Heat transfer from metallic filaments (whiskers) into helium under overcritical pressure for temperatures between 3.7 and 7.2 K

The heat transfer coefficient α, near the critical temperature, T_cO, was determined for several whiskers from the In-Pb alloy system. For this purpose the hysteresis of the voltage-temperature (V-T_B) transition curves at fixed currents, I, and of the V-I characteristics at fixed helium bath temperature, T_B, was determined. The advantage of using measurements made with whiskers is that there is no heat transfer to a substrate and negligible heat transfer to the contracts. The only heat transfer is that to the surrounding helium.     

Effects of wetted wall on laminar natural convection in vertical annular ducts

Abstract

A detailed numerical analysis is performed to investigate the effects of latent heat exchange, in connection with evaporation of the liquid film on the wall, on the natural convection heat transfer in vertical concentric annuli. Major governing parameters identified are Gr_T, Gr_M, Pr, Sc, and N. Results are specifically presented for an air‐water system under various heating conditions to illustrate the latent heat transport during the evaporation process. The effects of the channel length, ratio of radii N and wetted wall temperature on the momentum, heat and mass transfer are examined in detail. Tremendous enhancement in heat transfer due to the exchange of latent heat was clearly demonstrated.     

Investigation of heat transfer coefficient in two‐dimensional transient inverse heat conduction problems using the hybrid inverse scheme

A hybrid scheme of the Laplace transform, finite difference and least‐squares methods in conjunction with a sequential‐in‐time concept, cubic spline and temperature measurements is applied to predict the heat transfer coefficient distribution on a boundary surface in two‐dimensional transient inverse heat conduction problems. In this study, the functional form of the heat transfer coefficient is unknown a priori. The whole spatial domain of the unknown heat transfer coefficient is divided into several analysis sub‐intervals. Later, a series of connected cubic polynomial function in space and a linear function in time can be applied to estimate the unknown surface conditions. Due to the application of the Laplace transform, the unknown heat transfer coefficient can be estimated from a specific time. In order to evidence the accuracy of the present inverse scheme, comparisons among the present estimates, previous results and exact solution are made. The results show that the present inverse scheme not only can reduce the number of the measurement locations but also can increase the accuracy of the estimated results. Good estimation on the heat transfer coefficient can be obtained from the knowledge of the transient temperature recordings even in the case with measurement errors. Copyright © 2007 John Wiley & Sons, Ltd.     

改进遗传算法在非线性热传导参数识别中的应用

建立了基于优化算法的估计材料热传导系数和边界条件的热传导反问题求解方法。该方法以观测的温度值与有限元计算模拟的温度值最小二乘极小化原理为基础,然后采用具有全局搜索能力的遗传算法求解。为了加快收敛速度和提高反演识别精度,采用了浮点编码的遗传算法。根据先验信息,建立了高斯变异策略。数值计算结果表明,所建立的数值反演方法可以用来解决未知的热传导系数和边界条件识别问题,并且具有良好的抗观测噪音能力。     

Parameter estimation in heat conduction using a two-dimensional inverse analysis

This article is concerned with a two-dimensional inverse steady-state heat conduction problem. The aim of this study is to estimate the thermal conductivity, the heat transfer coefficient, and the heat flux in irregular bodies (both separately and simultaneously) using a two-dimensional inverse analysis. The numerical procedure consists of an elliptic grid generation technique to generate a mesh over the irregular body and solve for the heat conduction equation. This article describes a novel sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of the thermal conductivity, the heat transfer coefficient, and the heat flux. This sensitivity analysis scheme allows for the solution of inverse problem without requiring solution of adjoint equation even for a large number of unknown variables. The conjugate gradient method (CGM) is used to minimize the difference between the computed temperature on part of the boundary and the simulated measured temperature distribution. The obtained results reveal that the proposed algorithm is very accurate and efficient.     

A non‐iterative finite element method for inverse heat conduction problems

A non‐iterative, finite element‐based inverse method for estimating surface heat flux histories on thermally conducting bodies is developed. The technique, which accommodates both linear and non‐linear problems, and which sequentially minimizes the least squares error norm between corresponding sets of measured and computed temperatures, takes advantage of the linearity between computed temperatures and the instantaneous surface heat flux distribution. Explicit minimization of the instantaneous error norm thus leads to a linear system, i.e. a matrix normal equation, in the current set of nodal surface fluxes. The technique is first validated against a simple analytical quenching model. Simulated low‐noise measurements, generated using the analytical model, lead to heat transfer coefficient estimates that are within 1% of actual values. Simulated high‐noise measurements lead to h estimates that oscillate about the low‐noise solution. Extensions of the present method, designed to smooth oscillatory solutions, and based on future time steps or regularization, are briefly described. The method's ability to resolve highly transient, early‐time heat transfer is also examined; it is found that time resolution decreases linearly with distance to the nearest subsurface measurement site. Once validated, the technique is used to investigate surface heat transfer during experimental quenching of cylinders. Comparison with an earlier inverse analysis of a similar experiment shows that the present method provides solutions that are fully consistent with the earlier results. Although the technique is illustrated using a simple one‐dimensional example, the method can be readily extended to multidimensional problems. Copyright © 2003 John Wiley & Sons, Ltd.     

Simplified calculation of temperature field in heat treated cylinder using temperature measured at one point

Abstract

The calculation of the temperature field T(r) in a heat treated cylinder requires a knowledge of the heat transfer coefficient h(T_s) which may show a highly non-linear dependence on the surface temperature T_s. Since h(T_s) can very often not be explicitly determined, measurement of a temperature T_i near the surface is employed. As a result the analysis becomes an inverse (‘ill posed’) problem which cannot be handled using standard finite element codes that are applicable only to direct problems. By implementing a procedure for an explicit estimation of the surface temperature T_s the problem can be overcome via two direct calculations. Diagrams are presented for calculation of both the surface temperature T_s and the heat transfer coefficient h(T_s). The method is applied to the investigation of a duplex steel cylinder which is quenched in cold water. The accuracy of the method is discussed and the complex nature of h(T_s) is demonstrated.

MST/1497     

Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition

An inverse approach is developed to estimate the unknown heat conductivity and the convective heat transfer coefficient. The method relies on proper orthogonal decomposition (POD) in order to filter out the higher frequency error. The idea is to solve a sequence of direct problems within the body under consideration. The solution of each problem is sampled at a predefined set of points. Each sampled temperature field, known in POD parlance as a snapshot, is obtained for an assumed value of the retrieved parameters. POD analysis, as an efficient mean of detecting correlation between the snapshots, yields a small set of orthogonal vectors (POD basis), constituting an optimal set of approximation functions. The temperature field is then expressed as a linear combination of the POD vectors. In standard applications, the coefficients of this combination are assumed to be constant. In the proposed approach, the coefficients are allowed to be a nonlinear function of the retrieved parameters. The result is a trained POD base, which is then used in inverse analysis, resorting to a condition of minimization of the discrepancy between the measured temperatures and values calculated from the model. Several numerical examples show the robustness and numerical stability of the scheme.     

The influence of residual gas pressure on the thermal conductivity of microsphere insulations

Experimental results of investigations of the heat exchange by residual gas in microsphere insulations are presented. The results of measurements of microsphere effective thermal conductivity versus residual gas (N₂) pressure in the pressure range of 10^–3–10⁵ Pa are also given. A sample of self-pumping microsphere insulation was prepared and its thermal parameters were tested. In comparison to the standard microsphere insulation, the self-pumping insulation yielded lower thermal conductivity results over the entire pressure range. The stability of its thermal parameters as a result of considerable gas input into the insulation volume is discussed. Measurements of temperature and pressure distributions inside the microsphere layer were performed. Plots of temperature and pressure gradients inside the layer of the microsphere insulation are presented.Nomenclature d _m Mean value of the microsphere diameter - k Apparent thermal conductivity coefficient - ¯k Average thermal conductivity coefficient - k _c Component of the heat transfer by conduction - k _g Modified gas thermal conductivity under atmospheric pressure - k _r Component of the heat transfer by radiation - k _s Thermal conductivity of the sphere material - k _gc Component of the heat conduction by gas - k _go Gas thermal conductivity under atmospheric pressure - k _gr Sphere effective conductivity - k _ss Component of the heat conduction by the solid state - K 1–(k _g/k _gr) - Kn Knudsen number - ¯L Mean free path of gas molecules - m 1–_s; porosity - m Empty volume of a single sphere - p Residual gas pressure - ¯p Average pressure - p _g Pressure measured by gauge - p ₀ Residual gas pressure above the insulation bed - r Radial coordinate - T Temperature - T _c Temperature of the cold calorimeter wall - T _g Temperature of the pressure gauge - T _H Temperature of the hot calorimeter wall - T _i Gas temperature inside the bed - T _y Constant dependent on the sort of gas - v Volume - Accommodation coefficient - Density - _a Local distance between surfaces - _s Solid fraction - Constant dependent on the sort of gas - Time measured from the initiation of insulation cooling     

Heat Transfer of Heat-Releasing Fluid in the Top Portion of a Closed Volume

The method of analytic estimates is used to determine the characteristics of steady-state free-convection heat transfer of a fluid with internal heat sources in the top part of a closed volume with different conditions of heat removal on the top horizontal boundary at the Prandtl number value on the order of unity. It is demonstrated that, in the case of adiabatic condition on the top boundary of the volume, the maximal heat flux q _max attained in the region of intersection of the top horizontal and vertical boundaries depends only on the maximal temperature in the volume T _max and on the thermal characteristics of the fluid. The correction to the bulk temperature (outside of the boundary layers) T _b z ^1/4, which is a function of the vertical coordinate z, significantly prevails over perturbations in the horizontal section. When the turbulent Rayleigh-Benard (RB) convection arises, the heat removal through the top boundary is defined only by the energy release in the RB-layer. Given a fixed power of heat release Q, the RB-layer thickness increases by the linear law h=q/Q with increasing heat flux q through the top horizontal boundary.     

Numerical Solution of Inverse Radiative–Conductive Transient Heat Transfer Problem in a Grey Participating Medium

The problem of simultaneous identification of the thermal conductivity Λ(T) and the asymmetry parameter g of the Henyey–Greenstein scattering phase function is under consideration. A one-dimensional configuration in a grey participating medium with respect to silica fibers for which the thermophysical and optical properties are known from the literature is accepted. To find the unknown parameters, it is assumed that the thermal conductivity Λ(T) may be represented in a base of functions {1, T, T ², . . .,T ^K } so the inverse problem can be applied to determine a set of coefficients {Λ₀, Λ₁, . . ., Λ _K ; g}. The solution of the inverse problem is based on minimization of the ordinary squared differences between the measured and model temperatures. The measured temperatures are considered known. Temperature responses measured or theoretically generated at several different distances from the heat source along an x axis of the specimen set are known as a result of the numerical solution of the transient coupled heat transfer in a grey participating medium. An implicit finite volume method (FVM) is used for handling the energy equation, while a finite difference method (FDM) is applied to find the sensitivity coefficients with respect to the unknown set of coefficients. There are free parameters in a model, so these parameters are changed during an iteration process used by the fitting procedure. The Levenberg– Marquardt fitting procedure is iteratively searching for best fit of these parameters. The source term in the governing conservation-of-energy equation taking into account absorption, emission, and scattering of radiation is calculated by means of a discrete ordinate method together with an FDM while the scattering phase function approximated by the Henyey–Greenstein function is expanded in a series of Legendre polynomials with coefficients {c _l } = (2l + 1)g ^l . The numerical procedure proposed here also allows consideration of some cases of coupled heat transfer in non-grey participating media. The inverse method may be treated, after performing a suitable validation, as an alternative method in relation to other classical measurement methods for investigation of thermophysical parameters of solid states.     

The boundary-element method for the determination of a heat source dependent on one variable

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination. In this problem, if the heat source is taken to be space-dependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is time-dependent only, then the overdetermination is the transient temperature measurement recorded by a single thermocouple installed in the interior of the heat conductor. These measurements ensure that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or the L-curve criterion for the choice of the regularization parameter. The boundary-element method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed     

用三维有限元求解金属淬火过程的换热系数

在金属淬火过程的数值模拟中,换热系数的正确求解是工件温度场、应力/应变场模拟结果与实际相符合的先决条件.据此研究和分析了换热系数反求法的数学模型,分别采用一维和三维有限元法对该数学模型求解.研究表明:与采用一维有限差分的求解法相比较,计算过程由一维有限元法增加到三维有限元法,与实际情况更为接近;用有限元方法求解的换热系数曲线连续且平滑,结果可靠,且编程量小;用求得的换热系数计算金属淬火试件的中心温度场变化曲线,计算结果与实测数据相吻合.     

Critical-region thermal expansion in CuK2Cl4 · 2H2O

The Curie-point anomaly in thea-axis linear thermal expansion coefficient of CuK₂Cl₄ · 2H₂O (T _c=0.88° K) has been observed using the three-terminal capacitance technique. Length changes of the 3.8-mm single-crystal sample were determined to within approximately 0.1 Å. In the critical region our data suggest a logarithmic singularity as found previously for the specific heat. However, imperfections in the sample limit the divergence of the expansion coefficient at temperatures closer than 0.01T _c to the transition. From a comparison of the linear expansion coefficient with the specific heat in the critical region, the stress dependence of the Curie temperature is calculated. We find that the temperature derivative of the spin-correlation function describing nearest neighbor magnetic ions is not proportional to the temperature derivative of the spin-correlation function describing next nearest neighbors. Furthermore, the exchange parameters characterizing nearest and next nearest neighbor interactions do not have equal stress dependences. Between 1.5 and 2.5° K the thermal expansion coefficient is proportional to the inverse square of the temperature. Comparison of the expansion coefficient with the specific heat in this temperature range indicates that the temperature derivative of both spin-correlation functions is proportional toT ^–2. The stress dependence of the Curie temperature calculated from data in this region agrees within experimental error with the value found from different considerations using data in the critical region.Work supported by National Science Foundation.     

Relation of transformation temperature to the fracture toughness of transformation-toughened ceramics

The stress induced tetragonal to monoclinic ZrO₂ martensitic transformation contribution to fracture toughness is described in terms of the required external strain energy and the thermo-dynamic stability of the constrained tetragonal phase. The strain energy, derived from an externally applied stress acting on the main crack, required to achieve transformation toughening is shown to be a function of the term (T - M _s) whereT is the test temperature andM _s is the martensite start temperature for the case ofT > M _s. Thus for a givenT (T > M _s), the transformation toughening component increases asM _s approachesT and for a fixedM _s, the toughness decreases asT increases. Experimental data for partially stabilized zirconia ceramics confirm these results and show that increasing tetragonal precipitate size is the primary feature which affects an increase inM _s. In the case ofT M _s, autotransformation occurs, resulting in decreasing toughness with decrease inT due to a continuous loss in the tetragonal phase content. A temperature region is thus obtained over which transformation toughening exhibits a maximum in its contribution. The temperatures over which this occurs then is shown to be dependent on theM _s temperature of the material.     

Coexistence of Superconductivity and Itinerant Ferromagnetism in Ferromagnetic Metals UCoGe and UIr

A microscopic coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is studied in a single band homogenous system, following an equation of motion method and Green’s function technique. Self-consistent equations for superconducting order parameter (Δ) and magnetization parameter (M) are derived. It is shown that there generally exists a coexistent (Δ≠0, M≠0) solution to the coupled equations of the order parameters in the temperature range 0<T<min (T _C,T _FM), where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The expressions for electronic specific heat (C/T), density of states, free energy, transition probabilities, ultrasonic attenuation, and nuclear relaxation are also derived. The theory is applied to explain the observations in UCoGe and UIr. The specific heat capacity at low temperature shows linear temperature dependence as opposed to the activated behavior. Density of states increases as opposed to the case of a standard ferromagnetic metal. Free energy study reveals that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and, therefore, coexistence of FM and SC realized at a low enough temperature. The agreement between theory and experimental results for UCoGe and UIr is quite encouraging.     

Numerical Analysis of Heat Transport Behavior in the Ferromagnetic Metallic State of La0.80Ca0.20MnO3 Manganites

The lattice contribution to the thermal conductivity (κ_ph) in La_0.80Ca_0.20 MnO₃ manganites is discussed within the Debye-type relaxation rate approximation in terms of the acoustic phonon frequency and relaxation time. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity dominates in La–Ca–MnO manganites and is an artifact of strong phonon-impurity and -phonon scattering mechanisms in the ferromagnetic metallic state. The electronic contribution to the thermal conductivity (κ_e) is estimated following the Wiedemann–Franz law. This estimate sets an upper bound on κ_e, and in the vicinity of the Curie temperature (240 K) κ_e is about 1% of total heat transfer of manganites. Another important contribution in the metallic phase should come from spin waves (κ_m). It is noticed that κ_m increases with a T² dependence on the temperature. These channels for heat transfer are algebraically added and κ_tot develops a broad peak at about 55 K, before falling off at lower temperatures. The behavior of the thermal conductivity in manganites is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between electron, magnon, and phonon contributions. The numerical analysis of heat transfer in the ferromagnetic metallic phase of manganites shows similar results as those revealed from experiments.      

Development of compact heat exchangers for CO2 air-conditioning systems

Compact and lightweight heat exchangers are needed for motor vehicle air-conditioning systems and for several types of unitary equipment. The high-pressure natural refrigerant CO₂ is now being evaluated for use in such applications, and efficient heat exchangers are being developed and investigated. Carbon dioxide heat exchangers are designed for high refrigerant mass flux and use small-diameter tubes or extruded flat microchannel tubes. Refrigerant-side heat transfer coefficients are higher than with fluorocarbons, and reduced internal surface areas can therefore be tolerated. Both small-diameter mechanically expanded round-tube heat exchangers and brazed microchannel-type units have been built and tested successfully. Results show that compact heat exchangers optimized for CO₂ are very competitive with baseline HFC/HCFC units in terms of physical dimensions, exchanger mass and thermal performance. Smaller tube and manifold dimensions can give reduced size compared with HFC-134a equipment. The temperature approach between air inlet and refrigerant outlet is much lower in CO₂ gas coolers than in baseline system condensers of equal size and capacity, and the reduced refrigerant exit temperature has a marked influence on the coefficient of performance, Microchannel heat exchangers give the best overall efficiency. Refrigerant distribution in multiport manifolds and heat transfer tubes does not seem to be a problem.     

Hot-Wire Measurements of the Heat Transfer in a Partially Magnetized Potassium Plasma

A hot-wire device designed as a gas-loaded heat pipe has been used to study the axial magnetic field influence on the heat transfer in a potassium vapor plasma at low vapor pressures p _K=400 to 1200 Pa, temperatures T _w of the tungsten filament in the range 2000 to 2800 K, and magnetic field intensity B=0.182 to 0.364 T. As a result of the applied magnetic field B, the measured thermal flux Q decreases. The separation between the heat fluxes transferred by radiation Q _r, by atoms Q _a, and by electrons Q _e can be accomplished analyzing the decrement Q. A procedure to analyze the measured data in the presence and in the absence of the magnetic field in order to define the different mechanisms of the heat transfer has been introduced. The electron thermal conductivity can be obtained in the Frost approximation by means of the well-known transport phenomena theory using available electron–potassium atom cross sections in the range of electron energies =0.06 to 2 eV.     

Thermal Property Measurements and Enthalpy Calculation of the Lithium Bromide+Lithium Iodide+1,3-Propanediol+Water System

The lithium bromide+lithium iodide+1,3-propanediol+water [LiBr/LiI mole ratio=4 and (LiBr+LiI)/HO(CH₂)₃ OH mass ratio=4] solution is being considered as a potential working fluid for an absorption chiller. Heat capacities at four temperatures, 283.15, 298.15, 313.15, and 333.15 K, were measured in the range from 50 to 70 mass%. In addition, the differential heats of dilution at 298.15 K were measured in the range from 45.3 to 71.8 mass%. Each individual data set was correlated with a proper regression equation with a high accuracy. A new enthalpy calculation method for the working fluids containing organics was proposed. The calculation method correlated the heat capacity (at various temperatures and concentrations) and the differential heat of dilution (at ambient temperature and various concentrations). The present method was applied for the construction of enthalpy–concentration (H–T–X) diagrams with high confidence.