含体积热源方腔的耦合自然对流换热数值模拟

对具有内热源方腔的稳态层流耦合自然对流换热进行了三维的数值模拟,采用的模拟代码基于连续介质计算力学的开源库OpenFoam,解决了自然对流换热与固体传热的耦合问题。对外壁面为常温、方腔内充满含体积热源流体的自然对流计算结果表明,温度场、速度场与非耦合的工况有很大差异。Ra的变化从10^5到10^9。     

A numerical study of natural convection in a vertical cylinder bundle

Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary‐fitted coordinate system. Numerical calculations for center‐to‐center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 10⁸. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nu_i are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330–341, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10095     

Numerical investigation of natural convection in a square enclosure partially filled with horizontal layers of a porous medium

Two-dimensional buoyancy-induced flow and heat transfer inside a square enclosure partially occupied by copper metallic foam subjected to a symmetric side cooling and constant heat flux bottom heating was tested numerically. Finite Element Method was employed to solve the governing partial differential equations of the flow field and the Local Thermal Equilibrium model was used for the energy equation. The system boundaries were defined as lower heated wall by constant heat flux, cooled lateral walls, and insulated top wall. The three parameters elected to conduct the study are heater length (7 ≤ ζ ≤ 20 cm), constant heat flux (150 ≤ q″ ≤ 600 W m⁻²), and porous material thickness (5 ≤ H ≤ 20 cm). The porous material used was the copper metal foam of porosity = 0.9 and pore density PPI = 10, and saturated with a fluid of Prandtl number = 0.7. On the basis of the results obtained, it was concluded that at the porous layer thickness = 5 cm, the rate of heat transferred was (74.6%) higher than when the layer height was 20 cm (the cavity is fully filled) and at the same thickness it was found that the heat rate is (51.4%) higher than when using the half filling (H = 10 cm). Further, the local and mean Nusselt number is maximum when using the largest heater size and smallest porous layer thickness. Finally, better circulation and convective modes were observed at high values of heat flux.     

Study of conjugate natural convection between vertical coaxial rectangular cylinders

Laminar natural convection between two coaxial vertical rectangular cylinders is numerically studied in this work. The outer cylinder is connected with vertical rectangular inlet and outlet pipes. The inner cylinder dissipates volumetric heat. The fluid flow and heat transfer characteristics between the cylinders are analyzed in detail for various Grashof numbers. The heat transfer rates on the individual faces of the inner cylinder are reported. The bottom face of the inner cylinder is found to associate with much higher heat rates than those of the other faces. The average Nusselt number on bottom face is more than 2.5 times of the Nusselt number averaged on all the faces. At a given elevation, local Nusselt number on the inner cylinder faces increases towards cylinder edges. The effect of thermal condition of the walls of outer cylinder, inlet and outlet on the natural convection is analyzed. The thermal condition shows strong qualitative and quantitative impact on the fluid flow and heat transfer. The variation of induced flow rate, dimensionless maximum temperature and average Nusselt numbers with Grashof number is studied. Correlations for dimensionless buoyancy-induced mass flow rate and temperature maximum are presented.     

Fluid flow and heat transfer of natural convection over upward‐facing,horizontal, heated plate shrouded by a parallel insulated plate

The present paper describes experimental results on the fluid flow and heat transfer of natural convection between a horizontal, heated plate facing upward and an insulated cover plate. The experiments were carried out with water. The width of the test plates W and their gaps H were changed from W = 50 to 250 mm and H = 10 to 30 mm and ∞ (no cover plate). The visualization studies with dye and liquid crystal thermometry revealed that the roll cells whose axes are perpendicular to the flow direction appear and become dominant over the heated plate on decreasing the gap. These roll cells inhibit the heat transfer, and thus, the heat transfer coefficients become smaller than those without a cover plate. It was found that the flow and heat transfer in the region near the plate edges are unaffected by the cover plate. The conditions of the above reduced heat transfer were determined empirically. Moreover, nondimensional correlations for the local and the overall heat transfer coefficients of the heated plates are proposed based on the present heat transfer results. © 2000 Scripta Technica, Heat Trans Asian Res, 29(4): 333–346, 2000     

Investigation of natural convection in convergent vertical channels

Using air as the working fluid, natural convection heat transfer in a uniform wall temperature convergent vertical channel has been investigated numerically. The investigation encompassed half angles of convergence between 0° (parallel-walled channel) and 10° and the solutions were performed for (S/L) Ra_s range of 1 to 2 × 10⁴. In order to find a correlation format which will merge the convergent channel results for low Rayleigh number ranges (Ra′ < 10²) with those for the parallel-walled channel ones, the minimum (S_min), mean (S_avg), and maximum (S_max) interval spacing between channel walls were used as characteristic dimensions. It was found that merging was best achieved by the use of maximum interval spacing (S_max) as the characteristic dimension. These numerical findings agree with those for high Rayleigh number ranges (RA′ > 10²) reported in the literature.     

Experimental study on transient natural convection in a cube enclosure with an isolated vertical cyclically heated plate

INTRODUCTIONNaturalconvectioninsideenclosuresisatopicofconsiderablecurrentinterestandimportance.Ofparticularinterestarethetransientcoolingproblemsinenclosureswithinternalisolatedheatedbodies,inwhichnaturalconvectionisoftenthedominantheattransfermecha...     

封闭腔内Al_2O_3-EG纳米流体自然对流传热特性的数值研究

对梯形封闭腔内Al2O3-EG纳米流体自然对流传热进行了数值模拟,讨论了封闭腔尺寸比、瑞利数、纳米颗粒体积分数以及布朗运动对自然对流流动与传热特性的影响。数值模拟结果表明在考虑布朗运动时,腔体尺寸比与瑞利数对流动传热均有很大影响,且尺寸比为0.5时,对流换热平均Nusselt数达到最大值。随着纳米颗粒体积分数的增加,纳米流体换热效果逐渐增强;但当忽略布朗运动时,添加纳米颗粒削弱了换热效果。     

Numerical study of the laminar natural convection flow around horizontal isothermal cylinder

Natural convection around a horizontal circular cylinder under constant temperature or constant heat flux conditions in an infinite space has been the subject of numerous investigations in recent years. However, these studies use the inflow-outflow boundary in cylindrical coordinates that gives a sensible error, especially when the Rayleigh number is small. This investigation, that enters within the framework of general study dealing with natural convection from an array of cylinders, states the problem in cartesian coordinates system, involves the use of a control-volume method and resolves various apparent redundancies in boundary conditions. This problem was investigated numerically for laminar case by solving the full vorticity transport equation together with the stream function and energy equations. Results are obtained for 10¹ < Ra < 10⁶ and for Prandtl number equal to 0.7. Further, typical isotherms, local and mean Nusselt number, velocities and temperature distribution are clarified in detail. The numerical approach presented here appears to be sufficiently versatile to permit computation of a vertical array of cylinders.     

Numerical and experimental investigation of melting of ice involving natural convection

Two‐dimensional transient melting of ice in a rectangular enclosure was numerically and experimentally investigated. Natural convection in the liquid phase due to the temperature dependency of water density was considered in the numerical model. The implicit finite difference method with fixed staggered grid approach was utilized. The SIMPLER algorithm was followed for the solution of pressure and velocity fields in the liquid phase. The prediction of the model was found to be satisfactory through preliminary experimentation. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical study of the laminar natural convection flow around an array of two horizontal isothermal cylinders

Natural convection heat transfer from an array of heated cylinders has received attention in recent years. However, most of the previous investigations has been experimental and has been restricted to the influence of geometrical parameters on the overall heat transfer. The present work is devoted to the numerical study of lanunar natural convection flow from an array of two horizontal isothermal cylinders. This work, that enters within the framework of general study dealing with an array of several cylinders, states the problem in Cartesian coordinates system, involves the use of a control-volume method and solves the full vorticity transport equation together with the stream function and energy equations. The modifications of the average Nusselt number evolution compared with the single cylinder are explained in terms of velocity and temperature fields of the flow around the cylinders. Results are obtained for variety of combinations of spacing and numbers of Rayleigh.     

Three－Dimensional Numerical Simulation of Natural Convection Heat Transfer in an Inclined Cylindrical Annulus

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Numerical study of natural convection in a vertical porous annulus with discrete heating

In this paper natural convection flows in a vertical annulus filled with a fluid-saturated porous medium has been investigated when the inner wall is subject to discrete heating. The outer wall is maintained isothermally at a lower temperature, while the top and bottom walls, and the unheated portions of the inner wall are kept adiabatic. Through the Brinkman-extended Darcy equation, the relative importance of discrete heating on natural convection in the porous annulus is examined. An implicit finite difference method has been used to solve the governing equations of the flow system. The analysis is carried out for a wide range of modified Rayleigh and Darcy numbers for different heat source lengths and locations. It is observed that placing of the heater in lower half of the inner wall rather than placing the heater near the top and bottom portions of the inner wall produces maximum heat transfer. The numerical results reveal that an increase in the radius ratio, modified Rayleigh number and Darcy number increases the heat transfer, while the heat transfer decreases with an increase in the length of the heater. The maximum temperature at the heater surface increases with an increase in the heater length, while it decreases when the modified Rayleigh number and Darcy number increases. Further, we find that the size and location of the heater effects the flow intensity and heat transfer rate in the annular cavity.     

Numerical prediction of natural convection heat transfer in horizontal annulus

This paper deals with numerical prediction of natural convection heat transfer in a horizontal annulus in which the inner cylinder is hotter than the outer cylinder. A modified SIMPLE procedure is used for this purpose and it is shown that this procedure yields faster convergence. Results have been obtained for L/D_i = 0.8 and 0.15. This latter value is of interest in Horizontal Pressurised Heavy Water Reactors.     

Constructal design of vertical multiscale triangular fins in natural convection

Constructal design of vertical multiscale triangular fins in natural convection is investigated in this paper. The design consists of two parts. The first part is for single-scale triangular fins. The objective in the first design is to reach to the highest heat transfer density from the fins for three fin angles (15°, 30°, and 45°). The single-scale fins are placed in a horizontal array and considered as isothermal fins. The degrees of freedom are the fin angle, and the fin-to-fin spacing. The constraint is the fin height. The second part is for multiscale fins where small fins are placed between the large fins which are optimized in the first part. In the second part, the angles of the large and small scales fins are kept constant at (15°). The optimal fin-to-fin spacing which is obtained in the first part is considered a constraint in the second part. The Rayleigh numbers in this design are (Ra = 10³, 10⁴, and 10⁵). The two-dimensional mass, momentum, and energy equations for natural convection are solved with the finite volume method. The results show that there is a benefit of placing the small-scale fins where the percentage increase in the heat transfer density is (10.22%) at (Ra = 10³), and (50.6%) at (Ra = 10⁵) due to existence of the small fins between the large fins.     

Non—Darcian and Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

Natural convection heat transfer in a horizontal enclosure filled with anisotropic porous media,being isothermally heated at bettom and cooled at top while the vertical walls being adiabatic,is numerically studied by applying the Brinkman model-a modified form of Darcy model giving consideratioin to the viscous effect.The results show that:(1)a larger permeability ratio(K^*) causes a lower flow intensity in the enclosure and a smaller Nusselt number,all Nusselt numbers approach unity in the limit of K^*→∞;a larger thermal conductivity ratio(λ^*) causes a stranger distortion of isotherms in the enclosure and a higher flow velocity near the walls,all the Nusselt numbers approach unity in the limit of λ^*-→0,the permeability and thermal conductivity ratios generally have opposing effects on the Nusselt number.(2) an increasing Darcy number decreases the flow intensity and heat tansfer rates,which is more significant at a lower permeability ratio.In particular,with K^*≤0.25,the Nusselt number for Da=10^-3 would differ from that of Darcy flow up to an amount of 30%,an analysis neglecting the non-Darican effect will inevitably be of considerable error.     

Numerical simulation of natural convection heat transfer in the open space between two horizontal circular planes

Numerical simulations were conducted for natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier–Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer values are shown to be in good agreement with the experimentally obtained ones reported in a previous paper. From the obtained isotherms, streamlines, and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance: one is a simple convection due to a single renewal flow which replaces heated air with ambient air and the other is a combined convection due to several vortex flows and a renewal flow. Furthermore, the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 485–502, 2001     

Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium

An analytical method is carried out to investigate transient free convection boundary layer flow along a vertical surface embedded in an anisotropic porous medium saturated by a non-Newtonian fluid. The porous medium is anisotropic in permeability with its principal axes oriented in a direction that is non-coincident with the gravity force. A step increase in wall temperature or in surface heat flux is considered. On the basis of the modified Darcy power-law model proposed by Pascal [H. Pascal, Rheological behaviour effect of non-Newtonian fluids on steady and unsteady flow through porous media, Int. J. Numer. Anal. Methods in Geomech. 7 (1983) 207–224] and the generalized Darcy’s law described by Bear [J. Bear, Dynamics of fluids in porous media. Dover Publications, Elsevier, New York (1972)], boundary-layer equations are solved exactly by the method of characteristics. Scale analysis is applied to predict the order-of-magnitudes involved in the boundary layer regime. Analytical expressions are obtained for the limiting time required to reach steady-state, the boundary-layer thickness and the local Nusselt number in terms of the modified-Darcy Rayleigh number, the power-law index, the anisotropic permeability ratio, and the orientation angle of the principal axes. It is demonstrated that both the power-law index and the anisotropic properties have a strong influence on the heat transfer rate.     

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.     

Distribution of heat sources in vertical open channels with natural convection

In this paper we use the constructal method to determine the optimal distribution and sizes of discrete heat sources in a vertical open channel cooled by natural convection. Two classes of geometries are considered: (i) heat sources with fixed size and fixed heat flux, and (ii) single heat source with variable size and fixed total heat current. In both classes, the objective is the maximization of the global thermal conductance between the discretely heated wall and the cold fluid. This objective is equivalent to minimizing temperature of the hot spot that occurs at a point on the wall. The numerical results show that for low Rayleigh numbers (∼10²), the heat sources select as optimal location the inlet plane of the channel. For configuration (i), the optimal location changes as the Rayleigh number increases, and the last (downstream) heat source tends to migrate toward the exit plane, which results in a non-uniform distribution of heat sources on the wall. For configuration (ii) we also show that at low and moderate Rayleigh numbers (Ra_M ∼ 10² and 10³) the thermal performance is maximized when the heat source does not cover the entire wall. As the flow intensity increases, the optimal heat source size approaches the height of the wall. The importance to free the flow geometry to morph toward the configuration of minimal global resistance (maximal flow access) is also discussed.