Heat Conduction Behavior Research Articles

Second-order two-scale analysis for heating effect of periodical composite structure

The multi-scale analysis method is presented for the heat transfer problems of periodical composite structures under irradiation heating. This kind of physical problem can be described as a class of parabolic equations with small periodical oscillating coefficients equipped with the mixed boundary conditions of both Dirichlet and Neumann type. It needs more expensive cost in both computer's memory and CPU time to solve these problems by the usual finite difference method or finite element method, since it is necessary to partition the considering geometrical region finer to capture the heat conduction behavior at small scale. To reduce the computational complexity, an approximate solution is derived by the asymptotic expansion technique. The convergence of asymptotic solution to exact solution is technically proved as the micro-scale parameter tends to zero. Based on the asymptotic expansion formula, a second-order two-scale finite element method is proposed to fully solve this problem in practice. Numerical results show convergent behavior of the proposed method.

Heat conduction in two-dimensional momentum-conserving and -nonconserving gases.

Compared to that for two-dimensional (2D) lattices, our understanding of heat conduction in 2D gases is still limited. Here we study heat conduction behavior of 2D gas systems with momentum-conserving and -nonconserving interparticle interactions by using the nonequilibrium and equilibrium molecular dynamics methods. For the momentum-conserving system, we find that when the dimensionality of the system is changed from 2D to quasi-one-dimensional (quasi-1D), the heat conductivity κ diverges with the system size L as κ∼lnL (the theoretical prediction for 2D systems) for a short L and shows, in the thermodynamic limit, a tendency to κ∼L^{1/3} like that predicted in 1D fluids. This suggests that the dimensional-crossover effect of heat conduction exists in 2D systems with conserved momentum. In contrast, for the momentum-nonconserving system, as L increases, finite heat conductivity independent of L is observed. These findings are in agreement with the predictions given by hydrodynamic theory and thus further confirm the validity of the theory in 2D gases.

Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness

An exact thermal analysis of radially functionally graded (FG) disks with continuously varying thickness is performed by steady-state 1-D Fourier heat conduction equation at specific surface temperatures. By employing a simple-power material grading pattern together with the convergent/divergent hyperbolic disk profiles, the differential equation is obtained in the form of Euler-Cauchy type. Analytical solution of the differential equation gives the temperature field and heat flux distributions in the radial direction in a closed form. A numerical study is conducted to visualize both the temperature and heat flux variations with respect to the disk profile parameter for hyperbolic disks made of SUS-304 /ZrO2 (Stainless steel/Zirconium oxide) metal-ceramic pairs. Those exact expressions are also used to study parametrically the effects of both the inhomogeneity and profile parameters on the temperature field of the disks made of hypothetic FG metal-ceramic pairs. It is revealed that heat conduction behavior of such disks is strictly affected from the variation of both inhomogeneity and disk profile parameters.

Heat conduction and deflagration behavior of Al/PTFE induced by thermal shock wave under temperature gradient

In order to reveal the influence of sintered and unsintered aluminum/polytetrafluoroethylene (Al/PTFE) reactive material on heat conduction, ignition and deflagration characteristics under the condition of thermal loading, the sintered and unsintered samples prepared by molding process are heated by acetylene flame as heat source. The heat conduction and deflagration behaviors of samples are measured synchronously by infrared thermal imager and high-speed camera before and after ignition. Meanwhile, combining with the three-dimensional differential equation of heat conduction in cylindrical coordinate system, the temperature gradient, heat flux and ignition moments during the process of heat conduction are solved by numerical simulation. The results show that the two kinds of samples both undergo the evolutions of temperature gradient and thermal shock wave induced by temperature gradient. The instantaneous energy accumulation caused by thermal shock wave promotes the samples to deflagrate, and the heat conduction durations before ignition, ignition temperature of sintered sample are both smaller than that of unsintered sample. The micro-morphologies before ignition indicate that the unsintered sample needs to accumulate more energy to achieve deflagration. The deflagration reaction extent of unsintered sample is more intense than that of sintered sample, however, the deflagration durations of sintered sample lasts longer. The maximum flame area of unsintered sample is 30.6% larger than that of the sintered sample, and the maximum temperatures of the flame core of sintered and unsintered sample are 1284 K and 1425 K, respectively.

Wiedemann-Franz law of Cu-coated carbon fiber

We investigate the thermal and electrical conductivities of Cu-coated carbon fiber (Cu-CF), which is designed to reduce the weight of metal wires. The electrical and thermal properties of Cu-CF are assessed using the 3ω method. This material is formed by depositing a thin layer of Cu, approximately 100–200 nm thick, on a core of CF with a diameter of 7μm. This structure grants the wire metal-like electrical properties, i.e., a positive temperature coefficient of resistance (TCR), with phonon-driven heat conduction behavior. Therefore, metal-like electrical conduction and insulator-like thermal conduction are combined in the Cu-CF wire. Electrical conduction is completely dominated by the Cu layer regardless of temperature. In contrast, heat conduction is dominated by the inner-core CF near 300 K, but the Cu layer dominates at lower temperatures. Thus, the deviation of Lorenz number L of Cu-CF from its theoretical value of Lo = 2.44 × 10−8 W Ω/K2 increases as the Cu layer becomes thinner and the temperature increases.

Thermal rectification in the thermodynamic limit.

We show that an increasingly strong thermal rectification effect occurs in the thermodynamic limit in a one-dimensional, graded rotor lattice with nearest-neighboring interactions only. The underlying mechanism is related to the transition from normal to abnormal heat conduction behavior observed in the corresponding homogeneous lattices as the temperature decreases. In contrast and in addition to that by invoking long-range interactions, this finding provides a distinct scenario to make the thermal rectification effect robust.

Analytical and numerical analysis of time fractional dual-phase-lag heat conduction during short-pulse laser heating

In this study, we analytically and numerically investigate the non-Fourier heat conduction behavior within a finite medium based on the time fractional dual-phase-lag model. Firstly, the time fractional dual-phase-lag model and the corresponding fractional heat conduction equation for short-pulse laser heating is built. Laplace and Fourier cosine transforms are performed to derive the semi-analytical expression of temperature distribution in the Laplace domain. Then, by the L1 approximation for the Caputo derivative, the finite difference algorithm is developed for the short-pulse laser heating problem. The solvability, stability, and convergence of this algorithm are also examined. Meanwhile, the efficiency and accuracy of this method have been verified by using three numerical examples. Finally, based on numerical analysis, we study the non-Fourier heat conduction behavior and discuss the effect of variability of parameters, such as fractional parameter and the ratio between the relaxation and retardation times, on the temperature distribution graphically. We believe that this analysis, besides benefiting the laser heating applications, will also provide a deep theoretical insight to interpret the anomalous heat transport process.

非傅里叶热流边界条件对激光辐照生物组织热传导影响的研究

非傅里叶热流边界条件对激光辐照生物组织热传导影响的研究

Study on the Reverse Heat Conduction Behavior of Steel

This paper analyses the existing literature, and considered the new problems caused by the burning accident of thermal insulation materials attached to the steel structure in recent years. In the process of combustion, thermal insulation materials will drip and melt, producing a large amount of liquid fuel. The combustion of thermal insulation materials attached to steel (diameter longer than 0.2 m) can be regarded as large pool fire combustion, and a mathematical model is established to study the reverse thermal conduction behavior of the combustion of combustible materials attached to steel.

An adaptive integration scheme for heat conduction in additive manufacturing

Abstract Solidification dynamics are important for determining final microstructure in additively manufactured parts. Recently, researchers have adopted semi-analytical approaches for predicting heat conduction effects at length and time scales not accessible to complex multi-physics numerical models. The present work focuses on improving a semi-analytical heat conduction model for additive manufacturing by designing an adaptive integration technique. The proposed scheme considers material properties, process conditions, and the inherent physical behavior of the transient heat conduction around both stationary and moving heat sources. Both the adaptive integration scheme and a technique for calculating only the points within the melt pools are described in detail. The full algorithm is then implemented and compared against a simple Riemann sum integration scheme for a variety of cases that highlight process and material variations relevant to additive manufacturing. The new scheme is shown to have significant improvements in computational efficiency, solution accuracy, and usability.

Highly enhanced thermoelectric energy harvesting from a high-temperature heat source by boosting thermal interface conduction

Thermoelectricity is regarded as one of the promising waste heat recovery candidates. A fundamental but effective method for the best use of thermoelectric generators (TEGs) is to maximize the heat flow crossing thermoelectric materials. The main focus of the present study was to develop a thermal interface material (TIM) with high thermal conductivity and temperature resistance as the key to minimizing the overall thermal resistance of the heat flow path of a TEG module operating under high-temperature conditions. In combination with a polyimide matrix and a multi-dimensional filler compound, a new TIM having stable heat conduction behavior at high temperatures was produced. The developed TIM was stable without losing mass up to ∼500 °C, and its thermal conductivity reached 81.4 W/m·K. It was applied to the interface between a TEG and a heat source whose temperature ranged from 100 to 300 °C and, the effect of the thermal conductivity and interface thermal resistance of the TIM on thermoelectric power generation performance during onsite curing of the TIM was investigated. Reduction of the interface thermal resistance by the new TIM improved the power generation by, at most, 132.3 and 38.6% compared to cases without a TIM and with a conventional graphite foil TIM, respectively. In terms of energy conversion efficiency, the TEG with the new TIM showed maximum improvements of 73.2 and 20.9% over the cases without a TIM and with a graphite TIM for the same temperature difference across the TEG, respectively. In addition, thermal cyclic testing confirmed the long-lasting heat-conducting feature of the developed TIM. The present work clearly shows the potentially significant influence that TIMs have on the waste heat recovery performance of TEGs.

Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

As microelectronic devices are important in many applications, their heat management needs to be improved, in order to prolong their lifetime, and to reduce the risk of damage. In nanomaterials, heat transport shows different behaviors than what can be observed at macroscopic sizes. Studying heat transport through nanofilms is a necessary tool for nanodevice thermal management. This work proposes a thermodynamic model incorporating both ballistic, introduced by non-local effects, and diffusive phonon transport. Extended thermodynamics principles are used in order to develop a constitutive equation for the ballistic behavior of heat conduction at small-length scales. Being an irreversible process, the present two-temperature model contains a one-way transition of ballistic to diffusive phonons as time proceeds. The model is compared to the classical Fourier and Cattaneo laws. These laws were not able to present the non-locality that our model shows, which is present in cases when the length scale of the material is of the same order of magnitude or smaller than the phonon mean free path, i.e., when the Knudsen number K n ≤ O ( 1 ) . Moreover, for small K n numbers, our model predicted behaviors close to that of the classical laws, with a weak temperature jump at both sides of the nanofilm. However, as K n increases, the behavior changes completely, the ballistic component becomes more important, and the temperature jump at both sides of the nanofilms becomes more pronounced. For comparison, a model using Fourier’s and Cattaneo’s laws with an effective thermal conductivity has shown, with reasonable qualitative comparison for small Knudsen numbers and large times.

Analytical solutions of fractal-hydro-thermal model for two-phase flow in thermal stimulation enhanced coalbed methane recovery

Thermal stimulation is a useful supplementary mining technique for the enhancement of coalbed methane recovery. This technique couples the temperature change with gas-water two-phase flow in the mining process. Many integer dimension hydro-thermal models have been proposed but cannot well describe this coupling because two-phase flow and heat conduction are usually non-linear, tortuous and fractal. In this study, a fractal-hydro-thermal coupling model is proposed to describe the coupling between heat conduction and two-phase flow behaviors in terms of fractional time and space derivatives. This model is analytically solved through the fractal travelling-wave method for pore pressure and production rate of gas and water. The analytical solutions are compared with the in-situ coalbed methane production rate. Results show that our proposed fractal-hydro-thermal model can describe both heat and mass transfers in thermal stimulation enhanced coalbed methane recovery.

Influence of Blood Vessels on Temperature during High-Intensity Focused Ultrasound Hyperthermia Based on the Thermal Wave Model of Bioheat Transfer

The coupled effects of blood vessels and thermal relaxation time on temperature and thermal lesion region in biological tissue during high-intensity focused ultrasound (HIFU) hyperthermia are numerically investigated. Considering the non-Fourier behavior of heat conduction in biological tissue, the traditional Pennes bioheat equation was modified to thermal wave model of bioheat transfer (TWMBT). Consequently, a joint physical model, which combines TWMBT for tissue and energy transport equation for blood vessel, is presented to predict the evolution of temperature and the thermal lesion region. In this study, pulsatile blood flow is first introduced into numerical study of HIFU hyperthermia, and thermal relaxation time, ultrasonic focus location, blood vessel radius, and blood flow velocity are all taken into account. The results show that the thermal relaxation time plays a key role in the temperature and the thermal lesion region. Larger thermal relaxation time results in lower temperature and smaller thermal lesion region, which indicates that TWMBT leads to lower temperature and smaller thermal lesion region compared to Pennes bioheat transfer model. In addition, we found that the ultrasonic focus location and blood vessel radius significantly affected the temperature and thermal lesion region, while the heartbeat frequency and amplitude factor of pulsating blood flow as well as the average velocity of blood flow had only a slight effect.

Determination of the effect of elevated temperatures on dynamic compressive properties of heterogeneous concrete: A meso-scale numerical study

In the present study, considering the internal heterogeneity of concrete, a meso-scopic simulation method was established to explore the dynamic compressive behavior of heterogeneous concretes at and after elevated temperature. In the meso-scale numerical model, the concrete was regarded as a tri-phase composite material consisting of aggregate, mortar matrix and the Interfacial Transition Zones (ITZs). Both the high-temperature degradation effect and the strain rate enhancement effect of the meso-components were taken into account. The simulation method involved two steps: (1) the heat conduction behavior was simulated initially; and (2) using the “result output” as “initial conditions”, the dynamic mechanical behavior of concrete was simulated. Based on the great agreement between numerical simulation results and the experimental observations, the dynamic uniaxial compression failure behavior and meso-scale failure mechanism of concrete at and after elevated temperature were studied. Furthermore, the effect of high temperature on the macroscopic dynamic compressive strength and elasticity modulus of concrete were revealed. The results indicate that the concrete specimen still shows significant strain rate effect at and after elevated temperature while the mechanical properties of concrete specimens after natural cooling further degenerates comparing with those at elevated temperature.

High-order three-scale computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales

This study develops a novel high-order three-scale (HOTS) computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales. The heterogeneities of the composites are taken into account by periodic distributions of unit cells on the mesoscale and microscale. Firstly, the multiscale asymptotic analysis for these multiscale problems is given detailedly. Based on the above-mentioned analysis, the new unified micro-meso-macro HOTS approximate solutions are successfully constructed for these multiscale problems. Two classes of auxiliary cell functions are established on the mesoscale and microscale. Then, the error analyses for the conventional two-scale solutions, low-order three-scale (LOTS) solutions and HOTS solutions are obtained in the pointwise sense, which illustrate the necessity of developing HOTS solutions for simulating the heat conduction behaviors of composite structures with multiple periodic configurations. Furthermore, the corresponding HOTS numerical algorithm based on finite element method (FEM) is brought forward in details. Finally, some numerical examples are presented to verify the feasibility and validity of our HOTS computational method. In this paper, a unified three-scale computational framework is established for heat conduction problems of axisymmetric composite structures with multiple spatial scales.

Characterisation of temperature-dependent heat conduction in heterogeneous concrete

Considering the heterogeneity, a mesoscopic simulation method was developed to analyse the heat conduction behaviour of heterogeneous concretes. In the numerical homogenisation technique, the concrete was regarded as a heterogeneous material consisting of three components (aggregate, mortar matrix and interfacial transition zones (ITZs)). Both two- and three-dimensional random aggregate structures of concrete were established. The temperature-dependent thermal properties of the mortar and aggregate were obtained based on experimental data from the literature, and those of the ITZ were determined by comparing the simulation results with measured values. The heat conduction equations were solved using the finite-element method: the three components were meshed separately and continuity of the heat fluxes at interfaces was applied. Good agreement was found between the simulation results and available test observations. The simulation results indicate that both the effective thermal conductivity (ETC) and a more accurate temperature field of concrete can be obtained using this mesoscale simulation method considering the temperature dependency of the materials' thermal properties. Aggregate shape was found to have a negligible influence on the ETC of concrete, but the type of aggregate cannot be ignored due to their different thermal conductivities. The ETC of concrete increased with increasing aggregate content and decreased with increasing temperature.

On high-order approximations for describing the lagging behavior of heat conduction

This paper is dedicated to high-order effects of thermal lagging in correlation with heat transfer models in micro- or nanoscale, relating the number of energy carriers and the associated resonance phenomenon under high-frequency excitations. Thus, a class of constitutive equations is considered for the heat flux describing high-order effects in the lagging behavior of heat transport. Tzou’s model, which is based on time-differential dual-phase-lag approximations of heat conduction, is generalized, incorporating the microstructural interaction effect in the fast-transient process of heat transport. More precisely, polynomial approximations of order n for the heat flux vector and of order m for the gradient of the temperature variation are considered. Further, well-posedness is established for solutions of the specific initial boundary value problems for the mathematical model when: (i) ; (ii) ; and (iii) . This means that uniqueness and continuous dependences of solutions are established with respect to the given prescribed data. With this aim, some modified initial boundary value problems related to the operators of the constitutive equation are introduced and suitable time-weighted measures of the solution are presented, and are used to establish the uniqueness theorems and to generate some estimates describing the continuous dependence of solutions with respect to the given data for each of the three cases specified. Moreover, the spatial behavior of the transient solutions is studied and an influence domain result is established for , while for some exponential decay estimates of Saint-Venant type are established. All results are established without restrictions on the characteristic parameters of the constitutive equation other than that the product of the coefficients of the time derivatives of greatest order of the two operators involved in the constitutive equation is positive.

Dimensional crossover of heat conduction in amorphous polyimide nanofibers

ABSTRACTThe mechanism of thermal conductivity in amorphous polymers, especially polymer fibers, is unclear in comparison with that in inorganic materials. Here, we report the observation of a crossover of heat conduction behavior from three dimensions to quasi-one dimension in polyimide nanofibers at a given temperature. A theoretical model based on the random walk theory has been proposed to quantitatively describe the interplay between the inter-chain hopping and the intra-chain hopping in nanofibers. This model explains well the diameter dependence of thermal conductivity and also speculates on the upper limit of thermal conductivity of amorphous polymers in the quasi-1D limit.

Spurious heat conduction behavior of finite-size graphene nanoribbon under extreme uniaxial strain caused by the AIREBO potential

Although the AIREBO potential can well describe the mechanical and thermal transport of the carbon nanostructures under normal conditions, previous studies have shown that it may overestimate the simulated mechanical properties of carbon nanostructures in extreme strains near fracture. It is still unknown whether such overestimation would also appear in the thermal transport of nanostructrues. In this paper, the mechanical and thermal transport of graphene nanoribbon under extreme deformation conditions are studied by MD simulations using both the original and modified AIREBO potential. Results show that the cutoff function of the original AIREBO potential produces an overestimation on thermal conductivity in extreme strains near fracture stage. Spurious heat conduction behavior appears, e.g., the thermal conductivity of GNRs does not monotonically decrease with increasing strain, and even shows a “V” shaped reversed and nonphysical trend. Phonon spectrum analysis show that it also results in an artificial blue shift of G peak and phonon stiffening of the optical phonon modes. The correlation between spurious heat conduction behavior and overestimation of mechanical properties near the fracture stage caused by the original AIREBO potential are explored and revealed.