Numerical simulation of natural convection in a square enclosure filled with nanofluid using the two-phase Lattice Boltzmann method

Considering interaction forces (gravity and buoyancy force, drag force, interaction potential force, and Brownian force) between nanoparticles and a base fluid, a two-phase Lattice Boltzmann model for natural convection of nanofluid is developed in this work. It is applied to investigate the natural convection in a square enclosure (the left wall is kept at a high constant temperature (T_H), and the top wall is kept at a low constant temperature (T_C)) filled with Al₂O₃/H₂O nanofluid. This model is validated by comparing numerical results with published results, and a satisfactory agreement is shown between them. The effects of different nanoparticle fractions and Rayleigh numbers on natural convection heat transfer of nanofluid are investigated. It is found that the average Nusselt number of the enclosure increases with increasing nanoparticle volume fraction and increases more rapidly at a high Rayleigh number. Also, the effects of forces on nanoparticle volume fraction distribution in the square enclosure are studied in this paper. It is found that the driving force of the temperature difference has the biggest effect on nanoparticle volume fraction distribution. In addition, the effects of interaction forces on flow and heat transfer are investigated. It is found that Brownian force, interaction potential force, and gravity-buoyancy force have positive effects on the enhancement of natural convective heat transfer, while drag force has a negative effect.     

侧壁不连续边界下多孔介质自然对流数值模拟

采用局部非热平衡模型,在方腔左侧壁面布置不连续等温边界条件,数值模拟了固体骨架发热多孔介质方腔内的稳态非达西自然对流传热,探讨了不同等温边界布置方案及方腔的高宽比M/L对方腔内自然对流传热的影响规律。计算结果表明:由于单向重力影响,多孔介质方腔内流函数结构呈现上下不对称特性,而固体相温度场分布呈现出上下对称分布规律;流体相局部Nu数的大小及分布规律与等温边界的位置相关,局部Nu数随着Y=0.5值的增大而增加,固体相局部Nu数则以Y=0.5处为中心呈现上下对称分布规律。存在一个最佳ξ值及高宽比值,使得多孔介质方腔内的整体向外传热量达到最大值,等温边界布置于方腔上侧更有利于强化方腔整体的自然对流传热。     

Lattice Boltzmann simulation of alumina-water nanofluid in a square cavity

A lattice Boltzmann model is developed by coupling the density (D2Q9) and the temperature distribution functions with 9-speed to simulate the convection heat transfer utilizing Al₂O₃-water nanofluids in a square cavity. This model is validated by comparing numerical simulation and experimental results over a wide range of Rayleigh numbers. Numerical results show a satisfactory agreement between them. The effects of Rayleigh number and nanoparticle volume fraction on natural convection heat transfer of nanofluid are investigated in this study. Numerical results indicate that the flow and heat transfer characteristics of Al₂O₃-water nanofluid in the square cavity are more sensitive to viscosity than to thermal conductivity.     

Mixed convection flows in a square lid‐driven cavity with heat source at the bottom utilising nanofluid

This paper presents a numerical investigation of laminar mixed convection cooling of heat source embedded on the bottom wall of an enclosure filled with nanofluids. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influences of governing parameters, namely, Rayleigh number location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The present results are validated by favourable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed. © 2011 Canadian Society for Chemical Engineering     

Lattice Boltzmann simulation of double diffusive natural convection in a square cavity with a hot square obstacle

Double diffusion convection in a cavity with a hot square obstacle inside is simulated using the lattice Boltzmann method. The results are presented for the Rayleigh numbers 104,105 and 106, the Lewis ...     

在有方形障碍物的方腔中对双扩散自然对流的玻尔兹曼晶格模拟(英文)

Double diffusion convection in a cavity with a hot square obstacle inside is simulated using the lattice Boltzmann method. The results are presented for the Rayleigh numbers 104,105 and 106, the Lewis numbers 0.1, 2 and 10 and aspect ratio A (obstacle height/cavity height) of 0.2, 0.4 and 0.6 for a range of buoyancy number N=0 to?4 with the effect of opposing flow. The results indicate that for|N|b 1, the Nusselt and Sherwood numbers decrease as buoyancy ratio increases, while for|N|N 1, they increase with|N|. As the Lewis number increases, higher buoyan-cy ratio is required to overcome the thermal effects and the minimum value of the Nusselt and Sherwood num-bers occur at higher buoyancy ratios. The increase in the Rayleigh or Lewis number results in the formation of the multi-cell flow in the enclosure and the vortices wil vanish as|N|increases.     

密闭二维腔内水中热声波的数值模拟

以边长为1 mm密闭二维腔中的液态水为研究对象,用数值计算的方法,通过在左侧边界施加阶跃温度或阶跃热流来产生热声效应。分析水中热声波的产生与传播特性,并研究右侧边界中点产生的热通量的强度。计算结果表明,在相同的热边界和几何边界条件下,液态水中热声效应引起的压力波幅值和热通量远大于空气;当加热阶跃温度不同时,水中产生的压力波幅值和热通量随温度升高而急剧增大;当阶跃热流加热时,压力波和热通量与阶跃温度加热时的有较大差异。     

Natural convection in a vertical porous cavity filled with a non‐newtonian binary fluid

Numerical and analytical study of natural convection in a vertical porous cavity filled with a non‐Newtonian binary fluid is presented. The density variation is taken into account by the Boussinesq approximation. A power‐law model is used to characterize the non‐Newtonian fluid behavior. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. Both double‐diffusive convection (a = 0) and Soret‐induced convection (a = 1) are considered. Scale analysis is presented for the two extreme cases of heat‐driven and solute‐driven natural convection. For convection in a thin vertical layer (A ? 1), a semianalytical solution for the stream function, temperature, and solute fields, Nusselt and Sherwood numbers are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. Numerical results of the full governing equations show the effects of the governing parameters, namely the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, φ, the power‐law index, n, and the integer number a. A good agreement between the analytical predictions and the numerical simulations is obtained. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1704–1716, 2012     

Conjugate heat transfer of laminar mixed convection of a nanofluid through an inclined tube with circumferentially non-uniform heating

Laminar mixed convection of a nanofluid consisting of water and Al₂O₃ in an inclined tube with heating at the top half surface of a copper tube has been studied numerically. The bottom half of the tube wall is assumed to be adiabatic (presenting a tube of a solar collector). Heat conduction mechanism through the tube wall is considered. Three-dimensional governing equations with using two-phase mixture model have been solved to investigate hydrodynamic and thermal behaviours of the nanofluid over wide range of nanoparticle volume fractions. For a given nanoparticle mean diameter the effects of nanoparticle volume fractions on the hydrodynamics and thermal parameters are presented and discussed at different Richardson numbers and different tube inclinations. Significant augmentation on the heat transfer coefficient as well as on the wall shear stress is seen.     

Simulation of forced convection in a channel with nanofluid by the lattice Boltzmann method

This paper presents a numerical study of the thermal performance of fins mounted on the bottom wall of a horizontal channel and cooled with either pure water or an Al₂O₃-water nanofluid. The bottom wall of the channel is heated at a constant temperature and cooled by mixed convection of laminar flow at a relatively low temperature. The results of the numerical simulation indicate that the heat transfer rate of fins is significantly affected by the Reynolds number (Re) and the thermal conductivity of the fins. The influence of the solid volume fraction on the increase of heat transfer is more noticeable at higher values of the Re.     

Natural convection heat and moisture transfer with thermal radiation in a cavity partially filled with hygroscopic porous medium

This article deals with natural convection heat and moisture transfer with thermal radiation in a cavity partially filled with hygroscopic porous medium. The governing equations for the momentum and heat transfer in both free fluid and hygroscopic porous medium and moisture content transfer in hygroscopic porous medium were solved by the finite element method. The radiative heat transfer is calculated by making use of the radiosity of the surfaces that are assumed to be grey. Comparisons with experimental and numerical results in the literature have been carried out. Effects of thermal radiation and Rayleigh number on natural convection and heat transfer in both free fluid and porous medium and moisture content transfer in porous medium were analyzed. It was found that surface thermal radiation can significantly change the temperature and moisture content fields in the regions of free flow and porous medium. The mean temperature at the interface decreases, the temperature and moisture content gradients are created on the upper two corners of the porous medium region, and the moisture content in the porous medium decreases in the porous medium as Ra increases.     

Heat and mass transfer enhancement in a double diffusive mixed convection lid cavity under pulsating flow

This work assess the effectiveness of the pulsating flow regime for the enhancement of heat and mass transfer in double diffusive problems by studying a two-dimensional, heated, lid cavity. The research characterizes the influence of pulsating parameters such as temporal frequency, wave number and amplitude in the process. Results show that the pulsating regime enhances heat/mass transfer within a square cavity up to a 14%/38% respectively with respect to the non-pulsating case, due to the promotion of additional shear stress fields. As Richardson number, Brownian diffusion or the solute/thermal buoyancy ratio increase or the cavity becomes narrower, heat/mass transfer increases.     

Effects of stagnant and dispersion conductivities on non-darcian forced convection in square Packed-Sphere channels

This paper presents a numerical and experimental investigation of the effects of stagnant and dispersion conductivities on non-Darcian forced convection in square packed-sphere channels. The theoretical prediction of Nusselt number are found to be in good agreement with the experimental data. A larger near-wall damping of stagnant conductivity is found for the present water-steel medium than for that described by the mixing rule based on the volume fraction. A nonlinear Peclet number dependence, Pe^λ and λ = 0,88, for dispersion conductivity is found to induce better agreement between the theoretical and experimental results especially for the cases of high Peclet number and high D_c/d.     

Particle transport in a small square enclosure in laminar natural convection

The transport of particles with diameters in the range of 50 nm to 1 μm in laminar free convection of air in square enclosures was numerically investigated by an Eulerian–Lagrangian method. Two-dimensional square enclosures with widths from 2.5 mm to 5 cm, with two adiabatic surfaces and 100 and 200 °C temperature difference between the other two surfaces, were considered. The Rayleigh numbers varied from 100 to 8×10⁵. The air flow was simulated in Eulerian frame using a commercial CFD software, whose predictions were compared with published benchmark results. Lagrangian particle transport calculations were carried out by tracking 1000 particles that were initially randomly distributed in the flow field, and assuming one-way coupling between the particles and the carrier gas. Particle motion mechanisms considered included gravity, drag, lift force, thermophoresis and Brownian dispersion.The results showed that at Rayleigh numbers lower than about 10 000 the entire flow field was dominated by a single recirculation pattern. For these low Rayleigh number cases most of the particles disperse towards the walls, while a fraction of particles were trapped in a quasi-steady recirculation zone. Inside this recirculation zone the particles were at quasi-equilibrium with respect to the hydrodynamic and dispersive forces that acted on them, and left the zone due to Brownian dispersion only at a very low rate. This quasi-equilibrium zone was not observed at the higher Rayleigh numbers where a single recirculation pattern no longer governed the entire flow field. The results also confirmed the important role of thermophoresis and Brownian dispersion, in particular for submicron size particles.     

Dynamics of a spherical particle in mixed convection flow field

Numerical and experimental study on steady mixed convection gas flow around a hot spherical particle is presented for small values of Reynolds and Grashof numbers and all mixed convection parameter range. The flow regimes considered are the axis-symmetric co-flow and opposed flow for the non-dimensional Boussinesq model. The sensitivity of the numerical computations with respect to the dimension of the computational domain is discussed. The opposed flow regime and the formation of re-circulation secondary flow is analyzed. A qualitative expression for the drag force induced on the particle by the flow is given for all range of the mixed convection parameter, the expression holds for the co-flow configuration but brakes up in the opposed flow regime when re-circulation secondary flow evolves. Experimental measurements of the drag force induced on a small spherical particle allows further examination of the numerical computations and theory.     

The spatiotemporal instability on mixed convection in porous media

The absolute and convective instability on mixed convection in porous media is examined, and the phase transition from the oscillatory wave motion to the stationary vortex one is observed. Based on linear and weakly nonlinear analyses, the critical conditions to mark the onset of traveling transverse rolls are analytically obtained for small Péclet numbers. The flow change from transverse wave to longitudinal vortex is reproduced by numerical simulation. These criteria made good agreement with the available experiment data. This paper is dedicated to Professor Chang Kyun Choi to celebrate his retirement from the school of chemical and biological engineering of Seoul National University.