非均匀竖直平板自然对流耦合边界的数值研究

以板管式换热器为应用背景,采用SIMPLEC算法求解了竖直薄平板温度不均匀时边界导热与自然对流的耦合传热。数值计算结果表明,对自然对流而言,在≤108,采用铝平板已经可以获得足够好的传热性能,再增加平板的导热性能对传热几乎没有影响;而在≤104的情况下,采用钢平板可以获得跟铝平板几乎一致的传热效果;平板温度不均匀,明显增加了自然对流边界层厚度,但在顶端和底端加热盘管之间的平板区域其局部数与等壁温情况相差不大;对在104～107的范围内提出一个非均匀平板自然对流平均数计算公式,其误差约为5%。     

幂律流体连续运动平板边界层的数值研究

利用数值模拟方法研究了幂律流体在连续运动平板上的层流边界层问题。利用相似变换理论推导出无量纲剪切力的计算公式,数值求解了不同幂律指数n的流体在不同运动参数ξ的连续运动平板上的层流边界层流场,分析了各个参数对边界层速度分布和剪切力大小的影响。结果表明,边界层偏微分方程组的数值解与经过相似变换求得的非线性常微分方程的数值解吻合得很好,这既说明对幂律流体连续运动平板上的层流边界层问题的研究是有效且可靠的,同时也证明了连续运动平板问题存在相似解。     

指定压力边界条件在无限空间自然对流数值模拟中的应用

探讨了指定压力边界条件在无限空间自然对流模拟中的数值实施方法。指出了由边界的指定压力转化为速度的方法。以常壁温圆柱在无限空间的二维层流自然对流为例,实施了这种方法,计算结果与其它数值解、试验值和分析解的对比表明,本方法不但实施方便而且可以采用较小的计算区域而获得正确的结果,节省了计算时间和计算存储量。     

基于等效比热的MPCMs平板层流传热理论模型

采用边界层的能量积分方程法,基于等效比热模型,对微胶囊相变悬浮液(Microencapsulated Phase Change Materials slurry, MPCMs)的热边界层进行理论建模,推导出了MPCMs外掠平板换热加热等壁温边界条件层流工况下,包含斯蒂芬数的MPCMs的对流换热关联式,然后与数值模拟结果进行比较。结果表明,对流传热系数的解析解与数值模拟结果趋势上相一致,修正后的解析解与数值模拟结果高度吻合。     

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。     

大空间管排自然对流的数值模拟

对具有2，4，6根管的管排在大空间内的自然对流进行了数值模拟。参数范围为10^2〈Ra〈10^4，S／D=1．25，2，3，5，9，11，Pr=0．7，流态为层流。数值计算结果表明：Ra和S／D对换热都有重要的影响，在小间距时对流作用处于劣势，管排中的管处于换热削弱状态，随着间距的增大对流作用逐渐占优势，管排中的各管从下至上逐渐受到加强，管排中出现了涡，这种涡起着增强局部换热系数的作用。     

SCSD格式数值稳定性及计算精度的研究

概述对流项离散格式所引起的假扩散现象及选择不同的离散格式对数值计算过程的影响;在分析稳定性可控的对流项离散格式(stability controllable second-order difference scheme, SCSD)的基础上,提出求解二维对流扩散问题时,直接采用块修正技术和PDMA算法的强隐迭代算法,并对该格式在近边界节点的离散方程的处理上采用非均匀网格技术.通过典型算例验证,该方法不仅抑制了假扩散现象,保证了计算精度,同时也使稳定性得到增强.因此,采用SCSD格式离散对流项,应用非均匀网格处理近边界,并将TDMA算法和PDMA算法同时纳入求解离散方程的做法是合理的,整个程序的框架具有很强的通用性.     

硅橡胶平板暂态热路模型的建立与试验验证

为了研究光伏背板漏电起痕时表面温度特性,采用硅橡胶平板为研究对象并建立热路模型,实现放电表面温度的间接计算。首先根据光伏背板漏电起痕的特点对硅橡胶平板建立暂态热路模型,考虑到空气对流造成的影响,引入空气对流指数n对模型进行改进,提出空气对流指数和对流换热系数的求解方法。然后利用金属丝发热模拟平板表面放电时的发热状态,设计硅橡胶平板温升试验获得温度变化数据并与模型计算结果进行对比。结果表明,在求解得到对流换热系数和空气对流指数的基础上,暂态热路模型计算结果与试验结果的相对误差不超过10%,具有较高精度。     

低散热发动机对流散热场的数值分析

本文利用在非交错网格上求解非正交曲线上标系下的Ｎ－Ｓ方程的方法，对低散热发动机对流散热场进行了数值模拟，得到了不同瑞利（Ｒａｙｌｅｉｇｈ）数下的散热通道内流场和温度场的数值解。计算结果表明，通过冷却通道中空气自然对流换热方式所散失的热量很小。     

倾斜平板热面朝上自然对流换热实验研究

对不同倾斜角度的平板在空气中的自然对流换热系数进行了实验测量.采用直接电加热方法对倾斜平板进行加热,在倾斜铜板背面嵌人式布置热电偶测量平板表面平均温度,同时测量电加热时的电压及电流.实验结果表明,随着倾斜表面与空气温差的增加,实验得到的平均努谢尔特数与经典的准则关联式得到的努谢尔特数呈现不同的变化趋势;随着倾斜角度的增加自然对流换热得到了强化,而且当倾斜平板趋于水平或者竖直时实验结果与经典准则关联式的计算结果偏差逐渐增大,最大偏差达到51%.     

Numerical solution of power law fluids flow and heat transfer with a magnetic field in a rectangular duct

The steady laminar flow and heat transfer of an incompressible, electrically conducting, power law non-Newtonian fluids in a rectangular duct are studied in the presence of an external uniform magnetic field. The momentum and energy equations are solved iteratively using a finite difference method. Two cases of the thermal boundary conditions are considered; (1) T thermal boundary condition “constant temperature at the wall” and (2) H2 thermal boundary condition “constant heat flux at the wall”. The viscous and Joule dissipations are taken into consideration in the energy equation. A numerical solution for the governing partial differential equations is developed and the influence of the magnetic field on the velocity distribution, the friction factor and the average Nusselt number are discussed.     

Simultaneous determination of the heat source and the initial data by using an explicit Lie-group shooting method

Abstract

In this article, an explicit Lie-group shooting method (LGSM) is developed to solve the time-dependent heat source and the initial data for backward heat conduction problems. To recover both unknown data simultaneously, it is very difficult to obtain a stable solution by explicit or implicit schemes. To solve these problems by using conventional numerical schemes, numerical iterative regularization techniques and numerical integration techniques are necessary. To avoid these numerical techniques and to increase the computational efficiency, an explicit LGSM is developed. According to the solution of the quadratic equation of the LGSM, the initial condition can be directly obtained by using the final condition and boundary conditions at the initial time and final time. Using the reciprocal relationship of the solutions for the initial condition and the final condition, the proposed algorithm can avoid numerical integration and numerical iteration. Additionally, a closed-form formula from a two-point Lie-group equation can be directly used to calculate the heat source term. To illustrate the effectiveness and accuracy of the proposed algorithm, several benchmarks are tested. The numerical results indicate that the proposed algorithm can achieve an efficient and stable solution, even with noisy measurement data, by comparing the estimation results with the existing literature.     

Effect of ground boundary and initial conditions on the thermal performance of buildings

The adiabatic boundary condition and the surface heat flux continuum boundary condition for the ground layer beneath a building are examined by comparing the numerical predictions with the corresponding measurements. The effect of the ground depth on the validity of the deep ground boundary conditions is also addressed. Comparison of room air temperature predictions under free floating conditions for different boundary conditions is made for cavity brick and brick veneer housing test modules located on the campus of the University of Newcastle. The sensitivity of the different ground boundary conditions to the heating and cooling loads under air conditioned scenarios is also studied. Finally the effect of the initial condition on the solution is discussed. A new treatment of weather data is proposed to mitigate the effect of the initial condition.     

Onset of Rayleigh–Bénard MHD convection in a micropolar fluid

The present work is concerned with the effect of a uniform magnetic field on the onset of convection in an electrically conducting micropolar fluid. A flat fluid layer bounded by horizontal rigid boundaries, subjected to thermal boundary conditions of the Neumann type, is considered. The parallel flow approximation is used to predict analytically the critical Rayleigh number for the onset of convection. The onset of motion is found to depend on the Hartmann number Ha, materials parameters K, B, $\lambda$, and the micro-rotation boundary condition n. A linear stability analysis is carried out to study numerically the onset of convection. The predictions of the analytical model are found to be in good agreement with the numerical solution. The above results are also compared with those obtained numerically for the case of a system subject to Dirichlet thermal boundary conditions.     

A NEWTON-BASED BOUNDARY ELEMENT METHOD FOR NONLINEAR CONVECTIVE DIFFUSION PROBLEMS

Abstract

A Newton-based boundary element method for the solution of nonlinear convective diffusion problems is presented. The problems are formulated through the use of the exponential transformation. The numerical procedures for the boundary element implementation of the formulation are discussed, and the treatment of nonlinear boundary conditions using the Newton-Raphson method is described in detail. The coefficient matrices resulting from the boundary element implementation are so partitioned as to facilitate the construction and efficient computation of the Jacobian matrix. Three numerical examples are provided. The results agree well with the analytical solutions whenever available. The method is free from numerical oscillations even for high Peclet numbers. The Newton-based iterative scheme, when integrated with the BEM, provides an efficient algorithm for the solution of nonlinear convective diffusion problems and is superior to the successive substitution approximation.     

Effects of an unsteady thermal boundary condition on forced convection heat transfer

A numerical analysis based on adjoint formulation of unsteady forced convection heat transfer is proposed to generally evaluate effects of the thermal boundary condition on the heat transfer characteristics. A numerical solution of the adjoint problem enables us to predict the heat transfer characteristics, such as the total heat transfer rate or the temperature at a specific location, when the thermal boundary conditions change arbitrarily with time. Moreover, using the numerical solution of the adjoint problem, we can obtain the optimal thermal boundary conditions in both time and space to maximize the heat transfer at any arbitrary time. Numerical solutions of the adjoint problem in a lid‐driven cavity are presented to illustrate the capability of the present method. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 237–247, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10032     

Heat transfer for Herschel–Bulkley fluids in the entrance region of a rectangular duct

In this study, we present a numerical solution for combined laminar fluid flow and heat transfer of Herschel–Bulkley non-Newtonian fluids in the entrance region of a rectangular duct. The governing equations are solved iteratively by using finite difference method to obtain temperature, bulk temperature, and Nusselt number. Two cases of the thermal boundary conditions are considered; (i) T thermal boundary condition “constant temperature at the wall” and (ii) H2 thermal boundary condition “constant heat flux at the wall”. The results are presented in tables and figures for different parameters for the fluid and the duct geometry.     

Analytical solution of gaseous slip flow in long microchannels

In this paper we provide solution of the Navier–Stokes equations for gaseous slip flow in long microchannels with a second-order accurate slip boundary condition at the walls. The obtained solution is general enough to allow evaluation of various slip models proposed in the literature. We compare our solution against the first-order accurate slip boundary condition and show that the solution has a weak dependence on Reynolds number, which was neglected in the earlier theory. It is emphasized that first-order slip models do not predict the “Knudsen paradox” (appearance of a minima in normalized volume flux at Knudsen number approximately unity), or a change in curvature of centerline pressure at Knudsen numbers of 0.16. A comparison with Boltzmann’s solution suggests that the derived solution agrees reasonably well up to Knudsen number approximately 5, which shows that the validity of Navier–Stokes to rarefied gases can possibly be increased by using a high order slip boundary condition and proper choice of the slip coefficients. This result is significant from the perspective of numerical simulations of rarefied gases.     

Adiabatic-isothermal mixed boundary conditions in heat transfer

Mixed boundary conditions of the adiabatic-isothermal type often arise in the mathematical modeling of heat transfer phenomena. Under certain circumstances, the mixed condition gives rise to singular behavior which cannot be adequately treated by numerical means alone. The numerical procedure must be supplemented by an asymptotic analysis for the local behavior near the singularity. In the special case of a mixed boundary condition on a straight boundary, the strength of the singularity is given in terms of a path-independent integral, the value of which can be determined from the numerical solution for the far-field behavior. Implications of overlooking the singular behavior due to the mixed boundary condition are discussed.     

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.