不连续冷源布局多孔介质内热流耦合LBM数值模拟

为研究不连续冷源边界对内置发热体多孔介质方腔内传热及流动的影响,采用格子Boltzmann方法对REV尺度下多孔介质方腔内的自然对流进行计算,并研究瑞利数（Ra）、达西数（Da）、孔隙度对多孔介质方腔内传热流动的影响.发现Da对方腔内的流体流型影响很大,Da为10^-4时,多孔介质方腔内只有一个涡流,而Da为10^-2时,方腔内有两个涡流.增大Ra、Da、孔隙度可以提高冷源壁面的平均努赛尔数（Nu）,增强散热效果,孔隙率对平均Nu影响程度和Da的大小有关.当冷源布置在壁面上方,壁面的平均Nu随Ra的增加剧烈变化,方腔处于高Ra条件下时,将冷源布置在边界的上方可以提高散热效果.6种布置方案中Case 6的散热效果最好.     

Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number $(Da)$, heat source intensity i.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, $Nu_b$, side $Nu_s$) and mass transfer (bottom, $Sh_b$, side, $Sh_s$) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligible for $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. The maximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.     

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.     

Convectively driven flow past an infinite moving vertical cylinder with thermal and mass stratification

An analysis is performed to study the unsteady, incompressible, one-dimensional, free convective flow over an infinite moving vertical cylinder under combined buoyancy effects of heat and mass transfer with thermal and mass stratifications. Laplace transform technique is adopted for finding solutions for velocity, temperature and concentration with unit Prandtl and Schmidt numbers. Solutions of unsteady state for larger times are compared with the solutions of steady state. Velocity, temperature and concentration profiles are analysed for various sets of physical parameters. Skin friction, Nusselt number and Sherwood number are shown graphically. It has been found that the thermal as well as mass stratification affects the flow appreciably.     

Water diffusion in biomedical systems as related to magnetic resonance imaging

Water diffusion within the brain is studied numerically for various clinical conditions. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. A wide range of pertinent parameters such as Lewis number, cell volume, and the buoyancy ratio are considered in the present study. Comparisons with previously published work show excellent agreement. The results show that the diffusion coefficient, cell volume, and the buoyancy ratio play significant roles on the characterization of the mass and heat transfer mechanisms within the cell. Concentration maps are developed for various clinical conditions. Pertinent results for the streamlines, isotherms and the mass and heat transfer rates in terms of the average Sherwood and Nusselt numbers are presented and discussed for different parametric values. Experimental tests are also conducted to produce an 8 Tesla image which is compared with our numerical simulation. The present study provides essential maps for brain disorders classified based on several pertinent clinical attributes.     

热质双扩散与流固共轭传热及吸附的LBM模拟

采用格子Boltzmann方法,基于孔隙尺度,对填有均匀介质的复合方腔顶盖驱动双扩散混合对流及流固共轭传热、吸附进行数值模拟.在孔隙率ε=0.79,普朗特数Pr=0.7,格拉晓夫数Gr=10⁴和路易斯数Le=1.0时,就不同浮升力比（-100≤Br≤100）和吸附率常数（0.001≤k₁≤0.005）对方腔内部热质传输的影响进行比较.给出流线、等温线、等浓度线、平均努赛尔数Nu_av、舍伍德数Sh_av和吸附量等.结果表明Br通过改变介质所处流场的浓度分布影响吸附,而k₁的增加显著地提高吸附效率和吸附能力.     

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...     

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.     

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.     

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).     

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.     

基于LBM的部分热活跃边界下多孔腔体内自然对流换热

采用Boltzmann方法模拟部分热活跃边界下的多孔腔体内自然对流,探讨不同热边界布置方案、孔隙度、Da数及Ra数对其流动传热的影响.数值计算表明：Da=10^-4时,腔体内中央出现一个循环流模式,只在Ra数很大时孔隙度才对传热有影响; Da=10^-2时,腔体内出现两个循环流,在Ra数很小时孔隙度对传热产生强烈的的影响.热活跃边界位置影响腔体内流体对流传热的强度,加热边界布置在底部、而冷却边界布置在顶部（Bottom-Top布置方式）,对多孔腔体内对流传热最有利,优于全热边界布置方式的传热效果.     

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.     

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.     

Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects

This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.     

THERMOSOLUTAL CONVECTION WITH COUPLED HEAT AND MASS TRANSFER PROCESS IN A SQUARE ENCLOSURE

Thermosolutal convection flow and its effect on the heat and the mass transfer in a square enclosure is studied experimentally. Both thermal and solute diffusion are induced from the sides, and natural convection is initiated by the combined thermal and solutal buoyancies, which either augment or oppose to each other. The solute diffusion is initiated in an electrochemical system that uses copper sulfate-sulfuric acid solution as an electrolyte. Depending on the magnitude of buoyancy ratio, three different kinds of flow regimes and structures can occur, which lead to different distributions of concentration in the enclosure. The formation and growth of layered flow structure is attributed to the solutal boundary-layer flow that can intrude and accumulate along the horizontal wall. The nearly stagnant layer that occurs can reduce the heat transfer rate. The Nusselt numbers at different flow regimes are measured and correlated in terms of relevant nondimensional parameters. This suggests the correlation of Sherwood number in different ranges of buoyancy ratio. The visualization of flow structures and measurements of both heat and mass transfer allow better understanding of the complicated system.     

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.     

复杂多孔介质腔体内自然对流换热的数值研究

采用曲线坐标系下压力与速度耦合的SIMPLEC算法,数值研究复杂多孔介质腔体内的自然对流换热问题.腔体的曲面温度分别保持恒定,上下表面绝热.在曲线坐标系中用有限容积法离散方程,并采用Brinkman扩展达西模型及局部非热平衡模型求解,综合研究Rayleigh数,Darcy数、孔隙率等参数对腔体内自然对流换热的影响.计算结果表明:Rayleigh数和Darcy数的影响最大而孔隙率的影响很小,同时存在使得腔体内换热达到最强的最佳纵横比.     

Mesoscopic analysis of heatline and massline during double-diffusive MHD natural convection in an inclined cavity

Double-diffusive natural convection in an inclined cavity with the presence of magnetic field is studied numerically via heatline and massline approach. The governing equations are discretized using the Lattice Boltzmann Method (LBM). In this investigation, the controlling parameters involved are Rayleigh number (10³ ≤ Ra ≤ 10⁵), buoyancy ratio (−5 ≤ N ≤ 5), cavity inclination angle (0° ≤ Ø ≤ 180°), Lewis number (2 ≤ Le ≤ 10), Prandtl number (Pr = 5.0) and Hartmann number (0 ≤ Ha ≤ 50). The numerical results obtained by the effect of parameters mentioned above are reported as contours of streamlines, isotherms, isoconcentrations, heatlines, and masslines. The obtained results are compared with the existing literature to validate the coding. The heat and mass transfer rate decrease with increasing the magnetic field and increase with an increase in Rayleigh number. The impact of Ø is maximum for higher Ra and negligible for lower Ra (10³). Increasing Le influences the mass transfer rate to increase and heat transfer to reduce for both opposing and aiding flow.