Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

Effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls

We examined the effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non‐dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20319     

Numerical study of natural convection and acoustic waves using the lattice Boltzmann method

In this paper, the lattice Boltzmann method is used to study the acoustic waves propagation inside a differentially heated square enclosure filled with air. The waves are generated by a point sound source located at the center of this cavity. The main aim of this simulation is to simulate the interaction between the thermal convection and the propagation of these acoustic waves. The results have been validated with those obtained in the literature and show that the effect of natural convection on the acoustic waves propagation is almost negligible for low Rayleigh numbers (Ra ≤ 10⁴), which begins to appear when the Rayleigh number begins to become important (Ra ≥ 10⁵) and it becomes considerable for large Rayleigh numbers (Ra ≥ 10⁶) where the thermal convection is important.     

Role of Prandtl number in the interaction phenomenon of surface radiation with an opposing mixed convection within a differential heated cavity

A numerical analysis has been done for opposing mixed convection resulting due to wall movement and buoyancy induced by a clockwise fluid motion in a differentially heated cavity. The effect of Prandtl number (Pr) and wall surface emissivity (?) has been investigated for different values of Richardson number. The net radiation method has been employed to simulate the effect of surface radiation. The energy equation along with its nonlinear boundary condition is treated with the Newton‐Raphson scheme. As momentum and energy equations are coupled with each other through their source terms, an iterative solution procedure is employed. A vorticity‐stream function formulation of the momentum equation has been adopted and solved by using an underrelaxation parameter of 0.45. The effect of Prandtl number with respect to the transformation of a multi‐cellular structure of streamline into a unicellular structure has been analyzed. For the same Richardson number (Ri) with an increase in Prandtl number, the flow and heat transfer phenomena changes from a buoyancy‐induced dominated flow to a shear‐induced dominated flow, which leads to some exciting results with respect to wall movement as well. Furthermore, the role of surface radiation in this respect has been emphasized. Nusselt number variation with the Prandtl number and surface emissivity has also been presented. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21003     

Lattice Boltzmann simulation of MHD mixed convection in a two‐sided lid‐driven square cavity

In this paper the effects of a magnetic field on mixed convection flow in a two‐sided lid‐driven cavity have been analyzed by the lattice Boltzmann method (LBM). The Hartmann number varied from Ha = 0 to 100. The study has been conducted for different Richardson numbers (Ri) from 0.01 to 100 while the direction of the magnetic field was investigated in the x‐direction. Consequences demonstrate that the heat transfer augments with an increment of the Richardson number for different Hartmann numbers for two cases. The heat transfer declines with the growth of the magnetic field for various Richardson numbers for two cases. The difference between the values of heat transfer for the two cases at variant parameters is negligible but the trend of fluid flow for the two cases is multifarious. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20402     

Free convention heat transfer from an isothermal horizontal thin strip: The influence of the Prandtl number

Simultaneous free convection above and below a uniformly heated horizontal plate has been widely investigated,both in the case of an isothermal surface,and of a uniformly heated surface,but always assuming only air as fluid（Pr=0.7）.Nevertheless,there are works dealing with horizontal plates whose results show that the Nu dependence on Pr may not be simply expressed by a power law with the same exponent of the Gr one.So it was considered useful to study the Prandtl number influence in the case of the isothermal horizontal strip.Results show that,while for the lower surface of the strip the Nu dependence in Gr can be expressed by a power law with an exponent close to the Gr one,for the upper surface the exponent is sensibly different.Correlating equations related to the investigated situations are proposed.     

Study on forcing schemes in the thermal lattice Boltzmann method for simulation of natural convection flow problems

The present study addresses the effect of various schemes for applying an external force term on the accuracy and performance of the thermal lattice Boltzmann method (LBM) for simulation of free convection problems. Herein, the forcing schemes of Luo, shifted velocity method, Guo, and exact difference method are applied by considering three velocity discrete models of D2Q4, D2Q5, and D2Q9. The accuracy and performance of these schemes are evaluated with the simulation of three natural convection problems, namely, free convection in a closed cavity, in a square enclosure with a hot obstacle inside, and the Rayleigh-Benard problem. The obtained results based on the present thermal LBM with different forcing schemes and velocity discrete models are compared with the existing experimental and numerical data in the literature. This comparison study indicates that imposing all employed forcing schemes leads to similar performance for the simulation of free convection problems studied at the middle range of Rayleigh numbers. It is found that the Luo forcing scheme is simple for implementation in comparison with the other three forcing schemes and provides the results with acceptable accuracy at moderate Rayleigh numbers. At higher Rayleigh numbers, however, the Guo scheme is not only numerically stable but a more precise forcing scheme in comparison with the other three methods. It is illustrated that employing the discrete velocity model of D2Q4 has more appropriate numerical stability along with less computational cost in comparison with two other discrete velocity models for simulation of natural convection heat transfer.     

Improvement of the heat transfer quality by air cooling of three-heated obstacles in a horizontal channel using the lattice Boltzmann method

This study focuses on the cooling of three heated obstacles with different heights mounted on the bottom of the channel wall using different aspects that influence the enhancement of the heat exchange, as is known in the concept of cooling electronic devices. The lattice Boltzmann method associated with multiple relaxation times (LBM-MRT) was adopted to simulate the physical configurations of the studied system. In this context, the D2Q9 and D2Q5 models are applied to describe the fluid flow behavior and conjugate heat transfer, respectively. The evaluation of heat exchange between the cold fluid and three-heated obstacles has been accurately analyzed under the effect of several parameters such as Reynolds number, obstacle spacing, and thermal conductivity ratio. In addition, the setting of two and three fluids flow inlets were also studied. The results are presented in terms of streamlines, isotherms, and local Nusselt curves. The heat transfer increases with increasing solid-fluid thermal conductivity. It is also more pronounced for large Reynolds numbers. Moreover, the heat transfer significantly enhances for the second and third obstacles when obstacle spacing increases. The improvement of the heat transfer is performed by the implementation of several jet flows in the studied system.     

Cavity inclination effect on convection flow in a triangular geometry

In this study, the water convection flow within a right-angled, inclined, and isosceles triangle enclosure for various inclination angles was numerically analyzed using the lattice Boltzmann method with the multirelaxation time model. On the hypotenuse side, the enclosure is thermally insulated, while the left and horizontal walls are kept, respectively, at cold and hot temperatures. This study was conducted to show the effects of two key parameters, the tilt angle $\varphi$ and the Rayleigh number $Ra$, whose changes span from $0^{\circ }$ to $315^{\circ }$ and $5\times 10^3$ to $10^6$, respectively. The effect of these variables is presented in terms of streamlines, isotherms, velocity profiles, temperature plots, and the average Nusselt number. Furthermore, the impact of the size of a hot square obstruction inside the cavity on the isotherms and streamlines has been investigated. The findings demonstrate that the rate of heat transport is enhanced as the Rayleigh number increases. This result is in good agreement with earlier research without tilting the cavity. Depending on the Rayleigh number, the tilt angle has a significant effect on the rate of heat transmission.     

Numerical simulation of natural convection in an open-ended square cavity filled with porous medium by lattice Boltzmann method

In the present work, natural convection in an open-ended square cavity packed with porous medium is simulated. The double-population approach is used to simulate hydrodynamic and thermal fields, and the Taylor series expansion and the least-squares-based lattice Boltzmann method has been implemented to extend the thermal model. The effect of a porous medium is taken into account by introducing the porosity into the equilibrium distribution function and adding a force term to the evolution equation. The Brinkman–Forchheimer equation, which includes the viscous and inertial terms, is applied to predict the heat transfer and fluid dynamics in the non-Darcy regime. The present model is validated with the previous literature. A comprehensive parametric study of natural convective flows is performed for various values of Rayleigh number and porosity. It is found that these two parameters have considerable influence on heat transfer.     

The effects of Prandtl number on natural convection in triangular enclosures with localized heating from below

The effect of Prandtl number on natural convection heat transfer and fluid flow in triangular enclosures with localized heating has been analyzed by solving governing equations of natural convection in streamfunction–vorticity form with finite-difference technique. Solution of linear algebraic equations was made by Successive Under Relaxation (SUR) method. Bottom wall of triangle is heated partially while inclined wall is maintained at a lower uniform temperature than heated wall while remaining walls are insulated. Computations were carried out for dimensionless heater locations (0.15 ≤ s ≤ 0.95), dimensionless heater length (0.1 ≤ w ≤ 0.9), Prandtl number (0.01 ≤ Pr ≤ 15) and Rayleigh number (10³ ≤ Ra ≤ 10⁶). Aspect ratio of triangle was chosen as unity. It is observed that both flow and temperature fields are affected with the changing of Prandtl number, location of heater and length of heater as well as Rayleigh number.     

基于LBM多孔介质复合腔体交界面热滑移效应的研究

本文采用格子Boltzmann方法对真实多孔介质复合腔体内的对流换热进行研究,分析了不同Ra数、多孔介质高度Y和厚度δ条件下交界面处的热滑移效应,并确定热滑移系数。利用X-CT技术对真实多孔介质材料进行断层扫描,获得实际材料内部结构图片,并进行图片处理,再导入格子Boltzmann模型中进行求解。计算结果表明：等效热滑移系数随高度Y的影响较大,靠近壁面或固体表面的系数偏大,而间隙处的系数偏小,但两处各自的值基本相同;Ra数和厚度δ的变化对等效热滑移系数的作用较小。     

Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid

The Prandtl number dependence of unsteady laminar natural convection along an infinite vertical plate in a thermally stratified fluid is investigated. Flows are induced by an impulsive (step) change in plate temperature and by a suddenly imposed plate heat flux. Analytical solutions of the viscous equations of motion and thermodynamic energy are obtained for Prandtl numbers near unity by the method of Laplace transforms and a regular perturbation expansion. The zeroth-, first- and second-order terms in the expansion are obtained for an impulsive change in plate temperature, while the zeroth- and first-order terms are obtained for a sudden application of a plate heat flux. The developing boundary layers are thicker, more vigorous, and more sensitive to the Prandtl number at smaller Prandtl numbers (<1) than at larger Prandtl numbers (>1). The analytical results are confirmed and extended with results from numerical simulations for Prandtl numbers strongly deviating from unity.     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

Melting of nano-enhanced phase change material in a cavity heated sinusoidal from below: Numerical study using lattice Boltzmann method

Natural convection and melting of ice as a phase change material dispersed with copper nanoparticles are numerically investigated. Square cavity filled with nano-mixture (Cu−ice) subjected to sinusoidal temperature distributions from the hot bottom boundary. The phase change process and heat transfer are formulated and solved using the enthalpy-based lattice Boltzmann method. Home-built numerical code is developed and validated. The effect of Rayleigh number (Ra = 10⁴, 10⁵, and 10⁶) and copper nanoparticle concentration (ϕ = 0%, 1%, 3%, and 5%) on the flow characteristics and thermal performance of NePCM during the melting process is examined. According to the numerical results, the melting and charging times decrease by increasing the Rayleigh number. It is also observed that increasing the volume fraction of nanoparticle decrease melting time by up to 10%.     

Lattice Boltzmann Simulation of Natural Convection in a Differentially Heated Square Enclosure Containing Heat Generating Low‐Prandtl Number Fluid

Lattice Boltzmann simulations were conducted for the free convective flow of a low‐Prandtl number (Pr = 0.0321) fluid with internal heat generation in a square enclosure having adiabatic top and bottom walls and isothermal side walls. The problem of free convection with volumetric heat source has represented itself in connection with advanced engineering applications, such as water‐cooled lithium–lead breeder blankets for nuclear fusion reactors and liquid metal sources of spallation neutrons for subcritical fission systems. A single relaxation time (SRT) thermal lattice Boltzmann method (LBM) was employed. While applying SRT, a D2Q9 model was used to simulate the flow field and temperature field. Results have been obtained for various Rayleigh numbers characterizing internal and external heating from 10³ to 10⁶. Flow and temperature fields in terms of stream function and isotherms in the enclosure were predicted for these cases. The temperature of the fluid in the enclosure was found higher than the heated wall temperature at high values of internal Rayleigh numbers. The internal heat generation affected the rate of heat transfer significantly as two convection loops are observed in the enclosure. The average Nusselt number at the heated and cold wall was determined for all the cases.     

液层Pr比值对环形双液层热毛细对流的影响

为了解双层流体系统上液层流体与下液层流体普朗特数(Pr)对热毛细对流的影响,通过线性稳定性分析,确定了上液层流体与下液层流体Pr比值从0.164～5.417时环形双层流体热毛细对流失稳的临界条件,预测了它们的4种流动失稳型式,即轮辐状的几乎占据了整个液层的"轮辐波"、轮辐状的热流体波与同波数共同旋向的靠热壁处流胞、径向...     

基于格子玻尔兹曼方法的横向交变质量力对核沸腾影响的数值分析

采用格子玻尔兹曼方法的单组份伪势模型与有限差分耦合的混合热格子玻尔兹曼模型,对在横向交变质量力作用下的单汽泡核态沸腾过程进行了研究,探讨了在不同接触角和过热度下,横向交变质量力的振幅和交变频率对汽泡脱离底壁的脱离特性的影响。结果表明,施加横向交变质量力会造成汽泡脱离直径减小,同时加速汽泡脱离底壁。其次,壁面越疏水,汽泡的脱离行为受到横向交变质量力的影响越大;壁面过热度越大,汽泡的脱离行为受到横向质量力的影响也越大。另外,在模拟工况下,当横向交变质量力的振幅大于0.01时,添加横向交变质量力会使汽泡的脱离直径与脱离周期均减小;而横向交变质量力的交变频率仅在某一频段时,使得汽泡的脱离周期减小。     

Lattice Boltzmann simulation of mixed convection in an inclined cavity with a wavy wall

In the present study, the effect of inclination on mixed convection heat transfer and fluid flow in a lid‐driven cavity with a wavy wall is investigated using the lattice Boltzmann method. The double‐population approach with second‐order accuracy at velocity and temperature fields is used to simulate the curved boundary in the lattice Boltzmann method. The problem is investigated for different Richardson numbers (0.1 ≤ Ri ≤ 10), curve amplitudes (0.05 ≤ A ≤ 0.25), and inclination angles (0 ≤ θ ≤ 180) when the Reynolds number is equal to 100. Results show that the inclination phenomenon has important effects on both flow and temperature fields at high Richardson numbers. It is also found that the inclination loses its role on mixed convection heat transfer from the wavy wall by the increase of the curve amplitude of the wavy wall for all Richardson numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21005