Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties

This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.     

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.     

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.     

On applications of the microlocal parameter method in modelling of temperature distributions in composite cylinders

Summary The problems of transient heat conduction in a periodically stratified medium consisting of a large number of alternating concentric cylinders of two homogeneous isotropic rigid materials and in a rotationally periodic cylinder consisting of a large number of circular homogeneous isotropic rigid sectors are considered. The equations of the homogenized models with microlocal parameters are derived by using the homogenization procedure given in [17]. The obtained models take into account certain microlocal effects connected with the microperiodic structure of the considered composites. Some examples of the application of the presented models to the problems of temperature distributions in composite cylinders are detailed. Received 10 March 1997; accepted for publication 23 October 1997     

Heat transfer in specularly reflecting tubes

Heat exchange inside a specularly reflecting tube is analysed. Expressions are obtained for heat transfer between cross-sections, between incremental wall annuli, between finite wall annuli, and combinations of the above. The expressions are related to the angle factor for opposed discs, but are infinite summations; they are easily evaluated, requiring some 20 emissivity terms. The basic disc-to-disc expression also represents the fraction of radiation leaving a disc that is still propagating at some distance along the tube, including reflection. Special case results are obtained for the radiant loss from double and single ended holes. For the practical application considered, it was found that conduction and radiation could be treated separately, permitting evaluation of a radiation loss factor for a specularly reflecting tube between two heat reservoirs     

WAVE PROPAGATION IN A TRANSVERSELY ISOTROPIC THERMOELASTIC SOLID CYLINDER OF ARBITRARY CROSS-SECTION

The wave propagation in an infinite, homogeneous, transversely isotropic solid cylinder of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.     

Explicit equations for transient heat conduction in finite solids for <Emphasis Type="Italic">Bi</Emphasis> > 2

A set of correlations is developed for transient heat conduction in finite solids (plates, cylinders and spheres) exposed to high Biot number convection boundary conditions. For Bi ≥ 3, the error of the approximate solutions is well below 1% of the initial temperature difference driving the transient.     

Einfluß der Geometrie auf die Wärmeleitung in Kühlkanälen einer Flüssigkeits-Rakete

The paper presents some typical results of an analysis of two-dimensional, steady-state heat conduction in coolant channels subjected to the third kind of thermal boundary conditions usually encountered in a regeneratively or dump-cooled liquid rocket engine. Duct geometries of circular, rectangular, trapezoidal and isosceles triangular cross-sections with rounded corners are considered. The solution method is based on the boundary collocation technique of linear least-squares matching using Householder reflections. The results of maximum duct wall temperatures and total heat transfer to the coolant by the present analysis vis-a-vis those by one-dimensional analysis reveal that the latter predicts higher values of maximum wall temperatures in the curved region of non-circular ducts and lower values of total heat transfer to the coolant.     

Chirality in the Torsion of Cylinders with Trigonal Symmetry

Solutions are obtained for a class of torsion problems for cylinders of a material with trigonal material symmetry. In particular, the solutions for elliptical, circular and equilateral triangular cross-sections are presented. These solutions show that the stress distributions are non-chiral and the same as they would be if the material were isotropic; however the in-plane displacements are chiral and different from the isotropic case. The results show that there will be transverse, in-plane stress interactions between the layers of a composite cylinder composed of concentric cylinders of different trigonal materials in torsional loading. Such composite cylinders are structural designs used by nature and by man. This revised version was published online in July 2006 with corrections to the Cover Date.     

Natural convection in vertical concentric annuli under a radial magnetic field

Exact solutions for fully developed natural convection in open-ended vertical concentric annuli under a radial magnetic field are presented. Expressions for velocity field, temperature field, mass flow rate and skin-friction are given, under more general thermal boundary conditions. It is observed that both velocity as well as temperature of the fluid is more in case of isothermal condition compared with constant heat flux case when gap between cylinders is less or equal to radius of inner cylinder while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder.     

非傅里叶热传导研究进展

傅里叶定律能够精确描述大多数的热传导问题,但对于超短脉冲激光加热等热作用的周期时间极短的超急速、超常规热传导等问题,非傅里叶效应将会显得至关重要．对非傅里叶热传导的实质、模型、模型的求解及应用与实验等几个方面的研究进展做了一个较详尽的概括与评述,并指出了今后需要着重研究的方向．      

Numerical simulation and experimental analysis of heat transfer through the neck tube into vertical cryogenic insulated cylinders

The neck tube is an important support structure in cryogenic insulated cylinders. The heat flux from the outside environment through the neck tube into the cryogenic liquid occupies a great proportion of the total heat leak and can be more than half of the total heat loads. In this paper, conjugate convective-conductive heat transfer model between wall and the cold vapor in conditions of natural discharge is numerically investigated. Also a liquid nitrogen boil-off method was adopted in experiments to validate the result of numerical simulation. Experimental results indicate more favorable agreement with conjugate heat transfer (CHT) model compared with simple solid heat conduction (SSHC) model by ANSYS software. And the convection between the wall and vapor is also calculated. The research and results can provide reference in design for neck tube of the cryogenic cylinder.     

Natural convection of two staggered cylinders for various prandtl numbers and vertical and horizontal pitches

Natural convection heat transfer phenomena of two staggered cylinders were investigated for laminar flows. Numerical simulations were carried out to examine the effect of varying the Prandtl number and the vertical and horizontal pitch-to-diameter ratios for a Rayleigh number of 1.5 × 10⁸ using FLUENT. This study focused on phenomena related to very small vertical pitch. The heat transfer rates of the upper cylinders were influenced by plumes from the lower cylinders, exhibiting preheating, velocity, sweep, and side flow effects. The heat transfer rates of the lower cylinders were not affected by the upper cylinders at moderate vertical pitches. However, when the vertical pitch was very small, they were affected by stagnant flow, sweep, and side flow effects.     

An Exact Solution of Torsion Problem for an Incomplete Torus with Application to Helical Springs

An exact analytical solution for the torsion problem of an incomplete torus with a particular form of non-circular cross-section has been found. The solution extends for the close-coiled helical spring the known solution of the torsion problems for straight cylinders with circular and elliptical cross-sections. The pitch of helix is ignored. The hollow cross-sections of the particular form also demonstrate a closed form of analytical solution. The solution can be used for analysis of helical springs with non-circular wire profile.     

Solidification and melting heat transfer to an unfixed phase change material (PCM) encapsulated in a horizontal concentric annulus

The solidification and melting process of an unfixed PCM between two isothermal concentric horizontal cylinders was investigated by experimental techniques and by a combined analytical and numerical method. During the solidification process concentric solid PCM layers form at both tube walls, growing slowly into the annulus. Assuming quasi-steady heat conduction, this process is described by a simple analysis. The melting PCM reveals a different behaviour. Due to gravitational forces the solid phase moves downwards. Experiments prove that the solid retains contact with the lower part of the outer tube as well as with the upper part of the inner tube. In this process thin liquid films form between the solid body and the heated walls and heat transfer by conduction is the dominating mechanism during melting. Heat transfer by natural convection causes the melting at the upper interface. There, the melting rates, however, are comparatively small. The theoretical approach and the numerical analysis are based on a balance of the pressure forces in the thin liquid films and of the gravitational force acting on the solid material. As a result melting rates and heat fluxes may be predicted. For practical application a Nusselt correlation is derived.     

Natural convection to water from arrays of short wall-attached cylinders

Experiments of natural convection from arrays of one, two, and three horizontal cylinders attached vertically one above the other to a heated, vertical flat plate in water have shown that the lowest cylinder is essentially unaffected by cylinders above it and has a heat transfer rate less than that of an infinitely long cylinder. The effect on the heat transfer from cylinders in the wake of the lowest cylinder is primarily a function of the spacing between the cylinders, with the increase being larger for greater spacing. For these wake cylinders, increases are sufficient to cause the heat transfer to equal that of an infinite cylinder.     

INTERVAL ANALYSIS OF FUZZY-RANDOM HEAT CONDUCTION IN COMPOSITE TUBES

IntroductionThere are a lot of uncertainties such as fuzziness and random in the design andmanufacture in engineering.In generally speaking,methods to deal with the fuzzy-randomproblems are first to transfer the fuzzy set to real number set,and then the p…     

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper,we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field.The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity,induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli.The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables.It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder,while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder.These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases.It is also found that as the Hartmann number increases,there is a flattening tendency for both the velocity and the induced magnetic field.The influence of the induced magnetic field is to increase the velocity profiles.     

Numerical simulation of laminar flow and heat transfer over banks of staggered cylinders

A study is conducted to investigate forced convective flow and heat transfer over a bank of staggered cylinders. Using a novel numerical formulation based on a non‐orthogonal collocated grid in a physical plane, the effects of Reynolds number and cylinder spacing on the flow and heat transfer behaviour are systematically studied. It is observed that both the Reynolds number and cylinder spacing influence the recirculatory vortex formation and growth in the region between the cylinders; in turn, the rates of heat transfer between the fluid and the staggered cylinders are affected. As the cylinder spacing decreases, the size and length of eddies reduce. For sufficiently small spacings, eddy formation is completely suppressed even at high Reynolds number. Pressure drop and Nusselt number predictions based on numerical study are in excellent agreement with available correlations. The study provides useful insight on the detailed flow and heat transfer phenomena for the case of a bank of staggered cylinders. Copyright © 2002 John Wiley & Sons, Ltd.     

基于物理信息神经网络的功能梯度材料稳态/瞬态热传导分析

采用物理信息神经网络PINN(Physics-informed Neural Networks)求解稳态和瞬态功能梯度材料(FGMs)热传导问题。该方法利用控制方程、边界及初始条件的残差构造损失函数,在无任何响应数据的情况下得到了更具泛化能力的神经网络模型,同时避免了传统数值方法在求解计算力学问题时所需的微分、积分公式推导以及繁重的建模和划分网格等前处理工作。本文探究了PINN及其域分解的扩展物理信息神经网络XPINN(eXtended Physics-informed Neural Networks)在求解稳态和瞬态FGMs热传导问题时的适用性,讨论了网络结构对预测结果的影响。研究结果表明,PINN/XPINN在解决几何复杂的稳态和瞬态FGMs热传导问题时仍具有较高的可靠性和简洁的求解流程,同时,为极端环境下求解复杂多场耦合和夹杂等问题提供了新思路。