Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with Linearly Heated Wall(s)

In this study, the lattice Boltzmann method is used in order to investigate the natural convection in a cavity with linearly heated wall(s). The bottom wall is heated uniformly and the vertical wall(s) are heated linearly, whereas the top wall is insulated. Investigation has been conducted for Rayleigh numbers of 10³ to 10⁵, while Prandtl number is varied from 0.7 to 10. The effects of an increase in Rayleigh number and Prandtl number on streamlines, isotherm counters, local Nusselt number and average Nusselt number are depicted. It has been observed that the average Nusselt number at the bottom wall augments with an increase in Prandtl number.     

Enhancement of natural convection heat transfer from an inclined heated plate using rectangular grids

The effect of an inclination angle on the natural convection heat transfer from an inclined heated plate with rectangular grids is investigated. Heat transfer coefficients are measured in air when the plates are inclined at angles from ?30 to +60 from a vertical plane, grid heights are in the range of 5 to 10 mm, and diagonal lengths of the grid are 25, 50, 100, and 200 mm. For each configuration, the surface heat flux ranges from 50 to 200 W/m². It is found that the rectangular grids increase local heat transfer coefficients when the grids are applied to an inclined plate. The rectangular grids increase the average heat transfer coefficients along the horizontal centerline of the plate by up to 20% compared to those coefficients of a smooth plate, even when the angles of inclination are ±30° © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 408–419, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10043     

辐射侧加热腔内自然对流传热特性研究

为了明确辐射侧加热封闭方腔内半透明流体的自然对流传热现象及规律,采用有限体积法进行数值模拟研究,分析了瑞利数和光学厚度对流场、温度场以及传热特性的影响。结果表明：与传统侧壁加热腔内自然对流相比,辐射侧加热腔内等温线和流场分布规律不一致;随着瑞利数和光学厚度增加,涡心由中心位置沿直线向辐射入射侧斜上方偏移;随着瑞利数增加,等温线变得更均匀;随着光学厚度增加,等温线变密,努塞尔数Nu与瑞利数RaT的标度律指数减小,当光学厚度增加到一定时标度律不再变化,此时传热标度律与传统恒壁温侧加热腔内自然对流相当,满足Nu~Ra0.29T。     

Lattice Boltzmann simulation of natural convection in an open ended cavity

Natural convection in an open ended cavity is simulated using Lattice Boltzmann Method (LBM). The paper is intended to address the physics of flow and heat transfer in open end cavities and close end slots. The flow is induced into the cavity by buoyancy force due to a heated vertical wall. Also, the paper demonstrated that open boundary conditions used at the opening of the cavity is reliable, where the predicted results are similar to conventional CFD method (finite volume method, FVM) predictions. Prandtl number (Pr) is fixed to 0.71 (air) while Rayleigh number (Ra) and aspect ratio (A) of the cavity are changed in the range of 10⁴–10⁶ and of 0.5–10, respectively. It is found that the rate of heat transfer deceases asymptotically as the aspect ratio increases and may reach conduction limit for large aspect ratio. The flow evaluation in the cavity starts with recirculation inside the cavity, as the time proceeds the flow inside the cavity communicates with the ambient.     

Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

Lattice Boltzmann simulation of heat conduction problems in non‐isothermally heated enclosures

A numerical study following the lattice Boltzmann method (LBM) is performed to solve transient heat conduction problems with and without volumetric heat generation/absorption in 2D and 3D Cartesian geometries. Uniform lattices are considered for both geometries. To validate the correctness of LBM, a finite difference method (FDM) is also used to solve the 2D problem without heat generation/absorption and results are compared with that of LBM. For both 2D and 3D geometries one of the walls is heated and cooled with a sinusoidal function and the rest of the walls are cooled isothermally. Effects of amplitude of the sinusoidal function and volumetric heat generation/absorption on temperature profiles are analyzed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20406     

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     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Fluid flow and heat transfer of natural convection around array of vertical heated plates

Natural convective flows around an array of vertical heated plates were investigated experimentally. Main concerns were directed to the influences of plate numbers on the heat transfer characteristics of the plates. Both surfaces of the test plates were heated with constant and equal heat fluxes and their local heat transfer coefficients were measured. The results showed that the coefficients of the surfaces of the array facing outward became higher than those facing inward. The flow fields around the bottom of the plate array were visualized with smoke. The result showed that the ambient flow is directed from the sides to the center of the array and enters the parallel channel obliquely. These flows cause the above difference in the coefficients. While the difference gradually diminished in between the plates placed in the central section of the array, their coefficients asymptotically approach those of the analytical correlation that assumed a uniform velocity at the channel inlet. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20232     

Lattice Boltzmann simulation of mixed convection heat transfer in eccentric annulus

Mixed convection heat transfer in eccentric annulus was simulated numerically by lattice Boltzmann model (LBM) based on multi-distribution function double-population approach. The effect of eccentricity on heat transfer at various locations was examined at Ra = 10⁴ and σ = 2. Velocity and temperature distributions as well as Nusselt number are obtained. The results are validated with published results and shown that multi-distribution function approach can evaluate the velocity and temperature fields in curved moving boundaries with a good accuracy in comparison with the previous studies. The results show that the average Nusselt number increases when the inner cylinder moves downward regardless of the radial position.     

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.     

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.     

A numerical study of natural convection heat transfer in a composed thermal diode

The effects of inclination on the steady natural convection local heat transfer characteristics in an air-filled enclosure, which is composed of rectangular and parallelogrammic portions, are studied numerically. In this investigation, two geometrical aspect ratios are introduced: one for a parallelogrammic portion of an enclosure, the other for a rectangular one. The governing equations for a two-dimensional, laminar, natural convection process in an enclosure are discretized by the control volume approach which ensures the conservative characteristics to be satisfied in the calculation domain, and then solved by a modified SIMPLE algorithm. The momentum and energy equations are coupled through the buoyancy term. Computations are carried out for Prandtl number Pr = 1 and Rayleigh number Ra = 2.7 × 10⁸. In order to obtain a greater understanding of the flow and heat transfer behaviors, flow patterns with streamlines and isotherms at different inclination angles are shown. Also, the effects of numbers of installed guide vanes in a composed enclosure are studied to consider the enhancement of heat transfer of the inner diode. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 573–582, 1999     

基于格子Boltzmann方法的饱和土壤渗流与传热数值模拟

本文利用随机多孔介质生成算法重构了与真实土壤外貌相近的多孔介质几何结构。通过引入不可压耦合双分布格子Boltzmann模型（lattice Boltzmann model ,LBM）对孔隙尺度下单相饱和土壤渗流和传热进行了模拟。着重讨论了不同渗流压差、孔隙率、土壤固体颗粒尺寸分布对流动与传热的影响。结果表明：土壤渗流速度与渗流压差呈线性单调递增关系,平均温度随渗流压差增加而增大,但温升速率逐渐减缓;当孔隙率增大时,渗流速度增加,且当孔隙率大于0.58时,对流换热作用迅速增强,土壤温升速率显著加快;对于相同孔隙率,当土壤固相颗粒尺寸较大时,流动出现典型优先流效应;随着土壤固相颗粒尺寸减小,土壤温度变化逐渐趋于平缓,平均温度降低。     

Heat transfer enhancement of turbulent natural convection adjacent to a vertical heated plate

Enhancement of heat transfer was investigated experimentally on natural convection adjacent to a vertical heated plate. In order to promote heat transfer from the heated plate, a V-shaped promoter of which the edge faced upstream was attached onto the surface of the vertical plate. The promoter redirects high-temperature fluids toward both sides of the promoter and also introduces low-temperature ambient fluids behind the promoter. These two mechanisms enhance heat transfer, in particular, in the region behind the promoter. Local heat transfer coefficients around the promoter were measured using water as the test fluid. These coefficients behind the promoter reached 2.5 times of those without the promoter. The optimal heights and attack angles of the promoter that maximize the heat transfer were also studied experimentally. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res. 25(1): 39–50, 1996     

Fluid flow and heat transfer of natural convection adjacent to upward‐facing inclined heated plates

Turbulent transition mechanism and local heat transfer characteristics of the natural convective flows over upward‐facing inclined plates were investigated experimentally. The experiments were performed in the range of modified local Rayleigh numbers from 10⁴ to 8 × 10¹⁴ and of inclination angles θ from 0 to 90°. The flow fields over the plate and the surface temperatures of the plate were visualized with dye and liquid crystal thermometry. The results showed that longitudinal vortices play a main role in the turbulent transition over the plate of θ < 72°. These vortices appear first in the laminar boundary layer, then detach from the plate and, finally become distorted. It is found that the heat transfer is enhanced markedly by the detachment and the distortion of these vortices. The local heat transfer coefficients were measured in the laminar, transitional, and turbulent regions. The results show that the coefficients in the turbulent region become identical and independent of inclination angles. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 278–291, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10091     

Enhancement of natural convective heat transfer from tall,vertical heated plate to water

An enhancement technique was developed for natural convection heat transfer from a tall, vertical heated plate to water. Rectangular grid fins attached to the base plate were utilized as a heat transfer promoter. These grid fins redirect the high‐temperature fluid ascending along the base plate toward the outside of the boundary layer and introduce the low‐temperature ambient fluid toward the base plate instead. The heat transfer coefficients of thus‐treated surfaces were measured and compared with a nontreated surface and a surface with conventional vertical plate‐fins. The highest performance was achieved for the experimental surfaces. In particular, the experimental surfaces with 5‐mm‐high, nonconducting grids and with 10‐mm‐high, conducting grid fins show 27% and 80% higher heat transfer coefficients compared to the turbulent heat transfer coefficients of the nontreated surface, respectively. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(2): 178–190, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10083     

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity

Transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity is investigated numerically. The effective thermal conductivity and dynamic viscosity of nanofluids are predicted by using the proposed models that take the contribution of Brownian motion of nanoparticles into account. Three different Rayleigh numbers and five different volume fractions of nanoparticles are considered. The development of natural convection is presented through the evolutions of the average Nusselt number along the cold side wall. The predicted flow development times and time-averaged Nusselt numbers are scaled with Rayleigh number. In addition, the time-averaged Nusselt numbers are presented in terms of volume fraction of nanoparticles. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is lowered with increasing volume fraction of nanoparticles.