Buoyancy induced flow in a nanofluid filled enclosure partially exposed to forced convection

A numerical study was performed on natural convection for water–CuO nanofluid filled enclosure where the top surface was partially exposed to convection. The cavity has a square cross-section and differentially heated. Except exposed convection part on the top, all sides are adiabatic on horizontal walls. Effects of Rayleigh number (10³ ? Ra ? 10⁵), Biot number (0 ? Bi ? ∞), length of partial convection (0.0 ? L ? 1.0) and volume fraction of nanoparticles (0.0 ? φ ? 0.1) on heat and fluid flow were investigated. The results showed that for the case of high Biot number that heat transfer along the heated was enhanced by increasing the Rayleigh number mainly at the upper portion of the heated wall. When the top wall was totally exposed to convection, the results prevail that the heat transfer was more effective at high Biot number especially at the upper portion of the heated wall. For the case of high Biot number, the results prevailed that the heat transfer at the upper portion of the heated wall increases considerably at high exposed length to convection (L); however, for L ? 0.75 the effect of L was less pronounced. Contour maps for percentage of heat transfer enhancement were presented and it was shown that the location of maximum enhancement in heat transfer was sensitive to Ra, φ and L.     

Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid

Mixed convection flow of Cu–water nanofluid inside a lid-driven square cavity with adiabatic horizontal walls and sinusoidal heating on sidewalls has been investigated numerically. The effects of increase in shear force for a fixed buoyancy force and effects of increase in buoyancy force for a fixed shear force were investigated. Effects of variations of Richardson number, phase deviation of sinusoidal heating, and volume fraction of nanoparticles on flow and temperature field were studied. The obtained results showed that for a constant Grashof number at all Richardson numbers, a clockwise eddy was developed inside the cavity, also the rate of heat transfer increases with decrease in Richardson number and increase of volume fraction of nanoparticles. For a constant Reynolds number the clockwise eddy is observed up to Ri = 1. For Ri = 10 a multicellular flow pattern is formed inside the cavity. Moreover it was found that when the Reynolds number is kept constant, the rate of heat transfer increases with increase in Richardson number.     

Numerical investigation of natural convection heat transfer of nanofluids in a Γ shaped cavity

This paper analyzes the heat transfer and fluid flow of natural convection in a Γ shaped enclosure filled with Al₂O₃/Water nanofluid that operates under differentially heated walls. The Navier–Stokes and energy equations are solved numerically. Heat transfer and fluid flow are examined for parameters of non-uniform nanoparticle size, mean nanoparticle diameter, nanoparticle volume fraction, Grashof number and different geometry of enclosure. Finite volume method is used for discretizating positional expressions, and the forth order Rung-Kuta is used for discretizating time expressions. Also an artificial compressibility technique was applied to couple continuity to momentum equations. Results indicate that using nanofluid causes an increase in the heat transfer and the Nusselt number so that for R = 0.001 in Gr = 10³, the Nusselt number 25%, in Gr = 10⁴ 26%, and in Gr = 10⁵ 28% increases. Furthermore; by decreasing the mean diameters of nanoparticles, Nusselt number increases. By increasing R parameter (d_p,min/d_p,max) and nano particle volume fraction, Nusselt number increases.     

Thermal Lattice Boltzmann Flux Solver for Natural Convection of Nanofluid in a Square Enclosure

In the present study, mathematical modeling was performed to simulate natural convection of a nanofluid in a square enclosure using the thermal lattice Boltzmann flux solver (TLBFS). Firstly, natural convection in a square enclosure, filled with pure fluid (air and water), was investigated to validate the accuracy and performance of the method. Then, influences of the Rayleigh number, of nanoparticle volume fraction on streamlines, isotherms and average Nusselt number were studied. The numerical results illustrated that heat transfer was enhanced with the augmentation of Rayleigh number and nanoparticle volume fraction. There was a linear relationship between the average Nusselt number and solid volume fraction. and there was an exponential relationship between the average Nusselt number and Ra. In view of the Cartesian grid used by the immersed boundary method and lattice model, the immersed boundary method was chosen to treat the no-slip boundary condition of the flow field, and the Dirichlet boundary condition of the temperature field, to facilitate natural convection around a bluff body in a square enclosure. The presented numerical algorithm and code implementation were validated by means of numerical examples of natural convection between a concentric circular cylinder and a square enclosure at different aspect ratios. Numerical simulations were conducted for natural convection around a cylinder and square in an enclosure. The results illustrated that nanoparticles enhance heat transfer in higher Rayleigh number, and the heat transfer of the inner cylinder is stronger than that of the square at the same perimeter.     

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...     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

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.     

Effect of thermal stratification on free convection in a square porous cavity filled with a nanofluid using Tiwari and Das' nanofluid model

Natural convection in a square porous cavity filled with a nanofluid in conditions of thermal stratification has been numerically studied. The mathematical model has been formulated in terms of the dimensionless stream function and temperature using the Darcy–Boussinesq approximation and Tiwari and Das' nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids. Formulated partial differential equations along with the corresponding boundary conditions have been solved by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, thermal stratification parameter, porosity of the porous medium, solid volume fraction parameter of nanoparticles, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It has been observed an essential effect of thermal stratification parameter on heat and fluid flow fields.     

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.     

Buongiorno's model nanofluid natural convection inside a square cavity with thermal radiation

Natural convection flow and heat transfer characteristics of Buongiorno's mathematical model nanofluid flow inside square cavity with isothermal conditions on both side walls and adiabatic conditions on top and bottom walls is studied numerically in this analysis. Finite difference method is employed to solve the governing partial differential equations formulated in stream function, nanoparticle volume fraction and temperature numerically. The results are presented in the form of streamlines, isotherms, isoconcentrations, local Nusselt number and Sherwood number for various values of influenced parameters, such as, Rayleigh number (100 ≤ Ra ≤ 300), buoyancy ratio parameter (0.1 ≤ Nr ≤ 0.9), Lewis number (1.0 ≤ Le ≤ 10), thermophoresis number (0.1 ≤ Nt ≤ 0.5), Brownian motion number (0.1 ≤ Nb ≤ 0.9) and radiation number (0.1 ≤ R ≤ 0.9) and are represented through graphs. It is detected that the values of rate of heat transfer elevates with rising values of Rayleigh number (Ra).     

Mixed convection and entropy generation in a square cavity using nanofluids

In this work, two-dimensional mixed convection and entropy generation of water-(Cu, Ag, Al₂O₃, and TiO₂) nanofluids in a square lid-driven cavity containing two heat sources, have been numerically investigated. The upper lid and bottom wall of the cavity are maintained at a cold temperature T_C, respectively. The governing equations along with boundary conditions are solved using the finite volume method. Comparisons with the previous results were performed and found to be in excellent agreement. The effects of the solid volume fraction (0≤φ≤0.10), Rayleigh (10³≤Ra≤10⁵) and Reynolds (1≤Re≤500) numbers, and different types of nanofluids on the total entropy generation S_t and on entropy generation due to heat transfer S_h are presented and discussed. Moreover, the heat sources positions have an effect on the total entropy generation and Bejan number. It was found that S_t and S_h decrease with increase of φ, Ra, and Re.     

格子Boltzmann方法模拟填充纳米流体三角形腔内的自然对流

采用格子Boltzmann方法研究填充水-氧化铝纳米流体的等腰直角三角形腔体中的自然对流.讨论瑞利数、颗粒体积分数、热源位置等因素对对流换热的影响,以及不同纳米流体模型对模拟结果的影响.结果表明:在低瑞利数下,随着热源在左壁面向上移动,换热效率逐渐增加.而在高瑞利数(Ra=106)时,观察到相反的现象;采用单相纳米流体...     

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.     

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.     

Lattice Boltzmann simulation of 3-dimensional natural convection heat transfer of CuO/water nanofluids

The present study investigated fluid flow and natural convection heat transfer in an enclosure embedded with isothermal cylinder. The purpose was to simulate the three-dimensional natural convection by thermal lattice Boltzmann method based on the D3Q19 model. The effects of suspended nanoparticles on the fluid flow and heat transfer analysis have been investigated for different parameters such as particle volume fraction, particle diameters, and geometry aspect ratio. It is seen that flow behaviors and the average rate of heat transfer in terms of the Nusselt number (Nu) are effectively changed with different controlling parameters such as particle volume fraction (5 % ≤ φ ≤ 10 %), particle diameter (d _p = 10 nm to 30 nm) and aspect ratio (0.5 ≤ AR ≤ 2) with fixed Rayleigh number, Ra = 10⁵. The present results give a good approximation for choosing an effective parameter to design a thermal system.     

格子Boltzmann方法分析加热尺寸和瑞利数对可变形开口腔内自然对流的影响

采用格子Boltzmann方法对可变形腔体内自然对流问题进行数值研究，给出平均努赛尔数的经验关系式.腔体左壁加热长度分为左壁面的整个区域（H）和左壁面的中间区域（0.5H）两种情况，右壁向外界环境开放，上下边界绝热且可以上下移动，以此调节右出口尺寸.主要研究瑞利数（10⁴ ≤ Ra ≤ 10⁶），右出口尺寸（1.0H ≤ L ≤ 2.0H），左壁加热尺寸（L_h=0.5H或L_h=H）对腔体内等温线、流线、局部努塞尔数和平均努赛尔数的影响.结果表明：腔体内换热随着瑞利数的增大越来越强烈，表现为椭圆形准静止区域更加靠近上绝热壁，且热分层厚度逐渐变小，平均努赛尔数增加.而右出口尺寸的增加，对于两种加热尺寸下腔内的换热效果有不同程度影响，其中与加热尺寸为左壁面的全部区域L_h=H相比，加热尺寸为左壁面的中间情况L_h=0.5H时，右侧开口尺寸的增加对换热效果的影响不显著.此外，左壁加热尺寸为0.5H时显示出比加热尺寸为H时更高的平均传热效率.最后，针对不同的加热尺寸，提出加热面平均努赛尔数与Ra数及右壁面开口尺寸L^*之间函数关系的经验预测，拟合效果满足工程实践与设计需要.     

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.     

Long relaxation times and tilt sensitivity in Rayleigh Bénard turbulence

We study the influence of a small tilt angle ( rd) on the Nusselt number in a 1/2 aspect ratio Rayleigh-Bénard cell, at high Rayleigh number (5 x 10¹¹ < Ra < 4 x 10¹²). The small decrease observed is interpreted as revealing a two rolls structure of the flow. Transitions between different global flows are also observed, on very long times, comparable to the diffusion time on the whole cell. The consequence is that the Nusselt number observed in most high Ra experiments should significantly depend on initial conditions.Received: 19 May 2004, Published online: 12 August 2004PACS: 92.60.Ek Convection, turbulence, and diffusion - 47.27.Te Convection and heat transfer - 44.25. + f Natural convection     

Numerical study of the heat transfer and electro-thermo-convective flow patterns in dielectric liquid layer subjected to unipolar injection

In this article we study the electro-thermal convection in a dielectric liquid layer placed between two electrodes and subjected to the simultaneous action of an electric field and a thermal gradient. The full set of equations describing the electro-thermo-convective phenomena is directly solved using a finite volume method. We first heat the liquid from below at time t = 0, wait for the thermal steady state and then inject the electric charges by applying the electric potential. The development of the electro-convective motion is analysed in detail in two cases: 1) strong injection from the lower electrode, 2) strong injection from the upper one. We also study the heat transfer enhancement due to electro-convection. The evolution in time of the Nusselt number Nu for different combinations of the two usual non-dimensional parameters associated to the electro-thermo-convection phenomena (Rayleigh number Ra and the electrical parameter T) is also given and analysed.     

Effect of Brownian motion on flow and heat transfer of nanofluids over a backward-facing step with and without adiabatic square cylinder

A mathematical model to predict large enhancement of thermal conductivity of nanofluids by considering the Brownian motion is proposed. The effect of the Brownian motion on the flow and heat transfer characteristics is examined. The computations were done for various types of nanoparticles such as CuO, Al₂O₃, and ZnO dispersed in a base fluid (water), volume fraction of nanoparticles ? in the range of 1 % to 6 % at a fixed Reynolds number Re = 450 and nanoparticle diameter d_np = 30 nm. Our results demonstrate that Brownian motion could be an important factor that enhances the thermal conductivity of nanofluids. Nanofluid of Al₂O₃ is observed to have the highest Nusselt number Nu among other nanofluids types, while nanofluid of ZnO nanoparticles has the lowest Nu. Effects of the square cylinder on heat transfer characteristics are significant with considering Brownian motion. Enhancement in the maximum value of Nu of 29 % and 26 % are obtained at the lower and the upper walls of the channel, respectively, by considering the Brownian effects, with square cylinder, compared with that in the case without considering the Brownian motion. On the other hand, results show a marked improvement in heat transfer compared to the base fluid, this improvement is more pronounced on the upper wall for higher ?.