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.     

粗糙纳通道内流体流动与传热的分子动力学模拟研究

为研究粗糙表面对纳尺度流体流动和传热及其流固界面速度滑移与温度阶跃的影响,本文建立了粗糙纳通道内流体流动和传热耦合过程的分子动力学模型,模拟研究了粗糙通道内流体的微观结构、速度和温度分布、速度滑移和温度阶跃并与光滑通道进行了比较,并分析了固液相互作用强度和壁面刚度对界面处速度滑移和温度阶跃的影响规律. 研究结果表明,在外力作用下,纳通道主流区域的速度分布呈抛物线分布,由于流体流动导致的黏性耗散使得纳通道内的温度分布呈四次方分布. 并且,在固体壁面处存在速度滑移与温度阶跃. 表面粗糙度的存在使得流体剪切流动产生了额外的黏性耗散,使得粗糙纳通道内的流体速度水平小于光滑通道,温度水平高于光滑通道,并且粗糙表面的速度滑移与温度阶跃均小于光滑通道. 另外,固液相互作用强度的增大和壁面刚度的减小均可导致界面处速度滑移和温度阶跃程度降低. 关键词： 速度滑移 温度阶跃 流固界面 粗糙度     

格子Boltzmann方法模拟微尺度流动和传热

本文采用格子Boltzmann方法(LBM)对微尺度Couette流的流动及传热进行了模拟.为了获得壁面边界的速度滑移和温度阶跃,在含有粘性热耗散的热格子模型的基础上,提出了一种新的直接基于宏观量的边界处理格式.模拟得到的速度场和温度分布与解析解吻合得相当好,充分说明了本文采用的模型和边界处理的合理性同时在模拟中还发现:对于不同的Kn数,均存在使得其上壁面的温度阶跃为零的临界Ec数,并且其临界值均在3.0附近.     

非对称纳米通道内流体流动与传热的分子动力学

采用分子动力学方法研究了流体在非对称浸润性粗糙纳米通道内的流动与传热过程,分析了两侧壁面浸润性不对称对流体速度滑移和温度阶跃的影响,以及非对称浸润性组合对流体内部热量传递的影响.研究结果表明,纳米通道主流区域的流体速度在外力作用下呈抛物线分布,但是纳米通道上下壁面浸润性不对称导致速度分布不呈中心对称,同时通道壁面的纳米结构也会限制流体的流动.流体在流动过程中产生黏性耗散,使流体温度升高.增强冷壁面的疏水性对近热壁面区域的流体速度几乎没有影响,滑移速度和滑移长度基本不变,始终为锁定边界,但是会导致近冷壁面区域的流体速度逐渐增大,对应的滑移速度和滑移长度随之增大.此时,近冷壁面区域的流体温度逐渐超过近热壁面区域的流体温度,流体出现反转温度分布,流体内部热流逆向传递.随着两侧壁面浸润性不对称程度增加,流体反转温度分布更加明显.     

A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer

In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis     

The effects of porosity and permeability on fluid flow and heat transfer of multi walled carbon nano-tubes suspended in oil (MWCNT/Oil nano-fluid) in a microchannel filled with a porous medium

The forced convection heat transfer and laminar flow in a two-dimensional microchannel filled with a porous medium is numerically investigated. The nano-particles which have been used are multi walled carbon nano-tubes (MWCNT) suspended in oil as the based fluid. The assumption of no-slip condition between the base fluid and nano-particles as well as the thermal equilibrium between them allows us to study the nanofluid in a single phase. The nanofluid flow through the microchannel has been modeled using the Darcy–Forchheimer equation. It is also assumed that there is a thermal equilibrium between the solid phase and the nanofluid for energy transfer. The walls of the microchannel are under the influence of a fluctuating heat flux. Also, the slip velocity boundary condition has been assumed along the walls. The effects of Darcy number, porosity and slip coefficients and Reynolds number on the velocity and temperature profiles and Nusselt number will be studied in this research.     

Lattice Boltzmann scheme for simulating thermal micro-flow

Gaseous flow and heat transfer in micro-channels are simulated by the lattice Boltzmann method (LBM). Thermal LB model with viscous heat dissipation has been adopted in the simulation. A new boundary treatment is proposed based on macro variables in order to capture the velocity slip and temperature jump. The numerical results show the velocity and temperature profiles are in agreement with the analytic results in different cases, which exhibits the availability of this model and boundary treatment in describing thermal micro-flow with viscous heat effect. The variation rules of temperature jump with different parameters are also discussed in this study.     

基于总能形式的耦合的双分布函数热晶格玻尔兹曼数值方法

双分布函数热晶格玻尔兹曼数值方法在微尺度热流动系统中得到广泛的应用. 本文基于晶格玻尔兹曼平衡分布函数低阶Hermite展开式, 创新性地提出了包含黏性热耗散和压缩功的耦合的双分布函数热晶格玻尔兹曼数值方法, 将能量场内温度的变化以动量源的形式引入晶格波尔兹曼动量演化方程, 实现了能量场与动量场之间的耦合. 研究了考虑黏性热耗散和压缩功的和不考虑的两种热自然对流模型, 重点分析了不同瑞利数和普朗特数下流场内的流动情况以及温度、速度和平均努赛尔数的变化趋势. 本文实验结果与文献结果一致, 验证了本文数值方法的可行性和准确性. 研究结果表明: 随着瑞利数和普朗特数的增大, 方腔内对流传热作用逐渐增强, 边界处形成明显的边界层; 考虑黏性热耗散和压缩功的模型对流作用相对增强, 黏性热耗散和压缩功对自然对流的影响在微尺度流动过程中不能忽略.     

Lattice Boltzmann simulation of viscous-fluid flow and conjugate heat transfer in a rectangular cavity with a heated moving wall

In the present work, conjugate heat transfer in a rectangular cavity with a heated moving lid is investigated using the lattice Boltzmann method (LBM). The simulations are performed for incompressible flow, with Reynolds numbers ranging from 100 to 500, thermal diffusivity ratios ranging from 1 to 100, and Prandtl numbers ranging from 0.7 to 7. A uniform heat flux through the top of the lid is assumed. Results show that LBM is suitable for the study of heat transfer in conjugate problems. Effects of the Reynolds number, the Prandtl number and the thermal diffusivity ratio on hydrodynamic and thermal characteristics are investigated and discussed. The streamlines and temperature distribution in flow field, dimensionless temperature and Nusselt number along the hot wall are illustrated. The results indicate that increase of thermal diffusivity yields the removal of a higher quantity of energy from lid and its temperature decreases when increasing the Reynolds and the Prandtl numbers.     

Lattice-Boltzmann Simulations of Fluid Flows in MEMS

The lattice Boltzmann model is a simplified kinetic method based on the particle distribution function. We use this method to simulate problems in MEMS, in which the velocity slip near the wall plays an important role. It is demonstrated that the lattice Boltzmann method can capture the fundamental behaviors in micro-channel flow, including velocity slip, nonlinear pressure drop along the channel and mass flow rate variation with Knudsen number. The Knudsen number dependence of the position of the vortex center and the pressure contour in micro-cavity flows is also demonstrated.     

Asymptotic Theory for the Time-Dependent Behavior of a Slightly Rarefied Gas Over a Smooth Solid Boundary

A time-evolution of a slightly rarefied monoatomic gas, namely a gas for small Knudsen numbers, which is perturbed slowly and slightly from a reference uniform equilibrium state at rest is investigated on the basis of the linearized Boltzmann equation. By a systematic asymptotic analysis, a set of fluid-dynamic-type equations and its boundary conditions that describe the gas behavior up to the second order of the Knudsen number are derived. The developed theory covers a general intermolecular potential and a gas-surface interaction. It is shown that (i) the compressibility of the gas manifests itself from the leading order in the energy equation and from the first order in the continuity equation; (ii) although the momentum equation is the Stokes equation, it contains a double Laplacian of the leading order flow velocity as a source term at the second order; (iii) a double Laplacian source term also appears in the energy equation at the second order; (iv) the slip and jump conditions are the same as those in the time-independent case up to the first order, and the difference occurs at the second order in the jump conditions as the terms of the divergence of flow velocity and of the Laplacian of temperature. Numerical values of all the slip and jump coefficients are obtained for a hard-sphere gas by the use of a symmetric relation developed recently.     

Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium

This paper deals with the numerical solution for natural convection and volumetric radiation in an isotropic scattering medium within a heated square cavity using a hybrid thermal lattice Boltzmann method (HTLBM). The multiple relaxation time lattice Boltzmann method (MRT-LBM) has been coupled to the finite difference method (FDM) to solve momentum and energy equations, while the discrete ordinates method (DOM) has been adopted to solve the radiative transfer equation (RTE) using the S8 quadrature. Based on these approaches, the effects of various influencing parameters such as the Rayleigh number (Ra), the wall emissivity (ε_ι), the Planck number (Pl), and the scattering albedo (ω), have been considered. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in absence of radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in the temperature and velocity gradients along both thermally active walls. The maximum heat transfer rate is obtained when the surfaces of the enclosure walls are regarded as blackbodies. It is also seen that the scattering medium can generate a multicellular flow.     

Lattice Boltzmann Simulation for Complex Flow in a Solar Wall

In this letter,we present a lattice Boltzmann simulation for complex flow in a solar wall system which includes porous media flow and heat transfer,specifically for solar energy utilization through an unglazed transpired solar air collector(UTC).Besides the lattice Boltzmann equation(LBE) for time evolution of particle distribution function for fluid field,we introduce an analogy,LBE for time evolution of distribution function for temperature.Both temperature fields of fluid(air) and solid(porous media) are modeled.We study the effects of fan velocity,solar radiation intensity,porosity,etc.on the thermal performance of the UTC.In general,our simulation results are in good agreement with what in literature.With the current system setting,both fan velocity and solar radiation intensity have significant effect on the thermal performance of the UTC.However,it is shown that the porosity has negligible effect on the heat collector indicating the current system setting might not be realistic.Further examinations of thermal performance in different UTC systems are ongoing.The results are expected to present in near future.     

The variations of heat transfer and slip velocity of FMWNT-water nano-fluid along the micro-channel in the lack and presence of a magnetic field

Simulation of forced convection of FMWNT-water (functionalized multi-walled carbon nano-tubes) nano-fluid in a micro-channel under a magnetic field in slip flow regime is performed. The micro-channel wall is divided into two portions. The micro-channel entrance is insulated while the rest of length of the micro-channel has constant temperature (T_C). Moreover, the micro-channel domain is exposed to a magnetic field with constant strength of B₀. High temperature nano-fluid (T_H) enters the micro-channel and exposed to its cold walls. Slip velocity boundary condition along the walls of the micro-channel is considered. Governing equations are numerically solved using FORTRAN computer code based on the SIMPLE algorithm. Results are presented as the velocity, temperature, and Nusselt number profiles. Greater Reynolds number, Hartmann number, and volume fraction related to more heat transfer rate; however, the effects of Ha and ϕ are more noteworthy at higher Re.     

LBM simulation on natural convection flow in a triangular enclosure of green house under winter day conditions

Natural convection flow of roof top cross section in a green house has been numerically investigated using a thermal lattice Boltzmann method (TLBM). Two types of thermal boundary condition are considered; uniform and nonuniform bottom heating with symmetrically cold inclined walls. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for different Rayleigh number, Ra, ranging from 103 to 105 with other controlled parameters. The intensity of circulation is found to be higher and symmetric for lower values of Ra and the asymmetric behavior of the flow about the geometric centre line is seen for higher values of Ra in the case of uniform bottom heating. However, for nonuniform case, multiple circulation cells are observed for different Ra maintaining the symmetrical fluid properties. In addition, the average rate of heat transfer in terms of Nusselt number indicated the lower heat transfer rates for the nonuniform case compared to the uniform heating case. Finally, the results have been compared with the previous published works and found a good agreement.     

Lattice Boltzmann modeling of microchannel flow in slip flow regime

We present the lattice Boltzmann equation (LBE) with multiple relaxation times (MRT) to simulate pressure-driven gaseous flow in a long microchannel. We obtain analytic solutions of the MRT-LBE with various boundary conditions for the incompressible Poiseuille flow with its walls aligned with a lattice axis. The analytical solutions are used to realize the Dirichlet boundary conditions in the LBE. We use the first-order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel. We validate the LBE results using the compressible Navier–Stokes (NS) equations with a first-order slip velocity, the information-preservation direct simulation Monte Carlo (IP-DSMC) and DSMC methods. As expected, the LBE results agree very well with IP-DSMC and DSMC results in the slip velocity regime, but deviate significantly from IP-DSMC and DSMC results in the transition-flow regime in part due to the inadequacy of the slip velocity model, while still agreeing very well with the slip NS results. Possible extensions of the LBE for transition flows are discussed.     

Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method

The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.     

微通道内气体流动的格子Boltzmann方法研究

采用格子Boltzmann方法模拟了微通道在滑移区内不同Knudsen数下的微气体Poiseuille流,分析了微气体流动的速度分布以及流量与压降的关系,并给出了相对滑移长度和Poiseuille数随Knudsen数的变化特性。研究结果表明,微气体Poiseuille流的速度轮廓呈抛物线分布,但是边界速度大于0,出现速...     

Gas Flow in Microchannels – A Lattice Boltzmann Method Approach

Gas flow in microchannels can often encounter tangential slip motion at the solid surface even under creeping flow conditions. To simulate low speed gas flows with Knudsen numbers extending into the transition regime, alternative methods to both the Navier–Stokes and direct simulation Monte Carlo approaches are needed that balance computational efficiency and simulation accuracy. The lattice Boltzmann method offers an approach that is particularly suitable for mesoscopic simulation where details of the molecular motion are not required. In this paper, the lattice Boltzmann method has been applied to gas flows with finite Knudsen number and the tangential momentum accommodation coefficient has been implemented to describe the gas-surface interactions. For fully-developed channel flows, the results of the present method are in excellent agreement with the analytical slip-flow solution of the Navier–Stokes equations, which are valid for Knudsen numbers less than 0.1. The present paper demonstrates that the lattice Boltzmann approach is a promising alternative simulation tool for the design of microfluidic devices.     

滑移流区内微环缝槽道中的层流流动与换热

本文针对微环缝槽道采用速度滑移和温度跳跃边界条件求解了不可压缩气体的Ｎ－Ｓ方程和能量方程,理论分析了微环缝槽道在单侧或双侧不同热流密度加热条件下的流动与层流换热特性,讨论了Ｋｎ数、内外径比对流动阻力及换热特性的影响。结果表明：滑移流区微环继通道内的流阻和Ｎｕｓｓｅｌｔ数明显低于连续流区;且随着Ｋｎ数的增加,流阻和Ｎｕｓｓｅｌｔ数均减小;但其随内外径比ｒ＊的变化趋势与连续流区相似。