Theory Of Thermal Conductivity Research Articles

Effect of Zr4+ on the microstructure and electrical properties of 0.6Y2O3-0.4YCr0.5Mn0.5O3 NTC ceramics

In this study, 0.6Y2O3-0.4YCr0.5Mn0.5O3 negative temperature coefficient (NTC) ceramics doped with different ZrO2 contents were prepared using a two-step sintering method. The effects of Zr4+ content on the microstructure and electrical properties of 0.6Y2O3-0.4YCr0.5Mn0.5O3 were mainly investigated. For the microstructure, X-ray diffraction (XRD) reveals the presence of two main crystalline phases in the samples: Y2O3 and YCr0.5Mn0.5O3. Scanning electron microscopy (SEM) reveals a clear two-phase appearance, and the porosity tends to decrease with the addition of ZrO2. Combined with energy dispersive spectrometer (EDS) to derive the distribution of the elements, Zr4+ is mainly present in the Y2O3 phase, with a small amount in the YCr0.5Mn0.5O3 phase. In addition, the grain sizes of different groups were counted, and the grain size of Y2O3 decreased from 2.73 ± 1.80 μm to 1.65 ± 0.93 μm with the increase of ZrO2 content. For the electrical properties, the resistance-temperature curves were measured from 298.15 K to 1073.15 K, and all the samples exhibited NTC characteristics. And with the increase of ZrO2 content, the resistivity increased from 1.91 × 107 Ω cm to 1.96 × 108 Ω cm, and the B25/100 value decreased from 3315 K to 1310 K. In addition, the chemical state forms of the elements on the surface of the samples were analysed by X-ray photoelectron spectroscopy (XPS), and the valence states as well as the occupancy of the transition elements Cr and Mn were analysed in detail according to the principle of multiple splitting. Finally, the mechanism of influence on microstructure and electrical properties is explained by combining the theory of grain boundary migration and thermal ceramic conductivity.

Study on the delamination damage prediction of wind turbine blade spar cap based on morphology feature recognition

In order to study the degradation of local mechanical properties caused by delamination defects of wind turbine blades, a progressive damage prediction method of blade spar cap based on quantitative identification of delamination morphology features by infrared thermal image was proposed in this paper. Firstly, based on the thermal conduction theory of laminate plates, infrared thermal imaging technology was used to realize quantitatively identify delamination morphology features. Then, based on the cohesive zone model (CZM) and the classical laminate theory (CLT), a numerical analysis model of unidirectional laminate with delamination defects was established, and the accuracy of the numerical model was verified by comparison with the experimental results of axial tensile and compressive displacement loads. Finally, a 2 MW-45.3 blade spar cap with maximum chord cross-section was used as a prediction model, and the effect of different delamination sizes and depths on the failure mode, failure strength and damage evolution of the blade spar cap was successfully predicted by using the equivalent fatigue load. The research shows that the delamination depth has a more profound influence on the damage of spar cap compared with the delamination size. With the increase of delamination depth, the delamination failure modes undergo the evolution process of non-buckling, local buckling, delamination expansion and strength failure. Shallow delamination causes local buckling and strength failure of blade spar cap. When the delamination depth reaches half of the spar cap thickness, the delamination extends to intralaminar and interlaminar, the local failure changes to global failure.

Three-dimensional active-control hygrothermal dynamic behavior of PFMLs structure subjected to laser heat treatment with dual-ellipse distribution form

Based on three-dimensional transient thermal conduction theory, the refined plate theory and Hamilton variational principle, the constitutive equations, geometrical equations, and governing equations for fiber metal laminates with piezoelectric layer (PFMLs) under hygrothermal environment is presented. Subsequently, the Newmark method and Galerkin method are used to solve the governing equations which in terms of displacement functions. The results show that electric potential function, fiber orientation, external load as well as thickness ratio have great influence on the deflection as well as normal stress. The selection of (45°/0°) fiber orientation is more resistance to deformation and normal stress.

Transient Thermal Analysis of Space Rectangular Thin-Walled Structures by Carrera Unified Formulation

The accurate prediction of transient thermal fields of space structures is of paramount significance for the analysis of geometrical stability and thermal management systems. This paper proposes a novel method to solve the transient thermal field of the thin-walled cross section of beams in outer space. High-order beam elements are derived by means of the Carrera unified formulation (CUF), where the longitudinal direction of the beam is discretized by one-dimensional two-node and four-node elements, whereas arbitrary high-order expansion functions are used for the description of the temperature expansion within the cross section. The governing differential equations of the transient temperature field are derived according to the transient thermal conduction theory and the weighted residual method. The solution of the initial value problem for ordinary differential equations is obtained through the application of the Adams–Bashforth method, leading to the determination of the transient thermal field. In order to demonstrate the accuracy of the temperature results, a convergence analysis is conducted. Finally, temperature distributions within the cross section and along the longitudinal direction of the model are discussed to show the effects of several factors, including material properties, angle of solar radiation, and shadows induced by the shelter of other components.

Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space

This article considers a variant of the heat conduction theory of thermal conductivity, in which the heat flux pseudovector has a weight of 1. The pseudoinvariants associated to the heat flux pseudovector are sensitive to mirror reflections and inversions of threedimensional space. The primary purpose of the study was to find a heat flux vector that is algebraically equivalent to the microrotation pseudovector and to measure elementary volumes and areas using pseudoinvariants that are sensitive to mirror reflections. To represent spinor displacements, a contravariant microrotation pseudovector with a weight of +1 was selected. Thus, the heat flux and mass density were expressed as odd-weight pseudotensors. The Helmholtz free energy per unit doublet pseudoinvariant volume was employed as the thermodynamic state potential of the following functional arguments: absolute temperature, symmetric parts, and accompanying vectors for the linear asymmetric strain tensor and the wryness pseudotensor. The results obtained show that the thermal conductivity coefficient and heat capacity of elastic micropolar solids are pseudoscalars of odd weight, indicating their sensitivity to mirror reflections.

Solutions of the theory of thermoelasticity and thermal conductivity in the cylindrical coordinate system for axisymmetric temperature

The paper uses the system of Navier equations in the stationary case. A cylindrical coordinate system is considered, when the temperature does not depend on the angular variable. A partial solution of the system of Navier equations, which does not contain elastic displacements, is called a purely temperature solution. It was established that for purely temperature solutions the sum of normal stresses is zero and the volume deformation is equal T e  = 3 . An analytical expression of purely temperature displacements and stresses in the cylindrical coordinate system in the axisymmetric case was found. The solution of the boundary value problem of thermal conductivity, when the cylinder is heated on one end, cooled by liquid on the other with known heat losses on the side surface, is proposed. The solution of the boundary value problem of thermal conductivity for such a cylinder is given in the form of the sum of the basic temperature, which describes the heat balance, and the perturbed temperature. The basic temperature has a polynomial form and integrally satisfies the boundary conditions. The perturbed temperature has an exponential decrease with distance from the heated end and does not carry out integral heat transfer. The found dependencies were used and a new solution to the heat conduction equation was written in a cylindrical coordinate system. Simple formulas for expressing temperature changes have been obtained. A new temperature solution to the system of thermoelasticity equations in a cylindrical coordinate system has been written, when the temperature does not depend on the angular variable.

DETERMINATION OF THE TEMPERATURE CONDUCTIVITY COEFFICIENT a GRAPHICAL METHOD BASED ON NOMOGRAM FOR A SEMI-CONFINED ROD

The article presents a technique and formula for calculating the thermal diffusivity of solids using nomograms of temperature changes. The paper describes a technique by which the final formulas are simplified to algebraic equations using the relative temperature θM of heating a semi-restricted rod from the end.Known equations for solving direct problems of heat conduction using regular modes of the 1-st, 2-nd and 3-rd kind, in which the final formulas are simplified.The article provides methods and formulas for calculating the coefficient of thermal conductivity using nomograms.The method uses the maximum of the first derivative of θM and tabular values of the function erf (1/(2 x Fo )), which is a solution to the direct problem of thermal conductivity. The temperature at a specific point of the rod is measured – x1 and time –τ1 with start of heatingent of thermal conductivity of solid bodies using nomograms of temperature changes.The work describes a method by which the final formulas are simplified to algebraic equations using the relative temperature θM of heating a semirestricted rod from the end. Known equations for solving direct heat conduction problems using regular regimes of the 1-st, 2-nd and 3-rd kind, in which the final formulas are simplified. In work Kondratiev H.M. notes: "The theory of the regular thermal regime is one of the sections of the study of heat transfer insolids. The theory of the regular mode considers the process of cooling or heating not throughout, but only at the stage that has ceased to be affected by the initial state of the body.In work of Lykov O.V. «Theory of thermal conductivity» the solution of the problem is done by three methods: classical, operational and the method of Fourier transformation. Not all methods of pulsed heating are related to these types of regular mode, but it can be used due to the simple form of the exponent. In this work, the proposed method does not belong to regular mode methods. It is done by solving the inverse problem with the help of a well-developed graphic nomogram.According to the accepted classification, the problem is solved under boundary conditions of the 1-st kind, in which the surface temperature is specified as a function of time. Considered a simpler case when surface of the bodyremains constant throughout the heat exchange process.This is achieved with the help of special devices that maintain a constant temperature of a semi-restricted rod with thermal insulation of the side surface.

Study on early shrinkage and cracking of slab in UHPC light-weight composite deck based on ambient temperature and humidity effects

This study investigates the early performance and potential issues of ultra-high-performance concrete (UHPC) light-weight composite decks (LCBDs) used in municipal highway bridge design. The major objective of this research was to understand the complex evolution of temperature and humidity within immature UHPC thin layers, which can lead to deformation and secondary stress, potentially causing cracks and threatening the long-term applicability and safety of steel-concrete composite bridges. Understanding of the mechanism of this process will be the basis for subsequent work. The early performance of UHPC with ordinary concrete is compared. Besides, discussions are conducted on the basic thermal conductivity theory of three-dimensional porous media and the hydration mechanism of cement-based materials that are appropriate for early-stage UHPC. Subsequently, a refined thermo-mechanical coupling analysis method for steel-UHPC LCBD was proposed, implemented using ABAQUS, and validated through a UHPC composite beam test. This method was applied to calculate the early shrinkage of the UHPC layer in a steel-UHPC LCBD and evaluate the risk of cracking in an actual bridge expansion project, providing a rationality evaluation of a bridge design and its construction procedure.

Temperature Field Modelas a Factor to Improve a Horizontal Ground Heat Exchanger of a Heat Pump System: Review of Scientific Approaches and the Content of the Analytical Model

The article is devoted to the research of issues related to the organization of control systems for heat pump installations (HPS). HPS is used to use low-potential energy of the environment in the heat supply of buildings. HPS with horizontal ground heat exchangers (HGHE) are of great importance for improving energy efficiency. The efficiency and reliability of HPS with HGHE strongly depends on the state of the soil temperature field. A large number of scientific publications are devoted to modeling soil temperature fields forHGHEparameterdetermination; a significant part of them is devoted to the study of vertical ground heat exchangers. Scientific developments presented in foreign publications on modeling the temperature field of the HGHE location environment are focused on the use of HPS in the cold supply mode and/or in the heat supply mode under conditions of a slight decrease in temperature, which excludes soil freezing. The aim of the study was to apply the existing methods of the analytical theory of thermal conductivity to develop a soil-environment TP model for the placement of a HGHE HPS; the developed model is intended for engineering calculations of the main design HGHEparameters; the model is also applicable to determine the annual specific heat flow as an important parameter in the optimal control system of the HPI. The development of the model is based on the condition of a two-element structure of the soil massif: under the HGHE and above the HGHE; the target parameter is the temperature of the soil mass, depending on the coordinate and time, disclosed through the indicator 'relative temperature rise'; in accordance with the provisions of the thermal conductivitytheory, the relative excess temperature is given for the cases of a semi-infinite body (soil mass under the HGHE) and a slab (soil mass above the HGHE). The proposed model is implemented on the example of two constituent entities of the Russian Federation. The results obtained made it possible to determine the minimum guaranteed possibility of using HPS for heat supply in these climatic conditions. The model presented in the article can be used as a context for further studies of the main parameters of HGHE HPS operation and optimization of HPS operation modes.

DETERMINING HEAT LOSSES FROM THE BUILDING ENVELOPE USING THE NON-STATIONARY METHOD

One of the main causes of the climate change is accumulation of huge amount of carbon dioxide (CO2) in the atmosphere emitted from the combusting of organic fuels (coal, oil products and natural gas), consequently, to slow down the progress of the global warming is directly related to the limitation of CO2 emission which could be achieved through the rational use of fuel and energy in every sector (industrial, household, transport and building sectors), introduction of energy-saving measures including highly efficient technologies and innovative methods. The building sector accounts for about 40% of the energy saving potential, therefore reduction of energy losses is the best way to reduce energy consumption of buildings. To calculate the heat loss from the building envelope, it is necessary to know the thermal conductivity coefficient (λ) of each construction element. Currently developed methods of λ determination are entirely based on the laboratory test using the stationary regime. For more realistic results, it is necessary to take into account the daily variability of temperature and non-stationary thermal conductivity processes. Solving the non-stationary thermal conductivity tasks are associated with the significant difficulties due to the application of the relatively complex mathematical equations. Usually, the theory of non-stationary thermal conductivity refers to the method of separation of variables or the so-called Laplace Transform, which requires the use of operational counting methods. The article presents an innovative method for determining the coefficient of thermal conductivity (λ) of each construction element in the non-stationary temperature regime, which enables determination of heat losses from the building envelope in real environment using the precise definition of thermal flow velocity.

Evolution of local surface roughness in 193 nm ArF excimer laser ablation of ground Yb:YAG crystal

The surface quality of YAG crystals plays a decisive role in the output performance of the device. In this investigation, it was found that the surface quality of Yb:YAG crystal was improved by 193 nm ArF excimer laser ablation. The influence of laser energy density and pulse numbers on the surface roughness of Yb:YAG crystal was obtained. The possible laser ablation mechanism of YAG crystal was analyzed by thermal conduction and photodissociation theory. Surface profile analyses reveal that photochemical ablation was the dominant mechanism of material removal.

ВЫБОР ОПТИМАЛЬНЫХ ПАРАМЕТРОВ ПРОСТРАНСТВЕННО-ВРЕМЕННОЙ СЕТКИ ПРИ МАТЕМАТИЧЕСКОМ МОДЕЛИРОВАНИИ НАГРЕВА ЗАГОТОВОК В ПРОМЫШЛЕННЫХ ПЕЧАХ

The efficiency of two numerical methods for solving multidimensional problems of the theory of thermal conductivity ‒ the fractional steps method and the Liebman method - is evaluated. The efficiency of these methods is compared for the operating conditions of industrial furnaces by the example of calculating the symmetrical heating of a two-dimensional cylinder and a three-dimensional plate made of materials with different thermophysical properties (corundum, ceramic brick and carbon steel). A two-dimensional axisymmetric temperature field for a cylinder and a three-dimensional temperature field for a workpiece in the form of a parallelepiped were found by the grid method under boundary conditions of the II and III genera. The difference approximation of differential equations and boundary conditions is performed by the control volume method according to an implicit finite difference scheme. The developed algorithms for solving multidimensional problems of internal heat transfer by fractional steps and the Liebman method are implemented in the form of computer programs in the Object Pascal programming environment. When comparing the effectiveness of solving multidimensional problems with these methods, the criterion of the effectiveness of difference schemes (CERS) proposed by V.V. Bukhmirov and T.E. Sozinova was used as an optimization criterion. Nomograms are constructed to select the optimal parameters of the space-time grid and the best numerical method for solving multidimensional problems for a specific process of heating (cooling) a solid body

Effects of ohmic and activation energy on the physical characteristics of MHD flow and variable heat transfer to a different fluids

This study examines different fluid flow through an elaborated plate. In the modeling of the physical phenomena under investigation, the impacts of viscous dissipation, activation energy and chemical reaction are considered. Also, the heat transport phenomena are explained by the variable thermal conductivity theory. By using the right transformations, the flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters’ impacts on the velocity, temperature and mass fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using the numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the effectiveness of the velocity field is determined by the changing values of the magnetic parameter. The Prandtl values are decreased, the temperature profile becomes more pronounced.

Thermal Conductivity of Aluminum Alloys-A Review.

Aluminum alloys have been extensively used as heatproof and heat-dissipation components in automotive and communication industries, and the demand for aluminum alloys with higher thermal conductivity is increasing. Therefore, this review focuses on the thermal conductivity of aluminum alloys. First, we formulate the theory of thermal conduction of metals and effective medium theory, and then analyze the effect of alloying elements, secondary phases, and temperature on the thermal conductivity of aluminum alloys. Alloying elements are the most crucial factor, whose species, existing states, and mutual interactions significantly affect the thermal conductivity of aluminum. Alloying elements in a solid solution weaken the thermal conductivity of aluminum more dramatically than those in the precipitated state. The characteristics and morphology of secondary phases also affect thermal conductivity. Temperature also affects thermal conductivity by influencing the thermal conduction of electrons and phonons in aluminum alloys. Furthermore, recent studies on the effects of casting, heat treatment, and AM processes on the thermal conductivity of aluminum alloys are summarized, in which processes mainly affect thermal conductivity by varying existing states of alloying elements and the morphology of secondary phases. These analyses and summaries will further promote the industrial design and development of aluminum alloys with high thermal conductivity.

Theoretical insight into potential thermoelectric performance of ternary metal phosphide CaAgP

Metal phosphides have recently emerged as promising thermoelectric materials with high performance and low cost of constituent elements. In this work, we provide atomistic insight into thermoelectric performance of ternary metal phosphide CaAgP using first-principles calculations of transport properties, focusing on an accurate description of phonon–phonon and electron–phonon interactions. Applying a unified theory for lattice thermal conductivity and momentum, self-energy relaxation time approximation approaches for phonon-limited electronic transports result in overall agreement with experiment for transport properties of CaAgP. Having a promising thermoelectric figure of merit ZT over 0.48 at 650 K, nano-phasing or doping is suggested to further enhance the thermoelectric performance.

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

In this article, a mathematical analysis of thermoelastic skin tissue is presented based on a refined dual-phase-lag (DPL) thermal conduction theory that considers accounting for the effect of multiple time derivatives. The thin skin tissue is regarded as having mechanically clamped surfaces that are one-dimensional. Additionally, the skin tissue undergoes ramp-type heating on its outer surface, whereas its inner surface keeps the assessed temperature from vanishing. Some of the previous generalized thermoelasticity theories were obtained from the proposed model. The distributions of temperature, displacement, dilatation, and stress are attained by applying the Laplace transform and its numerical reversal approaches. The outcomes are explicitly illustrated to examine the significant influences on the distributions of the field variables. The refined DPL bioheat conduction model in this study predicts temperature, and the findings revealed that the model is located among the existing generalized thermoelastic theories. These findings offer a more thorough understanding of how skin tissue behaves when exposed to a particular boundary condition temperature distribution.

Intensive Urbanization, Urban Meteorology and Air Pollutants: Effects on the Temperature of a City in a Basin Geography.

A qualitative study of thermal transfers is carried out from a record of measurements (time series) of meteorological variables (temperature, relative humidity and magnitude of wind speeds) and pollutants (PM10, PM2.5 and CO) in six localities located at different heights in the geographic basin of Santiago de Chile. The measurements were made in two periods, 2010-2013 and 2017-2020 (a total of 2,049,336 data), the last period coinciding with a process of intense urbanization, especially high-rise construction. The measurements, in the form of hourly time series, are analyzed on the one hand according to the theory of thermal conduction discretizing the differential equation of the temporal variation in the temperature and, on the other hand, through the theory of chaos that provides the entropies (S). Both procedures demonstrate, comparatively, that the last period of intense urbanization presents an increase in thermal transfers and temperature, which affects urban meteorology and makes it more complex. As shown by the chaotic analysis, there is a faster loss of information for the period 2017-2020. The consequences of the increase in temperature on human health and learning processes are studied.

The Transition Region of Solar Flare Loops

The transition region between the Sun’s corona and chromosphere is important to the mass and energy transfer from the lower atmosphere to the corona; consequently, this region has been studied intensely with ultraviolet and extreme ultraviolet (EUV) observations. A major result of these studies is that the amount of plasma at low temperatures, <105 K, is far too large to be compatible with the standard theory of thermal conductivity. However, it is not clear whether the disagreement lies with a problem in the observations or a problem in the theory. We address this issue by analyzing high–spatial and temporal resolution EUV observations from an X1.6-class flare, taken with the Interface Region Imaging Spectrograph and the Solar Dynamic Observatory/Atmospheric Imaging Assembly (AIA). These data allow us to isolate the emission of flare loops from that of surrounding structures. We compare the emission measures (EMs) derived from the C ii 1334.525 Å and Si iv 1402.770 Å transition region spectral lines, the Fe xxi 1354.066 Å flare line, and the AIA 171 Å coronal images. We find that the EM ratios are incompatible with a standard conduction-dominated transition region model. Furthermore, the large increases in the EM magnitudes due to flare heating make it highly unlikely that the disagreement between data and theory is due to observational uncertainties in the source of the emission. We conclude that the standard Spitzer–Härm thermal conductivity must be invalid for, at least, flare loops. We discuss the possibility that turbulent suppression of thermal conduction can account for our results.

Hygrothermal dynamic behavior of fiber metal laminated structure under dual-ellipse distribution heat source

Refined plate theory could account for parabolic variation of transverse shear stress through the thickness, and satisfy the zero traction boundary conditions on the top and bottom surfaces of the plate without introducing shear correction factor, of which all displacement variables can be depicted in functions of shear and bending components. Based on three-dimensional transient thermal conduction theory and the refined plate theory, an analytical solution of fiber metal laminated (FML) plate under hygrothermal environment is presented. In present work, distinct from other literatures, the separate variable method and Newton-Cotes method is applied to solve the three-dimensional transient temperature field (subjected to moving dual-ellipse distribution laser heat source) firstly. Secondly, the constitutive equations and geometrical equations are derived. Subsequently, the governing equations in hygrothermal environment are obtained. Finally, the Newmark method and Galerkin method are used to solve the governing equations of which in terms of displacement functions. The results show that fiber orientation affects the bending stiffness, the selection of (45°/ 0°) fiber orientation is more resistance to deformation and normal stress, and bending part is more sensitive to shear factor between layers.

Coronal seismology by slow waves in non-adiabatic conditions

Slow magnetoacoustic waves represent an important tool for probing the solar coronal plasma. The majority of seismological methods with slow waves are based on a weakly non-adiabatic approach, which assumes the coronal energy transport has only weak effects on the wave dynamics. Despite it significantly simplifies the application of coronal seismology by slow waves, this assumption omits a number of important and confidently observed effects and thus puts strong limitations on the reliability of seismological estimations. We quantitatively assess the applicability of the weak thermal conduction theory to coronal seismology by slow waves. We numerically model the linear standing slow wave in a 1D coronal loop, with field-aligned thermal conduction κ‖ as a free parameter and no restrictions on its efficiency. The time variations of the perturbed plasma parameters, obtained numerically with full conductivity, are treated as potential observables and analysed with the standard data processing techniques. The slow wave oscillation period is found to increase with κ‖ by about 30%, indicating the corresponding modification in the effective wave speed, which is missing from the weak conduction theory. Phase shifts between plasma temperature and density perturbations are found to be well consistent with the approximate weakly conductive solution for all considered values of κ‖. In contrast, the comparison of the numerically obtained ratio of temperature and density perturbation amplitudes with the weak theory revealed relative errors up to 30–40%. We use these parameters to measure the effective adiabatic index of the coronal plasma directly as the ratio of the effective slow wave speed to the standard sound speed and in the polytropic assumption, which is found to be justified in a weakly conductive regime only, with relative errors up to 14% otherwise. The damping of the initial perturbation is found to be of a non-exponential form during the first cycle of oscillation, which could be considered as an indirect signature of entropy waves in the corona, also not described by weak conduction theory. The performed analysis and obtained results offer a more robust scheme of coronal seismology by slow waves, with reasonable simplifications and without the loss of accuracy.