rate between the plates (convective draft. We determined sizes of the regions and regime parameters when the local heat flux on the walls tends to zero due to the gas temperature approach to the surface temperature. It is shown that the mean heat transfer decreases as the relative channel length AR grows, whereas the integral gas flow rate (convective draft) and Reynolds number in the channel Re = 2wUm/ν increase. The use of a modified Rayleigh number Ra* = Ra · (w/L) (Elenbaas number) leads to generalization of calculation data on mean heat transfer. These data are in good agreement with the correlations for heat transfer [1, 2] and gas flow rate [3]. The reasons of variation of the data in the range of low Rayleigh numbers are discussed in detail.     

Flow and heat transfer of a hybrid nanofluid past a permeable moving surface

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al₂O₃) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Numerical simulation of turbulent natural convection of oxide heat generating melt in a core catcher at NPP with VVER-1000

The problem statement and simulation results are presented concerning turbulent natural convection in a vertical cylindrical molten pool with internal heat generation and other parameters (inner Rayleigh number Ra _i ∼ 10¹⁶–10¹⁷) corresponding to oxide core melt in a core catcher for NPP with VVER-1000. Commercial code FLUENT 6.3 was used for CFD calculations. The results on heat transfer are approximated by power law correlations for mean Nusselt numbers vs. Rayleigh number and pool height, describing the heat transfer at upper, lateral, and total boundaries of the cylinder. The influence of volumetric heat generation and material properties is studied. Spatial distribution of wall heat transfer is analyzed for different pool heights possible in the real core catcher. Along with serial calculations with isothermal boundary conditions, the cases with heat radiation conditions are considered. The results may be used for estimations of heat transfer and melt overheating in a VVER core catcher and for coefficient identification of simplified models of integrated system severe-accident codes.     

The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump

The forced convection of nanofluid flow in a long microchannel is studied numerically according to the finite volume approach and by using a developed computer code. Microchannel domain is under the influence of a magnetic field with uniform strength. The hot inlet nanofluid is cooled by the heat exchange with the cold microchannel walls. Different types of nanoparticles such as Al₂O₃ and Ag are examined while the base fluid is considered as water. Reynolds number are chosen as Re=10 and Re=100. Slip velocity and temperature jump boundary conditions are simulated along the microchannel walls at different values of slip coefficient for different amounts of Hartmann number. The investigation of magnetic field effect on slip velocity and temperature jump of nanofluid is presented for the first time. The results are shown as streamlines and isotherms; moreover the profiles of slip velocity and temperature jump are drawn. It is observed that more slip coefficient corresponds to less Nusselt number and more slip velocity especially at larger Hartmann number. It is recommended to use Al₂O₃-water nanofluid instead of Ag-water to increase the heat transfer rate from the microchannel walls at low values of Re. However at larger amounts of Re, the nanofluid composed of nanoparticles with higher thermal conductivity works better.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

Flow and heat transfer over a rotating porous disk in a nanofluid

The steady flow of an incompressible viscous fluid due to a rotating disk in a nanofluid is studied. The transformed boundary layer equations are solved numerically by a finite difference scheme, namely the Keller-box method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction parameter φ and suction/injection parameter h₀. Two models for the effective thermal conductivity of the nanofluid, namely the Maxwell-Garnett model and the Patel model, are considered. It is found that for the Patel model, the heat transfer rate at the surface increases for both suction and injection, whereas different behaviors are observed for the Maxwell-Garnett model, i.e. increasing the values of φ leads to a decrease in the heat transfer rate at the surface for suction, but increases for injection. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Study of heat transfer in a horizontal cylinder with fins

The purpose of this paper is to investigate, numerically, the effect of internal fins on the flow pattern, temperature distribution and heat transfer between concentric horizontal cylinders. A Galerkin finite element method is adopted for the discretization of the governing equations. The numerical procedure consists in solving series of transient problems of increasing Ra. Results are presented using air (Pr = 0.7) with Rayleigh numbers ranging from 10³ to 10⁶ for different fin configurations (1 and 2), geometries (sharp, round and divergent tip) and lengths (l = 0.25, 0.5 and 0.75). They are illustrated in terms of isotherms, velocity fields, Nusselt numbers and fin efficiencies. Configuration 2 presents a heat transfer rate 10% above that of configuration 1, at Ra = 10⁶. The heat transfer is about the same for the three geometries, but the best fin efficiency is associated with the fin with a round tip.     

Experimental quantification of natural convective heat transfer within annulus space filled with a H2O-Cu nanofluid saturated porous medium. Application to electronics cooling

This experimental study deals with cooling electronics contained in a hemispherical cavity whose cupola is maintained isothermal, being its base inclined at an angle varying from 0° (horizontal disc with the cupola oriented upwards) to 135°. The active component is a dome centered on this base. The space between the differentially heated elements of the assembly is filled with a porous medium of high porosity saturated by a water–copper nanofluid whose volume fraction varies between 0% (pure water) and 7%. The Rayleigh number based on the radius of the cupola reaches high values up to 7.29 × 10¹⁰ given the important surface heat flux generated by the device during operation. The ratio between the thermal conductivity of the solid matrix and that of the base fluid ranges between 0 (interstitial volume without porous medium) and 41.4 corresponding to the intended applications. This experimental study done with an industrial prototype at scale 1 quantifies the natural convective heat transfer via the Nusselt number determined for many configurations obtained by varying the solid-fluid thermal conductivity ratio, the inclination angle, the Rayleigh number, and the volume fraction. The study clearly shows that the cooling performance of the Cu-H₂O nanofluid degrades with its age and the number of times it has been used. Analysis of the results reproducibility also proves the irreversibility of the performance. The measured values were compared with those obtained in a recent numerical study based on the volume control method. The observed deviations taking into account the experimental uncertainty margins validate the mathematical model implemented in the numerical approach.     

Nanofluid MHD natural convection through a porous complex shaped cavity considering thermal radiation

Control volume based finite element method (CVFEM) is applied to simulate H₂O based nanofluid radiative and convective heat transfer inside a porous medium. Non-Darcy model is employed for porous media. Influences of Hartmann number, nanofluid volume fraction, radiation parameter, Darcy number, number of undulations and Rayleigh number on nanofluid behavior were demonstrated. Thermal conductivity of nanofluid is estimated by means of previous experimental correlation. Results show that Nusselt number enhances with augment of permeability of porous media. Effect of Hartmann number on rate of heat transfer is opposite of radiation parameter.     

Using nanofluid saturated porous media to enhance free convective heat transfer around a spherical electronic device

The thermophysical properties of the nanofluid saturated porous media are used in this work to optimize the thermal design of a spherical electronic device. Quantification of free convective heat transfer has been numerically determined by means of the finite volume method using the SIMPLE algorithm. The Rayleigh number based on the component diameter and water characteristics varies between 6.5x10⁶ and 1.32x10⁹, given the power generated during operation of this active component. The latter is disposed in the center of another sphere maintained isothermal. Its cooling is achieved by means of a porous medium saturated with a water based - Copper nanofluid whose volume fraction varies between 0 (pure water) and 10%. The thermal conductivity of the porous material's matrix ranges from 0 to 40 times that of the base fluid (water). Results of this work show that convective heat transfer systematically increases with this ratio according to a function depending on the Rayleigh number in the whole range of the considered volume fraction. The average Nusselt number also increases with the Rayleigh number according to a conventional power type law while influence of the fraction volume is moderate in the 2-10% range. The results are in agreement with those of previous works for particular thermal conditions. In order to optimize the thermal design of this electronic device, a correlation is proposed, allowing determination of the Nusselt number for any combination of the three influencing parameters for applications in various engineering fields, includind electronics.     

Unsteady radiative nanofluid flow near a vertical heated wavy surface with temperature-dependent viscosity

In the present contribution, a numerical treatment is provided to describe unsteady nanofluid flow near a vertical heated wavy surface. A memorable feature of the present work is the investigation of nanofluid flow associated with thermal radiation that acts as a catalyst for heat transfer rates. Likewise, the effectiveness of variable viscosity is examined as it controls fluid flow as well as heat transfer. It is necessary to study heat and mass transfer for complex geometries because predicting heat and mass transfer for irregular surfaces is a topic of fundamental importance, and irregular surfaces frequently appear in many applications, such as flat-plate solar collectors and flat-plate condensers in refrigerators. A simple coordinate transformation from the wavy surface into a flat one is employed. The non-dimensional boundary layer equations that governing both heat transfer and nanofluid flow phenomena along the wavy surface are solved via a powerful numerical approach called the implicit Chebyshev pseudospectral (ICPS) method with Mathematica code. A comparison graph of the current numerical computation and the published data shows a perfect match. Figures depict the effect of various physical parameters on nanofluid velocities, temperature, salt concentration, nanoparticle concentration, skin friction, Sherwood, nanoparticle Sherwood, and Nusselt numbers. According to the numerical results, increasing the variable viscosity parameter value causes a drop in the local skin friction coefficient value and an increase in the steady-state axial nanofluid velocity profile near the wavy surface. Furthermore, as heat radiation is increased, the local Nusselt number decreases but the nanoparticle Sherwood number increases.     

Simulation of COPO II Lo experiments on natural convection of heat generating liquid at high Rayleigh numbers

The methodology is described and the results are presented concerning numerical modeling of COPO II Lo experiments on heat transfer in liquid with internal heat generation at very high internal Rayleigh numbers typical for natural convection in a core melt that can appear during progress of severe accident at a nuclear power plant (NPP). The work is keeping in the course of development of CFD-based tool for quantitative analysis of heat transfer in a stratified molten pool of different configurations possible in severe accident scenarios with melt retention in the reactor vessel or in the VVER core catcher. Such CFD methodology would be used for testing of simplified correlation models for simulation of the core melt interaction with NPP structures in system code SOCRAT. During verification the available experimental data on the core melt thermohydraulics were analyzed, and it was concluded that they are insufficient to measures of CFD quality. The data uncertainties, along with the complexities of convective flow, uncertainties of the reactor core melt conditions, limitations of experimental possibilities and of turbulence modeling, actually constrain the multivariate CFD simulations of natural convection at very high Rayleigh numbers. RANS turbulence models only can be efficiently applied here, and they are to be checked for such purposes. In a series of numerical modeling of COPO II Lo experiments and some others, availability of a k-? realizable model with included buoyancy effects was estimated, and the optimal set of CFD options was formed for minimizing numerical artifacts. It was demonstrated that in the investigated range of Rayleigh numbers the k-? model works qualitatively correctly, but is inclined to systematical deformation of the melt boundary heat transfer distribution. This allows one to use this model for qualitative multivariate CFD estimations but requires improvement of the model or finding of its efficient and more exact equivalent.     

Experimental Study of Nanofluid Convective Heat Transfer for Implementation of Dispersion Model Considering Non-Uniform Particle Distribution

Thermal dispersion model has been used here to simulate heat transfer of water–Al₂O₃ nanofluid. A new form for dispersion thermal conductivity has been introduced in which non-uniform concentration distribution is applied on the model. It was observed that the non-uniformity of concentration increases at greater Reynolds numbers and average concentrations. An experimental set-up was made, and an experimental study was conducted to find the empirical coefficient in the dispersion thermal conductivity. The obtained results show that the developed dispersion model is able to properly simulate heat transfer of the nanofluid and provides more accurate results in comparison with a homogenous model.     

Numerical study of heat transfer enhancement of counter nanofluids flow in rectangular microchannel heat exchanger

This paper reports a numerical analysis of the performance of a counter-flow rectangular shaped microchannel heat exchanger (MCHE) using nanofluids as the working fluids. Finite volume method was used to solve the three-dimensional steady, laminar developing flow and conjugate heat transfer in aluminum MCHE. The nanofluids used were Ag, Al₂O₃, CuO, SiO₂, and TiO₂ and the performance was compared with water. The thermal, flow fields and performance of the MCHE were analyzed using different nanofluids, different Reynolds numbers and different nanoparticle concentrations. Temperature profile, heat transfer coefficient, pressure profile, and wall shear stress were obtained from the simulations and the performance was discussed in terms of heat transfer rate, pumping power, effectiveness, and performance index. Results indicated enhanced performance with the usage of nanofluids, and slight penalty in pressure drop. The increase in Reynolds number caused an increase in the heat transfer rate and a decrease in the overall bulk temperature of the cold fluid. The increase in nanoparticle concentration also yielded better performance at the expense of increased pressure drop.