Effects Of Temperature Dependent Thermal Conductivity Research Articles

Investigation on the Thermal Performance of a 363 kV Vacuum Circuit Breaker Using a 3D Coupled Model

Multi-break vacuum circuit breakers (VCBs) are the most potential approach for applying VCBs to high voltage power system. However, it has higher thermal stability requirements than normal single break VCBs due to its complex structure and high rated current. In this paper, a novel 363 kV/5000 A/63 kA SF6 gas insulate (GI) VCB with series and parallel structure is proposed. To analyze its temperature rise, a 3D coupled electromagnetic-thermal-fluid model is established based on actual size and calculated by finite element method under rated condition, which enables prediction of the temperature distribution of the contacts of VCB and bus bar. In the numerical model, the vacuum chamber is modelled as solid material with temperature dependent effective thermal conductivity while skin effect, nonlinear property of conductor resistivity and turbulence model are taken into consideration. The simulation results show that the hot spot is the contacts of VCB with a temperature of 102.2 K, while the temperature of busbars reach at 92.3 K. In addition, the influences of contact resistance, short circuit current on the temperature rise are discussed. Finally, the simulation results are validated by temperature rise experiment on prototype. Using the proposed model, the temperature rise and hot spot area can be predicted in advance, which could finally facilitate the design and performance evaluation of the 363 kV GI-VCB.

Thermal analysis of microwave GaN-HEMTs in conventional and flip-chip assemblies

Temperature rising which originates from self-heating degrades the electrical characteristics, reliability, and lifetime of high-power GaN-HEMTs. In this article, a systematic analytical approach for thermal evaluation of microwave GaN-HEMTs is constructed through combining and scrutinizing some of the basic static thermal analysis methods to provide a deeper insight into the process of the channel temperature rising and self-heating with a much lower computational burden. The proposed systematic thermal analysis has been applied to two different assembly methods: conventional mounting and flip-chip mounting. Although the mathematical and empirical equations used are simple enough to save time, the effects of several phenomena and different conditions on the channel temperature have been taken into account. These include heat crowding phenomenon, the effect of temperature-dependent thermal conductivity of the transistor constituent materials, transistor geometry, die-attach material properties, and bump dimensions. To validate the accuracy of the calculations, all the analytical analyses are followed by 3D thermal simulations in ANSYS software. The simulation results confirm the accuracy of the analytical calculations.

Effect of Temperature-Dependent Thermal Conductivity on Spreading Resistance in Flux Channels

When the thermal conductivity of a material varies with temperature, the governing heat conduction equation becomes nonlinear and the use of constant thermal conductivity may produce unreliable results in thermal analysis. In this paper, analytical solutions for the temperature distribution and thermal resistance of a three-dimensional flux channel with temperature-dependent thermal conductivity are discussed and used to study the effect of the temperature-dependent thermal conductivity on the temperature rise and thermal spreading resistance for different conductivity functions. A single eccentric heat source is considered in the source plane of the flux channel that spreads the heat into a convective heat sink. The analytical solutions of the problem are illustrated by means of the Kirchhoff transform, which is considered a powerful technique for solving nonlinear conduction problems with temperature-dependent thermal conductivity. For validation purposes of the analytical results, the results are compared with numerical solution results obtained by solving the problem based on the finite element method using the ANSYS commercial software package.

The effect of temperature-dependent thermal conductivity on the geothermal structure of the Sydney Basin

The thermal structure of continental crust is a critical factor for geothermal exploration, hydrocarbon maturation and crustal strength, and yet our understanding of it is limited by our incomplete knowledge of its geological structure and thermal properties such as hydrogeologic and thermo-mechanical feedbacks that come into play. One of the most critical parameters in modelling upper crustal temperature is thermal conductivity, which itself exhibits strong temperature dependence. In this study, we integrate new laboratory measurements of the thermal conductivity of Sydney Basin rocks under varying temperatures, with finite-element geothermal models of the Sydney Basin using deal.II (Bangerth et al. in ACM Trans Math Softw (TOMS) 33:24, 2007). Basin geometry and structure are adapted from Danis et al. (Aust J Earth Sci 58:517–42, 2011), which quantified the extent of Triassic sediment, Permian coal measures, Carboniferous volcanics and thickness of the crystalline crust. We find that temperature-dependent thermal conductivity results in lower lateral variations in temperature compared to constant thermal conductivity models. However, the average temperatures at depth are significantly higher when temperature-dependent thermal conductivity effects are included. A number of regions within the Sydney Basin demonstrate temperatures above 150 °C at depths of less than 2000 m in these models, for instance NW of Singleton, exhibits a strong thermal anomaly, demonstrating the potential for geothermal prospectivity of the region from experimentally constrained thermal parameters.

Effect of temperature dependent properties on the fin performance under dehumidifying operating conditions

The analysis for fin thermal performance under dehumidifying conditions is conducted using a numerical approach. Finite-Element method is used to account for the non-linear effects due to temperature dependent parameters and humidity-temperature relationship. The temperature profiles, as well as the overall fin efficiency, are studied. The fin efficiency is found to be highly dependent on the operating conditions and the degree to which the heat transfer coefficient is a function of temperature. It is found that the effect of temperature-dependent thermal conductivity on fin performance is less as compared to heat transfer coefficient over the considered range of operating conditions.

Constant effective thermal conductivity of intumescent coatings: Analysis of experimental results

This article presents the results of an investigation to obtain the constant effective thermal conductivities of intumescent coatings under the influence of different intumescent coating factors (type of intumescent coating, coating thickness, steel section factor, fire condition), based on the analysis of an extensive collection of fire test data. The constant effective thermal conductivity is not a fundamental property of the intumescent coating, but is a desired quantity for simplified practical fire resistance design. It is defined as the temperature-averaged value of the temperature-dependent effective thermal conductivity within the temperature range of interest for fire resistance design of steel structures. The results indicate that for each of the intumescent coating types examined, a consistent constant effective thermal conductivity exists. The constant effective thermal conductivity tends to increase with decreasing steel section factor and to decrease with increasing coating thickness. For intumescent coating–protected steel I-sections, incorporating the shadow effect gives more consistent values of constant thermal conductivity compared to those without accounting for the effect. The same constant effective thermal conductivity obtained from the ISO fire tests may be used for different fire conditions as long as the steel temperature is higher than 400 °C. The results of this research make it possible to develop a simple method to calculate temperatures of intumescent coating–protected steel sections under different fire conditions.

Experimental investigations on temperature-dependent effective thermal conductivity of nanoporous silica aerogel composite

This paper presents an inverse method for retrieving temperature-dependent effective thermal conductivity of nanoporous silica aerogel composite at temperature ranging from 280K to 1080K and gas pressure between 0.01Pa and 100kPa from experimentally measured transient temperature data. This was achieved by combining a forward method solving combined conductive and radiative heat transfer accounting for temperature-dependent thermal conductivity, and an inverse method based on a real-valued genetic algorithm (GA) optimization. First, the sensitivity coefficients for the transient temperature profiles with respect to the variation of effective thermal conductivity were investigated. Then, several numerical experiments, in which the “experimental data” was numerically generated, were performed to illustrate the robustness and accuracy of the inverse method for retrieving the temperature-dependent effective thermal conductivity from transient temperature history. The experimental data were used to retrieve the effective thermal conductivities of silica aerogel composite, the results fell within 0.014–0.044W·m−1·K−1 for the temperature between 280 and 1080K and gas pressure from 0.01Pa to 100kPa, and showed nonlinear increasing trend with increasing temperature, and with increasing gas pressure.

Numerical modelling of the Sydney Basin using temperature dependent thermal conductivity measurements

The Thermal structure of continental crust is a critical factor for geothermal exploration, hydrocarbon maturation and crustal strength, and yet our understanding of it is limited by our incomplete knowledge of its geological structure and thermal properties. One of the most critical parameters in modelling upper crustal temperature is thermal conductivity, which itself exhibits strong temperature dependence. In this study, finite-element geothermal models of the Sydney Basin are generated through the use of deal.II finite element libraries. Basin geometry and structure is adapted from Danis, et al. (2011), which quantified the extent of Triassic sediment, Permian coal measure, Carboniferous volcanics and Basement thickness. We find that temperature-dependent thermal conductivity result in lower lateral variation in temperature compared to constant thermal conductivity models. However, the average temperatures at depth are significantly higher when temperature-dependent thermal conductivity effects are included. A number of regions within the Sydney Basin demonstrate temperature above 150C at depths of less than 2000m in these models, for instance NW of Singleton exhibits a strong thermal anomaly, demonstrating the potential for geothermal prospectivity of the region from experimentally-constrained thermal parameters. Future work will address the repeatability and application of this type of thermal model in areas of varying geology and stratigraphy, as well as refining the model by adding new variables, such as pressure or fine tuning existing variables.

Research on temperature dependent effective thermal conductivity of composite-phase change materials (PCMs) wall based on steady-state method in a thermal chamber

Effective thermal conductivity (λ) is the key factor in characterizing thermal conductance and temperature field when studying the thermal performance of composite-phase change materials (PCMs). But relevant research focusing on the influence of temperature on λ of composite-PCMs is scarcely reported. This paper aimed to examine the relationship between λ of a kind of prevalent composite-PCMs wall (λpcw) and temperature as well as the percentage of the phase-changed amount of the wall. In this research, two walls with a dimension of 1.5m (W)×1.5m (H) and composed of cement mortar/shape-stabilized PCMs bricks, Portland vitrified bricks, respectively were built and tested by a steady-state method in a thermal chamber. Results showed a good positive linear relationship of λ with the increasing mean wall surface temperature for the regular vitrified brick wall as well as the composite-PCMs wall in solid and liquid states. In addition, as for the cases where the composite-PCMs wall partly experienced solid-liquid phase change, there was a negative proportional relationship between λ and the increasing percentage of the phase-changed part, which exhibited the major difference with that of the common walls.

An approach to correlate experimental and theoretical thermal conductivity of MWNT/PMMA polymer composites

In this paper an effort is made to correlate temperature dependent effective thermal conductivity measured by experimental method to theoretical results obtained from different models. MWNT/PMMA polymer nanocomposites were prepared by solution casting method, with different wt% of MWNT (0, 0.05, 0.1, 0.2, 0.3, 0.5, 1, 5, 10 wt%) dispersed in the PMMA matrix. The effective thermal conductivity from 30 °C to 110 °C is measured by Hot Disk Thermal Constant Analyser, based on transient plane source technique. Experimental study reveals that effective thermal conductivity increases with increasing concentration of MWNT in PMMA and increases exponentially at high temperatures for high (5, 10) wt% samples. This behavior of effective thermal conductivity is explained in terms of the interactions between polymer–MWNT and MWNT–MWNT. Consequently these results were found to be in agreement with theoretical models such as Series, Parallel, Lewis/Neilson and empirical formula. The discrepancy found in Lewis/Neilson model at high temperature for high wt% of MWNT in PMMA is due to some change in values of parameters incorporated in the model.

Combined Conduction–Convection–Radiation Heat Transfer of Slip Flow Inside a Micro-Channel Filled with a Porous Material

Combined conduction–convection–radiation heat transfer is investigated numerically in a micro-channel filled with a saturated cellular porous medium, with the channel walls held at a constant heat flux. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous–fluid system are studied by considering hydrodynamically fully developed flow and applying the Darcy–Brinkman flow model. One energy equation model based on the local thermal equilibrium condition is adopted to evaluate the temperature field within the porous medium. Combined conduction and radiation heat transfer is treated as an effective conduction process with a temperature-dependent effective thermal conductivity. Results are reported in terms of the average Nusselt number and dimensionless temperature distribution, as a function of velocity slip coefficient, temperature jump coefficient, porous medium shape parameter and radiation parameters. Results show that increasing the radiation parameter $$(T_{r})$$ and the temperature jump coefficient flattens the dimensionless temperature profile. The Nusselt numbers are more sensitive to the variation in the temperature jump coefficient rather than to the velocity slip coefficient. Such that for high porous medium shape parameter, the Nusselt number is found to be independent of velocity slip. Furthermore, it is found that as the temperature jump coefficient increases, the Nusselt number decrease. In addition, for high temperature jump coefficients, the Nusselt number is found to be insensitive to the radiation parameters and porous medium shape parameter. It is also concluded that compared with the conventional macro-channels, wherein using a porous material enhances the rate of heat transfer (up to about 40 % compared to the clear channel), insertion of a porous material inside a micro-channel in slip regime does not effectively enhance the rate of heat transfer that is about 2 %.

Thermal conductivities of alumina-based multiwall carbon nanotube ceramic composites

Composites incorporating various vol.% (0.0, 1.1, 6.4, and 10.4) of multiwall carbon nanotubes (MWCNTs) in alumina were consolidated by the spark plasma sintering. Their thermal transport properties were investigated over the temperature range 300–800 K as a function of nanotube contents. It was observed that the temperature-dependent effective thermal conductivity decreases with the addition of MWCNTs in alumina. This behavior was analyzed in terms of phonon mean free path, elastic modulus, average sound speed, and interface thermal resistance. Compared with 1/T behavior for pristine alumina, a subtle decrease in temperature dependence of the thermal conductivity of the composites with the addition of MWCNTs is observed, indicating the presence of extra phonon scattering mechanism beyond the intrinsic phonon–phonon scattering. Simulation of experimental results with theoretical model shows that the large interfacial thermal barrier between MWCNTs and alumina plays a dominant role in controlling thermal transport properties of the composites. In addition to dominant interface thermal resistance other secondary factors such as nanotube agglomeration, processing defects, porosity also contribute for low thermal conductivity at the higher volume fraction of MWCNTs in the composite.

Development, Use, and Accuracy of a Homogenized Fuel Region Model for Thermal Analysis of a Truck Package Under Normal and Fire Accident Conditions

In the current work, a geometrically-accurate two-dimensional model is developed of an isolated fuel assembly within isothermal compartment walls. Finite difference thermal simulations are performed to determine the cladding temperature for a range of compartment wall temperatures and assembly heat generation rates. The results for zero-heat-generation-rate are used to determine a temperature-dependent effective thermal conductivity of the fuel region. The effective volumetric specific heat of the region is determined from a lumped capacity model. These effective properties are then applied to a two-dimensional model of a legal weight truck cask with homogenized (smeared) fuel regions. Steady-state normal conditions of transport simulations are performed for a range of fuel heat generation rates. The generation rate that brings the zircaloy cladding to its radial-hydride formation temperature, predicted by the homogenized model, is greater than that determined by simulations that employ an accurate-geometry fuel region model. Transient regulator fire accident simulations are then performed for a range of fire durations. The critical fire duration is defined as the minimum that brings the fuel cladding to its burst-rupture temperature. That duration is found to decrease as the fuel heat generation rate increases. The critical durations predicted by the homogenized fuel-region model are shorter than those predicted by the accurate-geometry model.

MHD Convection of an Electrically Conductive Fluid with Variable Thermal Conductivity

The effect of temperature-dependent thermal conductivity on the magneto-convection in a low Prandtl number liquid is investigated numerically. The liquid is contained in a closed square cavity with isothermal vertical walls kept at different temperatures. The top and bottom walls are assumed to be insulated. To solve the governing non-linear differential equations (mass, momentum and energy) a finite volume code based on SIMPLER algorithm is utilized. The results for different Rayleigh numbers (Ra), Hartmann numbers (Ha) and temperature coefficient of thermal conductivity (η) are presented in form of streamlines, isotherms and Nusselt number. It is found that the heat transfer decreases appreciably across the cavity with a decrease in thermal conductivity. It is observed that at low Hartmann number (Ha=30) the thermal boundary layer is formed near the side walls and as η increases the thickness of these boundaries decreases. Also it is found that as non-dimensional thermal conductivity increases the peak of velocity profile increases; however, this phenomenon is very weak at high Hartmann number.

Two-Dimensional Hyperbolic Heat Conduction with Temperature-Dependent Properties

Introduction T HE phenomena of non-Fourier heat conduction are observed in many industrial applications, such as laser heating, cryogenic engineering, and nanotechnology. Various conduction models have been proposed to explain the non-Fourier conductive heat-transfer behavior in a very short period of time. These include the macrohyperbolic model1 and Tzou’s dual-phase model.2 The purpose of the present work is to present a numerical solution to the macrohyperbolic heat-conduction (HHC) model in temperature-dependent materials. Both the analytical3 and numerical4−8 methods have been used in solving HHC equation over the years. Glass et al.4 studied the effects of temperature-dependent thermal conductivity on the thermal wave propagation by using the MacCormack’s predictorcorrector scheme. Kar et al.5 solved a nonlinear HHC equation both analytically and numerically by using the Kirchhoff transformation to linearize the nonlinear terms. However, only one-dimensional problems were considered in their works.4,5 Present numerical approach employs the Roe–Sweby’s total-variation-diminishing (TVD)9 scheme to solve two-dimensional HHC equations. This scheme was used in a previous study for HHC in composite media.7 The present work investigates the effects of temperature-dependent properties on the thermal wave propagation in a homogeneous medium.

Temperature-dependent effective thermal conductivity and thermal diffusivity of catalysts and their supports in various gas media and in vacuum. 1. Thermal conductivity and thermal diffusivity of granular porous supports and catalysts

The basic characteristics of catalysis and their supports and the results of experimental studies of the thermal conductivity and thermal diffusivity of some supports and catalysts in the temperature range of 293–1073 K in vacuum (P=1.07 Pa) and in an atmosphere of air, argon, nitrogen, helium, hydrogen and in a gas mixture (0.2NH3+0.3N2+0.5H2) are reported. It is established that as the temperature rises in the all gas media and in vacuum the thermal conductivity and thermal diffusivity of a burden of the catalysts and their supports increase according to a linear law and depend on the size and shape of the granules rather than on their specific surface.

Effects of temperature and mantle dynamics on estimates of the thermal conductivity in the deep mantle

Estimates are made of the thermal conductivity k i of the deep mantle as a function of the temperature jump ΔT across a thermal boundary layer at the core-mantle boundary (CMB). Three types of boundary layer, corresponding to differing physical processes at the CMB, are investigated, and the effect of temperature-dependent thermal conductivity is calculated for each. The consequences of lateral heterogeneities are considered. Results indicate that if the temperature jump ΔT seen by most of the mantle at the CMB is large (1350 K) then k i cannot be more than 6 W m −1K −1 if the conductivity is constant, or 8 W m −1K −1 if it is temperature dependent. If ΔT is small (350 K) then k i may be 16 W m −1K −1 or higher. The dynamics of the boundary layer is important: results suggest that hot-spot plumes are not the only mechanism for removing heat from the core.

Non-Fourier dynamic thermoelasticity with temperature-dependent thermal properties

This study numerically investigates the effect of temperature-dependent thermal conductivity, specific heat, and density on coupled, non-Fourier dynamic thermoelastic models involving relaxation times. The thermal response of a semi-infinite slab to both a step change and linear, ramp increase in applied surface temperature is presented. It is observed that a thermal conductivity which decreases with temperature results in reduced temperature gradients, and therefore reduced maximum displacements and stresses. However, decreasing specific heat or density with temperature causes increased temperature gradients, and therefore increased displacements and stresses. In addition to altering the magnitudes of the displacements and stresses, the variable properties also result in phase shifts of the displacement and stress waves. The ramp increase in surface temperature results in displacement and stress waves of lower magnitudes that are spread over a longer time interval compared to the results for the step change in surface temperature. 20 refs.

Peak temperature in high-power chips

Graphs to facilitate calculation of steady-state peak temperature at transistor sites on chips are presented. The effect of temperature-dependent thermal conductivity is included through application of the Kirchhoff transformation. The Green's function solution method is used to evaluate the temperature field. The condition of uniform temperature on the bottom surface, which is in contact with the solder layer, is studied when cooling is by convection. This assists the linearization of working formulas for temperature-dependent thermal conductivity of materials such as Si, InP, and GaAs in the presence of convective cooling, as well as prescribed bottom surface temperature. >

Evaluating the second coefficient of viscosity from sound dispersionor absorption data

T HERMAL response of a viscoelastic rod subject to high- frequency cyclic loading is studied. The material con- sidered models a solid rocket propellant with temperature- dependent thermal conductivity. The mathematical model takes the form of a set of nonlinear, coupled partical differen- tial equations. An algorithm based on an iterative finite- difference method and an averaging technique have been developed to solve these coupled equations directly. The results indicate that the temperature of a material with temperature-dependent thermal conductivity is higher than that of one with constant thermal conductivity. This shows that noticeable errors can occur, especially at the thermal reso- nant frequencies where thermal conductivity is considered constant. Viscoelastic materials are dissipative in nature. They dissipate large amounts of mechanical energy in the form of heat when subjected to high-frequency loading. Solid pro- pellant, which is used as the rocket fuel, is also a viscoelastic material. Due to the high speed of the rocket, the solid fuel is subjected to high-frequency vibration. Heating due to vibra- tion near a resonance frequency may lead to melting or material failure. Tormey and Britton conducted vibration tests on solid fuel. They found that the heating due to vibraReceived Feb. 1, 1988; revision received Feb. 20, 1989. Copyright © 1989 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Assistant Professor, Mechanical Engineering Department. Member AIAA. tGraduate Student, Mechanical Engineering Department. tion increased the material temperature significantly to the ex- tent that it even flowed out of the motor. Henter derived a set of coupled partial differential equations for the propagation of stress, strain, and temperature distribution in a viscoelastic media. Huang and Lee studied longitudinal oscillations of viscoelastic rods. They solved the nonlinear coupled equations by iteration, thus determining stress and temperature distribu- tions along the rod. Mukherjee solved the same problem by a simpler method. He substituted a partially linear equation for the nonlinear differential equation and then solved this equa- tion by the finite-difference method. In all the papers cited certain parameters such as thermal conductivity and specific heat, which are weak functions of temperature, are assumed to be constants. This assumption, however, can lead to signifi- cant errors, especially at higher temperatures and critical fre- quencies.' This is due to the strong temperature dependence of the mechanical properties, which makes the system of equa- tions very sensitive to temperature variations. In this paper the effects of temperature-dependent thermal conductivity on the temperature distribution of a viscoelastic rod subjected to cyclic loading are discussed. Numerical solutions are obtained by the finite-difference method over a wide range of frequen- cies. The effects of frequency on the temperature and dis- sipated energy are studied. This leads to a critical frequency at which the temperature is maximum. Heating due to vibration near a critical frequency may cause the solid fuel to soften and melt the material. Therefore, accurate evaluation of these critical frequencies is vital. To simulate the solid rocket pro- pellant, a viscoelastic rod of length 1 insulated on its lateral surface, as shown in Fig. 1, is considered. The left end is free, while the right end is attached to a vibrator that has a pre- scribed stress given by a = a0 cosotf where a0 is the stress amplitude, co the frequency, and / the time. The temperature of the vibrator is assumed constant at T0, a convective boun- dary condition is assumed at x = 0, H is the surface conduc- tance, and K is the thermal conductivity of the material. It is also assumed that the solid rocket propellant is a ther- mohelogically simple material. The objective is to find the temperature distribution along the rod. Solving the governing equations (the energy balance equation, equation of motion, and stress-strain relationship), they reduce to the form