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

Experimental studies on heat transfer and fluid flow of water in a vertical annulus, circulating through a cold leg forming a closed loop thermo-siphon, have been carried out in this article. The annulus has a radius ratio (outer radius to inner radius) of 1.184 and aspect ratio (length to annular gap) equal to 352. The experiments were conducted for constant heat fluxes of 1, 2.5, 5, 7.5, 10, 12.5, and 15 kW/m². Transient behavior during the heat-up period of the system until the steady-state condition is attained and discussed. Variation in the heat transfer coefficient and Nusselt number along the annulus height represent the developing boundary layer at the entrance and fully developed flow in the remaining length. A large drop in the differential pressure is experienced when the liquid is circulated through the flow meters, which restrict the flow due to their very small passages. Flow restriction causes mass accumulation and rise of pressure at the exit of the annulus. It also causes a decrease in liquid head in the cooling leg. An increase in the heat flux leads to an increase in the heat transfer coefficient and Nusselt number. As a result of the data analysis correlations for the average Nusselt number, Reynolds number and circulation rate have been developed in terms of the heat flux.     

含盐胶体液滴的蒸发图案形成机理

研究了聚四氟乙烯(PTFE)胶粒与NaCl混合液滴的蒸发过程及其图案形成机理. 结果表明, PTFE颗粒对接触线具有强烈的钉扎作用, 胶体液滴蒸发伴有显著的“咖啡环”效应. 由于液滴中心液相区表面张力法向分力的作用, 使得凝胶区存在辐射状应力, 进而产生从液滴边缘向中心的辐射状裂纹, 裂纹数量随胶粒的体积分数增大而减少. NaCl与PTFE胶粒的混合液滴出现了复杂多样的蒸发图案. 盐的加入抑制了向外的毛细补偿流, 从而有利于获得宏观上厚度均匀的沉积膜. NaCl与PTFE胶粒耦合形成了凹凸不平的枝晶状形貌, 这可能是释放蒸发应力的结果.     

Higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations

In this article, we develop a higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations. A priori bounds on the exact solution and its derivatives, which are useful for the error analysis of the numerical method are given. We approximate the retarded terms of the model problem using Taylor's series expansion and the resulting time‐dependent singularly perturbed problem is discretized by the implicit Euler scheme on uniform mesh in time direction and a special hybrid finite difference scheme on piecewise uniform Shishkin mesh in spatial direction. We first prove that the proposed numerical discretization is uniformly convergent of , where and denote the time step and number of mesh‐intervals in space, respectively. After that we design a Richardson extrapolation scheme to increase the order of convergence in time direction and then the new scheme is proved to be uniformly convergent of . Some numerical tests are performed to illustrate the high‐order accuracy and parameter uniform convergence obtained with the proposed numerical methods.     

Numerical approximation of two‐dimensional convection‐diffusion equations with boundary layers

Our aim in this article is to show how one can improve the numerical solution of singularity perturbed problems involving boundary layers. Incorporating the structures of boundary layers into finite element spaces can improve the accuracy of approximate solutions and result in significant simplifications. In this article we discuss convection‐diffusion equations in the two‐dimensional space with a homogeneous Dirichlet boundary condition and a mixed boundary condition. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

正交梯度下双扩散对流的数值模拟

本文采用有限单元法求解涡量、流函数、能量和组分控制方程,数值模拟了在温度梯度和浓度梯度正交情况下竖直环形容器内的双扩散对流结构。通过改变浮升力比N=GrS／GrT和Le数的大小,分析了溶质浮升力方向及其大小和Le数对容器内双扩散对流的影响。结果表明:当溶质浮升力改变时,壁面处的流体流动状况、边界层厚度、Nu数和Sh数都发生了变化;随着Le数的增大,竖直壁面处Nu数逐渐降低而水平壁面处的Sh数逐渐增大。     

固液两相流中微对流强化的机理分析与数值模拟

本文对分散型固液两相混合物层流管流中非均匀剪切力场导致的微对流现象以及由此引起的导热系数增强效应作了机理和影响因素分析,认为除速度分布、颗粒浓度和粒径以外,还存在颗粒形状、粒径分布,壁面热流方向、颗粒表面性质及其与载流介质间的相容性等多个影响因素.模拟计算表明,由微对流导致的对流换热强化与流体在管壁面上的表观导热系数强化具有相同的数量。     

行星式化学气相沉积反应器内对流涡旋的数值模拟

针对三重进口行星式CVD反应器的输运过程进行了二维数值模拟研究。通过改变反应腔几何尺寸、导流管位置、三重进口流量组合、压强、温度等条件,研究反应器内对流涡旋的相应变化。根据模拟结果,对这类反应器中输运现象与外部参数的关系,特别是反应腔内对流涡旋的产生和发展作了较全面的分析和讨论,给出了抑制对流涡旋、获得薄膜生长所需的最佳输运过程的条件。     

方腔内竖直板自然对流分岔现象的数值研究

采用非稳态数学模型通过数值模拟研究了具有对称结构的封闭方腔内竖直板自然对流换热中的非线性现象。数值结果表明,Ra在4×104-7×104之间,会出现定常解、周期性振荡解和非周期性振荡解,即解存在分岔;初始条件与解的分岔相关;网格Pe数的考核表明,本文所考虑的解的振荡不是由于数值解的不稳定而引起的振荡,而是客观存在的物理振荡。     

相变储热/辐射器式热沉传热特性数值模拟

本文采用焓法建立了具有传导与对流换热耦合边界相变储热装置的三维数学模型,利用整场求解法对控制方程进行了计算。计算过程中考虑了相交材料液相自然对流和空穴的影响,与实验结果进行了对比,验证了模型和程序的可靠性,并对影响相变储热器性能的因素进行了分析.     

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

This article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier-Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) [42] showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper.