Heat Conduction Behavior Research Articles

Analysis of Bioheat Transfer with Thermoelastic Effect

The development of thermal therapy always requires more reasonable temperature distribution predictions. Controlling the amount of heating is a common practice within general thermal therapy operations. This paper used a modified three-phase lag (TPL) bioheat transfer equation to describe the behavior of heat conduction in tissue with thermoelastic effect. To explore the effect of thermal load, the tissue was subjected to a constant surface temperature and a pulsed surface heat flux, respectively. The modified TPL bioheat transfer equation involves mixed derivative terms and higher-order time derivatives of temperature. In analyzing such problems, there are mathematical difficulties. Therefore, the hybrid numerical scheme based on the Laplace transform and an improved discrete method was proposed to solve the present problem. The influence of thermoelastic parameters on the behavior of heat transfer in tissue has been investigated. The results depict the effect of thermal load on thermal response within heat transfer medium is obvious. The thermoelastic effect excites the thermal response oscillation, which is intensified for the reduction of material constant characteristic [Formula: see text] and phase lag [Formula: see text], in the heat conduction medium.

Effects of external magnetic field on the reflection and transmission of thermoelastic coupled waves with consideration of fractional order thermoelasticity

Effects of external magnetic field on the dispersion and attenuation feature as well as the reflection and transmission behavior of thermoelastic coupled waves are studied in the paper. The heat conduction behavior at instant heating is modeled by non-Fourier law with the fractional order derivatives. The effects of external magnetic field are incorporated into the motion equation by consideration of the Lorentz force. The dispersion and attenuation feature of the two longitudinal waves and one transversal wave and their reflection and transmission behaviors at interface are studied. The effects of external magnetic field on the dispersion and attenuation and on the reflection and transmission behavior are discussed based on the theoretic formulation and the numerical examples. It is found that the external magnetic field have influences on three kinds of coupled wave while the fractional order heat conduction only has evident influences on the thermal wave.

Solid chamber for satellite electronic modules and evaluation of its heat conduction behavior

A novel solid chamber configuration for cooling satellite electronic modules enduring high heat is proposed. Solid chamber modules with different inner structures and solid materials with high thermal conductivity are designed, and their thermal performances were experimentally studied. The equivalent heat conduction coefficient and contact thermal resistance of a solid chamber module are defined and the estimation methods for the thermal behavior are proposed. It is found that the thermal performances of the two solid chamber modules with the inner structures respectively composed of Graphite/Al 630/30 composites and graphite plate are obviously better than those of the other modules. Based on the assessment of the thermal resistance and cracks generated in the modules after thermal tests, it is found that the powder metallurgy technology makes the interlayers bonded more tightly than diffusion welding in the manufacture of solid chamber, and the tightness of the interlayer interface plays a key role in the contact thermal resistance.

Comparative analysis of thermal damage to laser-irradiated breast tumor based on Fourier conduction and non-Fourier heat conduction models: A numerical study

In recent decades, laser technology has been widely used in surgeries and thermal therapies. To ensure patient safety and enhance therapeutic effectiveness in laser applications, it is crucial to accurately analyze burn injuries during the treatment process. In this study, a bioheat transfer model that includes the effects of metabolic heat generation, capillary blood vessels, and relaxation times of heat flux and temperature gradient was developed to study the non-Fourier heat conduction behavior in 2-D spherical breast tumor during the laser hyperthermia process. By employing different heat conduction models and the Arrhenius burn integration, the temperature distribution and laser-induced thermal damage to tumors were obtained. The progression of burn injury in time and the effect of various parameters on it were investigated. It was observed that the DPL model provides more reliable results in comparison with the CV model in predicting thermal damage to bio-tissue when non-Fourier effects are taken into consideration. The results showed that increasing heat flux phase lag leads to severe thermal damage, earlier onset of empyrosis, and wider and deeper burn injury. However, a greater phase lag of temperature gradient results in lower and superficial thermal damage, milder burn, later onset of empyrosis, and smaller burned area. The effect of laser power density on the onset time of different degrees of burn and their sensitivity to input power were investigated, and the results were represented graphically. Finally, investigation of wave propagation in various tissues revealed that the wave propagation speed is not constant and reduces as time increases.

Efficient transient thermal analysis of chiplet heterogeneous integration

Thermal issue has significant effect on the reliability and performance of integrated circuits with the increase of integrated density, especially for 2.5-D and 3-D heterogeneous integration packaging systems. In this paper, a new highly efficient 3-D transient thermal distribution model has been constructed to capture the heat conduction behavior of multiple heat sources for chiplet heterogeneous integration (CHI) by improving the alternating direction implicit finite difference method (ADI-FDM). Firstly, a new floating optimization algorithm (FOA) of coefficient matrix assignment of heat conduction equation and a new boundary treatment utilizing virtual points are proposed to modify the ADI-FDM and improve the model efficiency of thermal analysis. Furthermore, a universal equivalent thermal conductivity model is also built up to describe the design features of through silicon via (TSV), bump and redistribution layer structures, which can enhance the flexibility of FDM-based thermal simulator. Compared with previous finite element analysis results, the present FOA-accelerated thermal model can not only obtain an accurate simulation result of temperature profile, but also give a simulation efficiency of 3.74 times faster than Douglas-Gunn approach for the coefficient matrix assignment. Finally, the effect of power consumption variation and the floorplaning effects of chiplets, TSVs and bumps on the temperature distribution are investigated in detail by utilizing the present FOA-based thermal solver. The simulated results of the present work demonstrate the viability and computational efficiency for temperature field optimization and indicate that the new proposed simulator is helpful in thermal analysis of packaging structures and can be adopted to assist in physical design optimization of 2.5-D CHI or 3-D heterogeneous stacked chips.

Exploring the increasing behavior of thermal conductivity for high-entropy zirconates at high temperatures

Up to present, the discussion on the increase of thermal conductivity at high temperatures for thermal barrier coatings is not comprehensive enough. The present study systematically explored the increased behavior of high temperature thermal conductivity for (La0.2Gd0.2Y0.2Yb0.2Er0.2)2(Zr1-xTix)2O7 high-entropy ceramics. Above 600 ℃, the thermal conductivities of x = 0.1–0.5 components increase with composition and temperature. The significantly reduced emissivity and improved transmittance imply that the reason for the increase of high temperature thermal conductivity is the remarkable improvement of photon thermal conductivity. Importantly, this study provides a route to explore the different behavior of high temperature thermal conductivity by investigating phonon, photon and electronic heat conduction behaviors, which is also conducive to design and develop advanced thermal barrier coatings with low thermal conductivity.

Numerical thermal analysis of armchair (6,6) and zig-zag (12,0) carbon nano-tubes (CNTs)

In this study, the thermal behaviour of small-sized single-atom CNTs was examined. CNTs are composed of crystals that form a nanostructure with different geometric shapes by arranging them in different ways according to the length-diameter ratio. Due to the mechanical, electrical, and thermal properties of CNTs, the thermal conduction of CNT materials is critical in controlling the performance and stability of CNTs. CNTs, which are low-dimensional materials with a single atomic layer thickness, have excellent thermal conductivity. According to the simulation technique in ANSYS, CNTs containing the same number of atoms and bonds were developed. The heat transfer of different structures of CNTs in armchairs (6,6) and zig-zag (12,0) were compared. A comparison of zig-zag and armchair CNTs thermal behaviour shows that zig-zag CNTs lattice structure has more advantages than armchair CNTs lattice structure by heat transfer. Highlights In this study, finite element-based thermal analysis of single and double-walled armchair and zig-zag carbon nano-tubes (CNTs) using the lattice method was investigated. A simulation technique was developed and applied in the ANSYS program for single and double-walled carbon nanotubes (CNTs). Armchairs (6,6) and zig-zag (12,0) CNTs in different lattice structures with equal atomic numbers and bond numbers are modelled according to different diameters and length ratios. The CNTs, which have the same material properties as the trays placed at both open ends of the pipes, are kept at different temperature values, and conduction heat transfer behaviour is investigated for certain temperature values. According to the investigated heat conduction behaviour of zig-zag and armchair CNTs, the lattice structure of the zig-zag carbon nano-tubes is more advantageous in terms of heat conduction than the cage structure of armchair CNTs, and it transmits heat faster than the armchair CNTs.

HOMOTOPY PERTURBATION ANALYSIS ON SHAPE EFFECT OF VASODILATORS DURING ARTERIAL FLOW

In this study, the homotopy perturbation method was employed to study the influence of the thermal and applied magnetic fields on the movement and efficiency of differently shaped nanoparticles. Extensive Hartmann number, nanoparticle shape factor, and nanofluid volume fraction values were used to investigate the influence of differently shaped nanoparticles in a flow-through diseased artery. To analyze the flow and heat conduction behavior of nanoparticles in an artery, the wall impedance and local Nusselt number values were evaluated using the homotopy perturbation method and the results were compared with existing results for the same case. The results of both approaches were compared graphically for the volume fraction and magnetic interaction parameters. In addition, a graph was plotted to compare the behavior of nanoparticles in both the Hamilton-Crosser and modified Hamilton-Crosser models.

Multiscale heat conduction and fractal oxidation behaviors of needle-punched carbon/carbon composites

Abstract Needle-punched (NP) carbon/carbon composites (CCCs) are widely used in structures re-entering the atmosphere of aerospace, thanks to their excellent mechanical properties. They are easily oxidized at high temperatures with atmospheric oxygen. The oxidation behavior is influenced by the process of heat conduction. In this study, longitudinal and transverse heat conduction in micro- and mesoscale models of CCCs was investigated. It was established that the heat transfer interface of a fiber bundle demonstrated peak-like morphology, while the punching structures of composites slowed down the process of heat conduction. Oxidation behavior of NP CCCs was predicted with a fractional Brownian motion strategy. It was found that the oxidized fiber bundles formed “bamboo shoots” morphology due to different oxidation rates of the matrix and fibers. Stochastic oxidation behavior was successfully described with this fractal strategy.

Two dimensional MHD nanofluid flow analysis of fractional dual-phase-lag heat conduction between inclined cylinders with variable thickness

PurposeThis study aims to investigate the two-dimensional magnetohydrodynamic flow and heat transfer of a fractional Maxwell nanofluid between inclined cylinders with variable thickness. Considering the cylindrical coordinate system, the constitutive relation of the fractional viscoelastic fluid and the fractional dual-phase-lag (DPL) heat conduction model, the boundary layer governing equations are first formulated and derived.Design/methodology/approachThe newly developed finite difference scheme combined with the L1 algorithm is used to numerically solve nonlinear fractional differential equations. Furthermore, the effectiveness of the algorithm is verified by a numerical example.FindingsBased on numerical analysis, the effects of parameters on velocity and temperature are revealed. Specifically, the velocity decreases with the increase of the fractional derivative parameter α owing to memory characteristics. The temperature increase with the increase of fractional derivative parameter ß due to a decrease in thermal resistance. From a physical perspective, the phase lag of the heat flux vector and temperature gradients τq and τT exhibit opposite trends to the temperature. The ratio τT/τq plays an important role in controlling different heat conduction behaviors. Increasing the inclination angle θ, the types and volume fractions of nanoparticles Φ can increase velocity and temperature, respectively.Originality/valueFractional Maxwell nanofluid flows from a fixed-thickness pipe to an inclined variable-thickness pipe, and the fractional DPL heat conduction model based on materials is considered, which provides a basis for the safe and efficient transportation of high-viscosity and condensable fluids in industrial production.

Annealing treatment on waterborne polyurethane film-forming and structural features induced heat conduction performance in conductive adhesive

Thermal annealing treatment (60, 80, 100, 120 and 150 °C) on waterborne polyurethane (WPU) film-forming and further the structural features induced heat conduction behavior was investigated. It was found that the WPU films annealed at 100 °C or 120 °C showed a higher thermal conductivity than others, which was attributed to more ordered structural sequences as shown by x-ray diffraction (XRD) and differential scanning calorimetry (DSC). Combined with Fourier transform infra-red spectroscopy (FTIR), atomic force microscopy (AFM) and dynamic mechanical analysis (DMA), it is concluded that appropriate annealing can facilitate the creeping of polymer chains and further occurring rearrangement for forming ordered structural sequences. As concluded, annealing is an easy way of regulating morphological structures and further boosting microphase separation in engineering applications. Also for practical application in heat management domains, it is a good sign to see the WPU materials, such as conductive adhesive, with more ordered structural sequences (or high crystallinity) display a good heat transfer performance.

Highly stable monolithic titanium silicalite‐1 catalyst for 1‐butene epoxidation

AbstractA monolithic titanium silicalite‐1 (TS‐1) catalyst was prepared by coating TS‐1 onto a specially designed stainless‐steel support. The catalyst was used in 1‐butene epoxidation, a strong exothermic reaction, to produce butene oxide in a fixed‐bed reactor. Compared with the traditional extruded TS‐1, the monolithic catalyst demonstrates excellent catalytic stability and reusability. To understand the reason for this performance, heat conduction behaviors of the monolithic and extruded catalysts were studied and compared. This was accomplished by firstly developing a kinetic model to determine reaction kinetic parameters, and then simulating the temperature distribution within the reactor. It revealed a much lower temperature‐rise over the monolithic catalyst than over the extruded catalyst. This study demonstrates that the stainless‐steel support of the monolithic catalyst is effective in dissipating high reaction heat of 1‐butene epoxidation, thus limits local temperature‐rise within the reactor. This inhibits the formation of channel‐blocking byproducts and improves the catalytic stability.

Numerical analysis of steady-state heat conduction behavior in high-temperature superconductor Roebel cable

In this work, the steady-state heat transfer characteristics of REBCO tape and impregnated Roebel cable are studied numerically. By establishing three-dimensional finite element models of tape and impregnated cable, the temperature-dependent equivalent thermal conductivities of REBCO tapes and impregnated Roebel cables are estimated based on numerical homogenization technique. Effects of different geometric and material parameters are discussed. The steady-state heat transfer characteristics of a transposed tape in Roebel cable are further investigated. The equivalent thermal conductivities of REBCO tape or impregnated cable show strong anisotropy. Various sensitivities to geometric and material parameters are observed in equivalent thermal conductivities. The total heat flux distribution of the transposed tape is closely related to the Roebel angle and the curvature radius at outer corner or inner corner of this region. The corresponding structure and components should be optimized in actual application.

Multiscale analysis on the anisotropic thermal conduction of laminated fabrics by finite element method

In this paper, we present a novel “Two-scale finite element method” (tFEM) based on virtual fiber models to investigate the heat conduction behavior of stacked quartz woven fabrics and predict their anisotropic thermal conductivity. Considering the random fiber distribution and the twisted characteristic of yarns, the yarn-scale model was established. Furthermore, the single-layer fabric was composed of interwoven virtual yarns, which are stacked to be the multi-laminate fabric-scale model. Both the yarn-scale model and the fabric-scale model were combined with air matrix to form the two-phase composite model. Hot-Disk thermal constant analyzer was used to measure the anisotropic thermal conductivity of yarns and woven fabrics. Excellent agreement between simulations and experiments is obtained, which indicates the multiscale finite element models in this paper is accurate. The innovations of the study are that not only the effects of fiber numbers and diameters on the thermal conductivity of twist yarns and quartz ply-fabrics are analyzed, but also the detailed heat flux distribution and temperature distribution between fibers and the air are simulated and analyzed. Moreover, the isotropic thermal conductivity of the yarn radial direction and the anisotropic thermal conductivity of quartz fabrics are illustrated.

Numerical investigation of convection heat transfer characteristics in sloshing corium pools

The convection flow and heat transfer actuated by internal decay heat and the sloshing of vessels are the primary problems in the study of thermal behaviors in volumetrically heated reactor corium pools under ocean conditions. The wall-modeled large eddy simulation (WMLES) method, volume of fluid model, and phase-change model combined with dynamic mesh technology, were used to develop a three-dimensional flow and heat transfer process simulation model of the sloshing corium pool. In addition, the heat conduction behavior in the crust and vessel wall, as well as the pressure-vessel-wall integrity evaluation was considered. The predicted internal heat transfer characteristics (the temperature distribution, the wall heat flux, and the shell thickness) in the corium pool and the evolution feature of the free surface height near the wall were in good agreement with the LIVE-L4 test results and sloshing experimental data, respectively. Furthermore, the coupled heat transfer phenomenon of the melt and vessel was simulated. The simulation results indicated that the time required to reach stable heat transfer was shortened, the structure of thermal stratification was transformed, and the heat flux along the inner surface of the vessel wall of the shell was improved at the resonance state. The comparisons of local Nusselt (Nu) number at the near-wall between static and sloshing corium pool conditions showed that heat transfer characteristics were significantly influenced by sloshing (T = 2.5 s, A = 0.07 rad) motion, and the Nu number of forced convection fraction had a strong correlation with the local Reynolds number in sloshing corium pools. Conclusively, the transient heat flux distribution of the sloshing melting pool differed from that of the static corium pool, increasing the molten range, and molten peak depth of the pressure-vessel-wall.

Heat Conduction Behavior of Two-Dimensional Nanomaterials and Their Interface Regulation※

Heat Conduction Behavior of Two-Dimensional Nanomaterials and Their Interface Regulation^※

Effect of elevated temperature on dynamic flexural-tensile failure of geometrical-similar concrete beam: A meso-scale study

The investigations on the influence of geometric dimension on concrete failure at normal temperature have made a fruitful progress, while the investigations on the size effect of concrete at elevated temperature approach blank. For investigating the influence of elevated temperature and dimension on static and dynamic failures of concrete, a 3D thermo-mechanical coupling method considering the meso-structural characteristics of concrete and the strain rate effect of material was established. Flexural-tensile failure analyses of concrete beams with different geometric dimensions were conducted after heat conduction analysis. The results reveal that the speed of the heat transfer is relatively fast in small-sized concrete and the heat conduction behavior quickly approaches an equilibrium state. There is a significant degradation behavior on dynamic flexural-tensile strength for concrete exposed to fire. The elevated temperature can weaken the strain rate hardening-effect of concrete. At normal temperature, the influence of geometric dimension on dynamic flexural-tensile strength can be weakened at low strain rates while there is a reverse size effect at high strain rates. At elevated temperature, with the increasing geometric dimension, the flexural-tensile strength first decreases and then increases at low strain rates while the strength increases steadily as subjected to high strain rates.

A localized collocation scheme with fundamental solutions for long-time anomalous heat conduction analysis in functionally graded materials

This paper makes the first attempt to develop a novel localized collocation scheme based on fundamental solutions for long-time anomalous heat conduction analysis in functionally graded materials. In the present numerical framework, the Laplace transformation and Fixed Talbot numerical inverse Laplace transformation are employed to deal with the time fractional derivative in anomalous time fractional heat conduction model. The localized collocation scheme based on fundamental solutions is applied to solve Laplace-transformed time-independent partial differential equations (PDEs), and the generalized reciprocity method (GRM) coupled with the derived problem-dependent generalized fundamental solution is proposed to deal with the inhomogeneous term in Laplace-transformed time-independent PDEs. Numerical tests demonstrate that the developed computational strategy can be considered as one of the competitive alternatives in the simulation of anomalous heat conduction behavior of functionally graded materials. Furthermore, the effect of time fractional derivative order on the behavior of anomalous heat conduction is numerically investigated.

Determination of the Temperature-Dependent Thermal Material Properties in the Cooling Process of Steel Plates

Accelerated cooling (ACC) is a key technology in producing thermomechanically controlled processed (TMCP) steel plates. In a TMCP process, hot plates are subjected to a strong cooling resulting in a complex microstructure leading to increased strength and fracture toughness. The microstructure, residual stresses, and flatness deformations are strongly affected by the temperature evolution during the cooling process. Therefore, the full control (quantification) of the temperature evolution is essential regarding plate design and processing. It can only be achieved by a thermophysical characterization of the material and the cooling system. In this paper, the focus is on the thermophysical characterization of the material properties which govern the heat conduction behavior inside of the plates. Mathematically, this work considers a specific inverse heat conduction problem (IHCP) utilizing inner temperature measurements. The temperature evolution of a heated steel plate passing through the cooling device is modeled by a 1D nonlinear partial differential equation with temperature-dependent material parameters which describe the characteristics of the underlying material. Usually, the material parameters considered in IHCPs are often defined as functions of the space and/or time variables only. Since the measured data (the effect) and the unknown material properties (the cause) depend on temperature, the cause-to-effect relationship cannot be decoupled. Hence, the parameter-to-solution operator can only be defined implicitly. By proposing a parametrization approach via piecewise interpolation, this problem can be resolved. Lastly, using simulated measurement data, the presentation of the numerical procedure shows the ability to identify the material parameters (up to some canonical ambiguity) without any a priori information.

Energy transport and diffusion in low-dimensional lattices

Scientific studies in many disciplines have entered the low-dimensional mesoscopic world. This creates a valuable chance for not only improving near-equilibrium statistical mechanics, but also investigating the foundations of statistical mechanics, establishing thermodynamics and statistical mechanics for small systems, and developing the theory of nonequilibrium systems far from the equilibrium state. Predicting transport coefficients, as a main task of the near-equilibrium statistical mechanics, was formally fulfilled in the 1960-1970s, Green-Kubo formula which bridges the states of equilibrium and nonequilibrium. The Green-Kubo formula has played a crucial role in understanding nonequilibrium transport processes though so far only qualitatively, as the exact values of a systems transport coefficients cannot be worked out explicitly given the systems Hamiltonian. A quantitative description of transport behavior, therefore, is still required. Specifically, the “last mile” problem remains unsolved, and is still the bottleneck of near-equilibrium theory. Encouragingly, though, achievements in recent years may lead to a breakthrough in the near future. On one hand, the rapid development of computing technology has made it possible to effectively investigate the dynamics of nonlinear lattices, providing an important method of studying transports; on the other hand, various low-dimensional materials have now been synthesized in laboratories. With the help of advanced measurement and testing techniques, it has also become possible to perform experimental studies of transport in low-dimensional systems; theoretical results can be checked directly, which could in turn stimulate new ideas for improving theories. In addition, some theoretical approaches, such as nonlinear fluctuation hydrodynamics and wave turbulence theories, have been successfully applied to transport and diffusion studies—there are more effective theoretical tools available now than ever before. We therefore anticipate a first-principle formula that gives transport coefficients explicitly by solving the Green-Kubo formula based on microscopic dynamics. In the last four decades, thermal transport and diffusion in one-dimensional lattices has been studied intensively and extensively by researchers all over the world, and many insights have been obtained. In this work, we review the advances made by the group in Xiamen University—the most important of which being the discovered relation between heat conduction behavior and symmetry of internal interaction potential. We find that the latter both affects the exponent of the power-law decaying tail of the thermal current correlation function (TCCF) that characterizes hydrodynamic transport and dominates rapid decay behavior due to the kinetic process. When the potential is asymmetric, at certain temperatures and nonlinear interaction strength regions, the TCCF may decay by several orders due to the kinetic process exclusively, resulting in system size-independent heat conductivity such that the Fourier heat conduction law is obeyed formally. In contrast, when the potential is symmetric, though the TCCF still undergoes rapid decay in the kinetic process stage, the rate of decay rate can be much lower than exponential, leading to a system size-dependent heat conductivity. If, besides internal interactions, the system is also subject to any on-site potentials, its heat conductivity will converge to a finite constant, as the total momentum is not conserved in this case, and the TCCF in general only decays exponentially. These findings demonstrate that the kinetic process plays a crucial role not only in a fluid, but also in a lattice, which must be taken into account for calculating transport coefficients; in other words, a complete transport theory must be established on the basis of both kinetics and hydrodynamics. In addition, we review the general laws followed by the energy equipartition process in lattices and their deep connections with the transport behavior, in addition to several novel effects observed in coupled transport.