Experimental studies on natural convection boiling of water in a vertical annulus of a closed-loop thermo-siphon

Experimental studies on natural convection boiling of water in an internally heated narrow vertical annulus, with the liquid circulating through a cold leg forming a closed-loop thermo-siphon, have been carried out. The radius and aspect ratios of the annulus are 1.184 and 352, respectively. The experimental data, which consist of wall and liquid temperatures, liquid and vapor flow rates, and differential pressure across the test section, are recorded on a data logging system. The experiments have been performed for a constant heat flux of 15–35 kW/m² from the startup period until the steady state to study the transient behavior of the system. The boiling and non-boiling zones in the annulus have been identified and presented graphically through the liquid and wall temperatures for the steady state. They have been also verified through the visual photographs of the flow patterns in the annulus. The flow is found to be oscillatory in nature with no particular trend. Although the experimental data seems to be scattered, but when analyzed for a short duration, they are found well within the ±3σ (three sigma). This confirms the quasi-steady-state condition of the system. The steady-state values of Reynolds number and liquid circulation rate come out to be 133.1–453.5 and 7.0–23.87 g/s, respectively, while the Nusselt number and heat transfer coefficient are 7.98–13.57 and 1433.57–2435.35 W/m²K, respectively. Mathematical correlations for liquid mass flow rates, heat transfer coefficient, Reynolds number, and Nusselt number have been developed and compared with the existing correlations, which are in good agreement.     

Experimental and numerical study of swirling subcooled flow boiling of water in a vertical annulus

In this paper, the effect of making swirling flow inside an annulus on the subcooled boiling heat transfer has been studied and discussed both experimentally and numerically. The Eulerian-Eulerian model and control volume technique have been used for numerical modeling of the problem. The experimental results show that the critical heat flux values are enhanced by making swirling flow. The experimental and numerical results also indicate that by making swirling flow inside the annulus, the subcooled boiling heat transfer coefficients are increased. Moreover, the experimental and numerical values of the boiling heat transfer coefficients show good agreement with each other.     

偏心环形腔内冷水稳态自然对流的数值模拟

为了了解偏心环形腔内非Boussinesq流体自然对流换热的特有现象和规律,本文利用有限容积法对垂直偏心环形腔内的冷水自然对流进行了二维数值模拟,得到了半径比为1.5时不同密度倒置参数、偏心率和Rayleigh数下的流场和温度场,并对不同条件下的平均Nusselt数进行了比较和分析。结果表明:密度倒置参数对流型结构起着决定性的作用,偏心率和Rayleigh数对流场影响较小;相同条件下,当密度倒置参数在0.5附近时,平均Nusselt数最小。     

Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface

The non-similarity solution for natural convection from a permeable isothermal vertical wall is considered. The governing boundary-layer equations for non-similarity flow and temperature fields are solved using the homotopy analysis method. The homotopy-Pade' technique is applied to accelerate the convergence of the homotopy-series solution. The influence of physical parameters on the non-similarity flows is investigated in detail. Different from the previous analytic results,the homotopy-series solutions a...     

Natural convection with damped thermal flux in a vertical circular cylinder

Natural convection flows of an incompressible Newtonian fluid inside a circular cylinder are studied. The heat transfer process is described by a generalized fractional constitutive equation for the thermal flux-temperature gradient. Caputo time-fractional derivative operator, which provides the damping of thermal flux, is considered into the studied model.Analytical solutions to the fluid temperature, thermal flux, fluid velocity and volume flow rate are obtained with the integral transforms method (Laplace transform and finite Hankel transform).Temperature behaviors for small and large values of the time t, as well as the post-transient and transient velocity components are determined. The influence of the memory parameter (the order of the time-fractional derivative) on the temperature, thermal flux, velocity and the volume flow rate is numerically and graphically studied.     

自然对流状态下深冷竖直平板霜层导热系数实验研究

利用设计的竖直平板结霜实验台,对自然对流状态下竖直平板表面非稳态结霜过程进行了动态描述,分析了霜层厚度变化规律,描述了湿空气在竖直平板附近的流动状态及温度分布。基于实验观测,把竖直平板非稳态结霜过程分为沿平板法线方向增厚和沿平板切线方向推进两个阶段。利用最小二乘法,拟合了竖直平板霜层导热系数在推进阶段随推移距离的关系式。通过反复实验,不断完善数据,可使拟合结果具有更高的适用性,也为工程设计提供依据。     

Analysis of frost visualization over a fin and tube heat exchanger by natural convection

In this article, studies are made on frost formation and flow over a fin and tube heat exchanger due to natural convection for various conditions of relative humidity, air ambient temperature, and mean refrigerant temperature. The results include frost deposition, steps of frost formation, and its effect on heat transfer rate for different conditions. The results show that frost is formed only on the tip of the fins with higher thickness from top to bottom due to small distance between the fins. Frost causes to trap the air which increases the thermal resistance and reduces heat transfer in the system.     

自然对流情形下激光辐照液体贮箱的尺度律

根据质量守恒、动量守恒及能量守恒原理,建立了自然对流情形下激光辐照液体贮箱的理论模型。通过方程分析法,导出了该问题的尺度律,在此基础上给出了激光辐照液体贮箱的缩比方法,并对一组实例进行了数值计算,得到了缩比模型与原型结果完全相似的结论,模拟结果证明了该问题尺度律的成立。为验证理论模型与数值求解的正确性,本文还针对小尺度模型进行了实验研究,数值模拟结果与实验测量结果符合较好,表明理论模型可靠有效。     

竖直恒温面自然对流边界层不稳定性研究

在无扰动、随机式扰动以及正弦式扰动下,通过对竖直恒温面处状态Ra为1.328×10^9、Pr为6.24的自然对流进行模拟,探索了热边界层的不稳定性和共振强化自然对流换热。结果表明:(1)竖直自然对流边界层上游位置的随机式扰动对热边界层的影响主要体现在稳定阶段;(2)该状态下的竖直自然对流边界层的特征频率为15 067,且相比于无扰动状态,频率为15 067的正弦式扰动能在竖直恒温面处提高5.15%的换热量;(3)在竖直自然对流边界层上游位置加入特征频率的正弦式扰动,竖直恒温面处的局部努塞尔数Nu均出现明显波动,且波动随着边界层高度的增加而增大。     

Experimental study of transient heat transfer characteristics of single-phase natural convection in multidimensional porous bed with volumetric heat generation

Natural convection in an internally heated porous bed of height and diameter of 450 mm and 500 mm, respectively, and superposed with the fluid layer has been experimentally investigated. The onset of natural convection in the bed is indicated by change in the rate of temperature rise within the bed. An empirical model based on local Nusselt number and local Rayleigh number has been developed. A comparison of the present model with the models in literature is made to draw out the differences between the local heat transfer of large multidimensional beds and the average heat transfer of small beds.     

Experimental and numerical investigation of natural convection of magnetic fluids in a cubic cavity

In this article, natural convections of a magnetic fluid in a cubic cavity under a uniform magnetic field are investigated experimentally and numerically. Results obtained from experiments and numerical simulations reveal that the magnetic field and magnetization are influenced by temperature. There exist relative larger magnetization and magnetic forces in the regions near the upper wall and center inside the cavity than in the region near the bottom and side walls. A weak flow roll occurs inside cavity under the magnetic force, and it brings the low temperature fluid downward in the center region, and streams the high temperature fluid upward along the regions near the sidewalls. With the magnetic field imposed, the heat transfer inside the cavity is enhanced significantly compared to that without the magnetic field, and increasing the strength of the magnetic field the heat transfer is increased further.     

倾斜多孔腔体内瞬态自然对流的实验研究

本文对充满水和玻璃球的倾斜多孔介质腔体,在其一侧壁温维持恒定值、而相对侧壁温以此恒定值为时均值并按一定的幅值随时间周期性变化的情况下,实验研究了周期性壁温变化和腔体倾角对多孔介质腔体内的瞬态自然对流换热的影响.结果表明,通过多孔介质腔体的净热流总是从腔体的较低壁面指向较高壁面.     

Experimental Study of Natural Convection from Electrically Heated Vertical Cylinders Immersed in Air

Abstract

An experimental study of laminar steady-state natural convection heat transfer from electrically heated vertical cylinders immersed in air has been undertaken. Three stainless steel (316 SS) test sections of different slenderness ratios were employed. Surface temperature profiles along the vertical cylinders were obtained using miniature thermocouples when the cylinders were heated with different power levels resulting in different total wall heat fluxes. After the mandatory corrections for the radiation heat fluxes were made, three correlation equations relating the local Nusselt number Nu_y with the local modified Rayleigh number Ra^* _y and the position-to-cylinder diameter y/d were developed. The correlation equations are valid for Ra^* _y ≤ 2 × 10¹².     

Influence of radiative heat flux in nonlinear convection of quartic order in Casson fluid past a vertical permeable plate with variable suction and Hall current

The current study centralizes on unsteady free convection slip flow of Casson fluid past a vertical permeable plate with Hall current, radiative heat flux, and variable suction. The nonlinear convection is subjected to quartic order. Perturbation method is used to convert the non-linear coupled partial differential equation of the momentum and energy to a system of ordinary differential equations. The dimensionless governing equations are solved analytically for velocity and temperature profiles. The graphs are plotted for sundry parameters for variations in the distinct flow fields w.r.t distance from the plate. Variation in the skin friction for the axial and transverse cases are presented in the form of graphs for various parameters. It is observed that with the increase in the order of non-linear convection and value of radiation parameter, the velocity field increases in Casson fluid. The increase in heat absorption parameter and Prandtl number decreases the temperature profile and increase in radiative heat flux parameter increases the temperature profile.     

用格子Boltzmann模型模拟垂直平板间的热对流

引入一个新的能量分布函数，利用该能量分布函数与粒子速度分布函数耦合来求解一个热流场. 因而，这一能量分布函数与粒子速度分布函数和Boltzmann方程构成了一个新的格子Boltzmann模型. 这一模型满足质量、动量和能量守恒的准则. 用该模型对垂直平板间的狭缝热对流进行了数值模拟，数值结果表明，在Prandtl数为1，Grashof数在1.3×10²—1×10⁶之间时，流场将出现多个旋涡结构的流型. 得出了与Lee相一致的结论. 关键词： 能量分布函数 Boltzmann方程 热对流     

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.     

Experimental Investigation of Natural Convection in Inclined Channel in Presence of Electrostatic Field

The influence of external electrohydrodynamic forces on natural convection from a flat plate has been studied. Temperature distribution in the aforementioned channel at α = 45°, 90°, and 150° angles in different 10-, 12-, and 15-kV electrostatic fields has been reviewed. Corona wind and the shape of the created vortex by electrohydrodynamics were detected. The results showed that heat transfer was enhanced by increasing the electrostatic field in all angles. In the presence of the field, enhancement of heat transfer of the plate at acute angles is better than for obtuse ones. The optimal angle in terms of heat transfer was 45°, noting heat transfer improvement by 61%.     

Development and validation of a new LBM-MRT hybrid model with enthalpy formulation for melting with natural convection

This article presents a new model to simulate melting with natural convection of a phase change material. For the phase change problem, the enthalpy formulation is used. Energy equation is solved by a finite difference method, whereas the fluid flow is solved by the multiple relaxation time (MRT) lattice Boltzmann method. The model is first verified and validated using the data from the literature. Then, the model is applied to a tall brick filled with a fatty acid eutectic mixture and the results are presented. The main results are (1) the spatial convergence rate is of second order, (2) the new model is validated against data from the literature and (3) the natural convection plays an important role in the melting process of the fatty acid mixture considered in our work.     

Characterization of size effect of natural convection in melting process of phase change material in square cavity

The accelerating effect of natural convection on the melting of phase change material(PCM) has been extensively demonstrated. However, such an influence is directly dependent on the size and shape of domain in which phase change happens, and how to quantitatively describe such an influence is still challenging. On the other hand, the simulation of natural convection process is considerably difficult, involving complex fluid flow in a region changing with time, and is typically not operable in practice. To overcome these obstacles, the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation, and ultimately a correlation equation to represent its contribution is proposed. Firstly, the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method.Subsequently, a comprehensive investigation is performed numerically for various domain sizes. The results show that the melting behavior of paraffin is dominated by the thermal convection. When the melting time exceeds 50 s, a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall, and then its influencing range gradually increases to accelerate the melting of paraffin. However, its intensity gradually decreases as the distance between the melting front and the heating wall increases. Besides, it is found that the correlation between the total melting time and the domain size approximately exhibits a power law. When the domain size is less than 2 mm, the accelerating effect of natural convection becomes very weak and can be ignored in practice. Moreover, in order to simplify the complex calculation of natural convection, the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time, and an empirical correlation is given for engineering applications.     

Computational analysis of non-isothermal temperature distribution on natural convection in nanofluid filled enclosures

In this study, the problem of steady state natural convection in an enclosure filled with a nanofluid has been analyzed numerically by using heating and cooling by sinusoidal temperature profiles on one side. The governing partial differential equations, in terms of the dimensionless stream function–vorticity and temperature, are solved numerically using the finite volume method for various inclination angles 0^°≤?≤90^°$0^{°}\le ?\le 90^{°}$, different types of nanoparticles (TiO₂ and Al₂O₃) and fractions of nanoparticles 0≤φ≤0.1$0\le \phi \le 0.1$, whereas the range of the Rayleigh number Ra is 10³–10⁵. It is found that the addition of nanoparticles into water affects the fluid flow and temperature distribution especially for higher Rayleigh numbers. An enhancement in heat transfer rate was registered for the whole range of Rayleigh numbers. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers.