Conduction Model Research Articles

Instantaneous thermal fracture behaviors of a bimaterial with a penny-shaped interface crack via generalized fractional heat transfer

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to pronounced thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model.

East European sedimentary basins long heated by a fading mantle upwelling

A strong negative anomaly of seismic wave velocities at the core-mantle boundary (the Perm Anomaly) beneath the East European platform is attributed to the remnant of a deep mantle upwelling. The interaction between the upwelling and the East European lithosphere in the geological past and its resulting surface manifestations are still poorly understood. Using mantle plume modelling and global plate motion reconstructions, we show here that the East European lithosphere is likely to have been situated over the weakening Perm Anomaly upwelling for about 150–200 million years. As the East European platform moved above the Perm Anomaly in post-Jurassic times, the vertical tectonic movements recorded in sedimentary hydrocarbon-rich basins show either hiatus/uplift or insignificant subsidence. Analytical modelling of heat conduction through the lithosphere demonstrates that the basins have been slowly heated for a long time by the Perm Anomaly upwelling, creating suitable conditions for hydrocarbon maturation. This suggests a profound relationship between mantle plume dynamics, basin evolution, and hydrocarbon generation.

Influence of cationic vacancy diffusion on the aging behavior of low-temperature SrCo1-xRuxO3 thermosensitive ceramics

The thermosensitive ceramics of negative temperature coefficient (NTC), SrCo1-xRuxO3 (0 ≤ x ≤ 0.8), were synthesized using the solid-phase method. The research systematically explored the phase structure, microstructure, elemental chemical states, electrical properties, and aging performance. X-ray diffraction (XRD) data indicates that with the increase of Ru content, the lattice parameter increases. Scanning electron microscopy (SEM) images reveal a dense and uniform microstructure. X-ray photoelectron spectroscopy (XPS) data indicates the presence of Co2+/Co3+ and Ru4+/Ru5+ ion pairs. Resistive temperature data indicates its potential use as a low-temperature thermosensitive resistance material in the range of 2–300 K. Fitting the resistance-temperature curve using the thermally activated band conduction model and Mott's 3D variable range hopping model. Proposed the Ru–O2--Co hopping model, elucidating the hole hopping transport mechanism in NTC ceramics. Impedance spectroscopy analysis indicates that grain boundary resistance dominates the overall resistance of the sample. After aging at 77 K for 864 h, the maximum aging drift rate of the ceramic material is 1.55 %. Proposed a novel cationic vacancy diffusion model to explain aging phenomena, offering a new perspective for designing high-stability low-temperature NTC thermistors.

Correction to: Hyperbolic conduction: A fast, physical conduction model implemented in Smoothed Particle Hydrodynamics

Correction to: Hyperbolic conduction: A fast, physical conduction model implemented in Smoothed Particle Hydrodynamics

A stabilized state-based peridynamic heat conduction model for interface thermal resistance problems

As the demand for micro/nano-scale electronic devices and composite materials grows, numerical modeling of interfacial thermal resistance problems has become an integral part of the design for these devices and materials. In this work, a stabilized state-based peridynamic heat conduction model considering the Kapitza thermal resistance is proposed. A stabilized scheme is first developed to eliminate the numerical oscillations in the state-based peridynamics. The main idea is to formulate the temperature gradient for each individual bond by penalty function. The corresponding heat flow state is then constructed based on this newly developed bond-augmented temperature gradient in the framework of the Lagrangian formalism. The stabilization scheme is combined with the embedded discontinuous peridynamic concept to capture the temperature jump conditions of interface thermal resistance. The effectiveness of the proposed model is demonstrated by numerical examples. It paves the way for investigating the interfacial thermal resistance problems of materials with complex heat transfer constitutive relations.

Numerical study of hybrid binary Al2O3-Cu-H2O nanofluid coating boundary layer flow from an exponentially stretching/shrinking perforated substrate with Cattaneo-Christov heat flux, heat source, suction and multiple slip effects

Modern coating systems are increasingly deploying nanomaterials which offer improved thermal performance. The optimization of these systems can benefit from more elegant fluid dynamic models of the coating process. Inspired by these advancements, the present investigation introduces a novel mathematical model to analyze the boundary layer transport in Al2O3-Cu-H2O hybrid binary nanofluid coating deposition on an exponentially stretching porous substrate (sheet). Lateral mass flux (suction) at the wall is also considered a heat source (generation) for hot spot manufacturing effects. To add further sophistication to the thermal conduction model, a non-Fourier approach is adopted which accurately incorporates thermal relaxation effects i.e. the Cattaneo-Christov heat flux (CCHF) model. The Tiwari-Das volume fraction nanoscale formulation is implemented for different combinations of Alumina (Al2O3) and Copper (Cu) metallic nanoparticles in an aqueous base fluid (H2O). Hydrodynamic wall and thermal slip are also included as they feature in coating processes. The fundamental equations governing mass, momentum, and energy conservation, along with the corresponding conditions at the wall (substrate) and free stream, are made dimensionless through suitable scaling similarity transformations. The resulting nonlinear coupled ordinary differential boundary value problem is subsequently addressed using the efficient MATLAB bvp4c routine. Special cases of the non-Fourier model are validated against published results, and the general model is further confirmed through validation using an Adams-Moulton 2-step predictor-corrector algorithm (AMPC). Furthermore, dual solutions of the generalized model are extracted and visualized. A comprehensive study of the effects of key thermophysical key parameters on momentum and thermal characteristics (velocity, temperature, skin friction and local Nusselt number) is conducted and solutions are visualized graphically. The computations show that higher temperatures are present with intensification in the thermal relaxation parameter (Cattaneo-Christov hyperbolic model parameter), which predicts therefore larger temperatures than the classical Parabolic heat conduction model using Fourier analysis. Effectively, thermal relaxation is responsible for finite heat wave propagation and produces more accurate estimations of heat transfer than the Fourier model. An increase in stretching parameter enhances the skin friction coefficient and elevates the local Nusselt number. As the thermal relaxation parameter increases, the temperature magnitudes corresponding to the first and second solutions are both enhanced as are thermal boundary layer thicknesses. An increase in wall suction induces an escalation in the first solution for velocity whereas it reduces the second solution velocity. Stronger wall suction suppresses temperatures. With increasing thermal slip, the boundary layer is cooled i.e. temperature plummets and thermal boundary layer thickness is decreased. Strong deceleration is induced with greater hydrodynamic (velocity) slip. Both first and second solutions for skin friction are elevated with shrinking whereas they are depressed with stretching. With greater velocity slip both the first and second solutions for skin friction are depleted with greater velocity slip for the shrinking case, whereas they are generally enhanced for the very strong stretching case. The computations offer some new insights into multi-physical thermal fluid dynamics of nanofluid-based coating systems.

Two-Fluid and Discrete Element Modeling of a Parallel Plate Fluidized Bed Heat Exchanger for Concentrating Solar Power

Abstract A novel high-temperature particle solar receiver is developed using a light trapping planar cavity configuration. As particles fall through the cavity, the concentrated solar radiation warms the boundaries of the receiver and in turn heats the particles. Particles flow through the system, forming a fluidized bed at the lower section, leaving the system from the bottom at a constant flowrate. Air is introduced to the system as the fluidizing medium to improve particle heat transfer and mixing. A laboratory scale cavity receiver is built by collaborators at the Colorado School of Mines and their data are used for model validation. In this experimental setup, near IR quartz lamp is used to provide flux to the vertical wall of the heat exchanger. The system is modeled using the discrete element method and a continuum two-fluid method. The computational model matches the experimental system size and the particle size distribution is assumed monodisperse. A new continuum conduction model that accounts for the effects of solid concentration is implemented, and the heat flux boundary condition matches the experimental setup. Radiative heat transfer is estimated using a widely used correlation during the post-processing step to determine an overall heat transfer coefficient. The model is validated against testing data and achieves less than 30% discrepancy and a heat transfer coefficient greater than 1000 W/m2 K.

Chemically doped, purified bulk multi-walled carbon nanotube conductors with enhanced AC conductivity to 40 GHz

Metals used in radio frequency (RF) communications technologies degrade in alternating current (AC) conductivity with frequency due to the skin effect. Bulk carbon nanotube (CNT) materials have demonstrated favorable trends such as constant or increasing AC conductivity, and are emerging as potential alternative conductors. However, the resistive inter-CNT junctions present in these bulk assemblies limit overall conductivity. In this work, a waveguide-based transmission technique is used to measure the AC conductivity from 10 to 40 GHz of a commercial multi-walled CNT (MWCNT) material modified by purification to remove carbon and iron impurities, and by chemical doping with potassium tetrabromoaurate (KAuBr4). Iron impurity removal yields a frequency-independent real AC conductivity. Laser thinning and solvent plying are employed to change transmission by altering the MWCNT sheet thickness, thus enabling accurate measurement of the KAuBr4-doped MWCNT samples. Doping of the purified MWCNTs yields enhanced real AC conductivity of ∼160 kS/m, which remains constant with frequency to 40 GHz and represents a 5–6 × improvement over the as-received material at 40 GHz. KAuBr4 doping is hypothesized to enhance AC conductivity by increasing carrier density, supported by the elevated plasma frequency determined from fitting of a generalized Drude conduction model to the AC conductivity data.

Numerical simulation of enhanced gas recovery from methane hydrate using the heat of CO2 hydrate formation under specific geological conditions

Methane hydrate (MH) is found under the seabed in Japan's exclusive economic zone and is attracting attention as a domestic natural gas resource. One of the methods for extracting methane gas (MG) from sub-seabed MH reservoir is depressurisation. However, the production decelerates after a certain time partly due to the cooling of the reservoir caused by the heat absorption during MH dissociation. Therefore, several enhanced gas recovery (EGR) methods have been proposed, such as injecting CO2 into a sub-seabed sand layer to form CO2 hydrate (CDH) and, using the heat of CDH formation. This method is two functions: EGR and the reduction of greenhouse gas emission. In this study, a numerical method was developed to investigate the performance of the EGR from MH, using the heat of CDH formation. In our previous study, CDH formation model had been installed into a programme code for two-phase flow of CO2 and water in porous media. Based on this code, we newly implemented the state equation, enthalpy model, viscosity model, and heat conduction model of MG and the dissociation model of MH. Then, simulations were performed to form CDH in specific sand-mud alternate layers and to dissociate MH. As a result, it was suggested that increasing the CO2 injection amount potentially increases MH dissociation and the vertical distance between the mud layer capping the injected liquid CO2 and the bottom-simulating reflector of CDH is important to ensure a large CDH region to generate a large amount of heat. It was also shown that even after stopping CO2 injection, MH dissociation can continue for a certain period.

Universal Synaptic Plasticity of Interface‐Based Second‐Order Memristors

AbstractSecond‐order memristors with their internal short‐term dynamics display behavioral similarities with biological neurons and constitute an ideal basis unit for hardware neuromorphic networks, aims at treating spatio‐temporal tasks. Here, La0.7Sr0.3MnO3/BaTiO3/La0.7Sr0.3MnO3 second‐order memristive devices are investigated whose resistances and temperature dependencies range, on the same chip, from semiconductor to metal, but exhibit a universal neuromorphic plasticity. All devices may be described using a compact phenomenological model of current conduction, showing that resistive switching originates from interfaces, through charge trapping. Remarkably, the processes of short‐term memory gain/loss and long‐term consolidation/forgetting are the same whatever the device type. Only the synaptic transmission weights and the excitation/relaxation times with respect to stimuli differ, as it occurs for synapses/neurons in the brain. The weights may be tuned by the sole use of the frequency of stimuli (the activity rate), their evolution being dependent on previous activities (the history). Metal and semiconductor devices display the same in‐operando dynamics of potentiation or of depression, the transition from one regime to another being history‐dependent. The threshold frequencies are slightly lower in semiconducting devices. This work contributes to better understanding of memristive switching and plasticity and is relevant for the development of brain‐mimetic neural networks with new programming paradigms.

Numerical Analysis of Non-Fourier Model-Based Bio-Heat Transfer in the Laser-irradiated Axisymmetric Living Tissue.

The current work is related to the numerical investigation of non-Fourier heat transfer inside the short-pulsed laser-irradiated axisymmetric soft tissue phantom. It utilizes the modified discrete ordinate method to solve the transient radiative transfer equation (TRTE) for determining the intensity field. The laser energy absorbed by the soft tissue phantom behaves like a source in the Fourier/non-Fourier heat conduction model based-bio-heat transfer equation (BHTE), which is solved by employing the finite volume method (FVM) to determine the temperature distribution. Despite the prevalent use of non-Fourier BHTE for this purpose, a second law analysis is considered crucial to detect any potential anomalies. Equilibrium entropy production rates (EPR) are initially computed based on classical irreversible thermodynamics (CIT), which may yield negative values, possibly contravening the second law. Consequently, the EPR based on CIT is adjusted using the extended irreversible thermodynamics (EIT) hypothesis to ensure positivity. After that, the current research findings are compared with the results from the literature, and found good agreement between them. Then, the independent study is performed to select the optimum grid size, control angle size, and time step. A comparative analysis of results between the traditional Fourier and non-Fourier models has been performed. The impact of different parameters on the temperature fields and EPRs, is discussed. The effect of the optical properties of the inhomogeneity on the temperature distribution has been investigated. This study may help to enhance the effectiveness of the laser-based photo-thermal therapy.

An electrical conduction model for calcium-bearing shaly sandstone based on the effective medium Hanai-Bruggeman theory

An electrical conduction model for calcium-bearing shaly sandstone based on the effective medium Hanai-Bruggeman theory

Vertically aligned carbon fiber/polydimethylsiloxane composites prepared by lyophilization with exceptional thermal conductivity and electromagnetic interference shielding performance

Composites with high thermal conductivity and exceptional electromagnetic interference (EMI) shielding properties are crucial for ensuring the long-term stability of electronic devices. One-dimensional carbon fibers (CFs) stand out as promising materials due to their excellent thermal and electrical conductivity. However, the anisotropic nature of CFs limits the overall electrical and thermal conductivity of the composite, thus impeding its practical application. To address this limitation, we investigated the effect of different freezing methods on CF orientation using the ice template method. Subsequently, CF-150/PDMS and CF-250/PDMS composites with varying average lengths of CFs were prepared using the unidirectional freezing technique. We studied the influence of CF content and average length on the anisotropic thermal conductivity and EMI shielding properties of the composites. The CF-250/PDMS composite, with a CF content of 15.71 vol%, exhibits a remarkable thermal conductivity of 9.07 W·m−1·K−1 and a low thermal resistance of 2.61 °C·cm2‧W−1. The thermal conductive mechanism of CF/PDMS composites was simulated by thermal conduction model and finite element analysis. Furthermore, it demonstrates longitudinal electromagnetic interference shielding effectiveness (EMI SE) reaches up to 39.66 dB, while the transverse EMI SE reaches up to 52.55 dB. The vertically aligned CF/PDMS composites exhibit significant potential for a range of applications in thermal management and EMI shielding.

Methodology for geometry assessment of self-drilling micropiles using distributed fibre optic sensors

Self-drilling micropiles (SDMs) are gaining popularity as bearing foundation elements, as this construction technique allows for considerable time and cost savings. However, the irregular geometry and variability in the bearing capacity present uncertainty and a significant risk that has limited SDM deployment. To date, no reliable technology has been used to measure the SDM geometry. This paper proposes a methodology that uses distributed fibre optics (DFO), heat conduction modelling and inverse analysis to measure the pile geometry, and could also be extended to assess its bearing capacity. The temperature distribution during cement hydration was measured using two DFO investigative technologies and was compared to traditional temperature measurements using point sensors. An inverse analysis of SDM geometry was subsequently carried out based on the DFO measurement of temperature, a finite-element heat conduction model and a calibration pile. Finally, the calculated pile geometry was compared to the geometry of an excavated pile in the uppermost part. The methodology presented here is not only intended as a tool for designing SDMs but can also be deployed as a structural health monitoring system to detect and monitor crack formation.

Generalized thermoelastic wave response in a hollow cylinder with temperature-dependent properties based on the memory-dependent derivative of the heat conduction model

High-temperature pipelines are susceptible to defects due to the long-term service in high-temperature environments. The guided wave technology is promising for online non-destructive testing. Before implementing it in engineering, it is essential to better understand guided wave characteristics, especially attenuation, which significantly decreases the test distance and the resolution. However, describing the large attenuation is challenging due to the strong thermoelastic coupling, resulting in limitations of available models. To address these limitations, this paper aims to introduce a memory-dependent generalized thermoelastic model for investigating guided waves propagating in a hollow cylinder with temperature-dependent material properties. The analytical solutions are obtained using the Legendre polynomial method. The influence of the memory-dependent effect, temperature variation, and boundary conditions are studied. Some interesting findings are revealed: (1) The time delay factor is more dominant when adjusting κ and n to accurately describe guided wave propagation at high temperatures. (2): The mode conversion is accompanied by the attenuation and group velocity jump when the adjacent flexural torsional and longitudinal modes intersect, which is advisable to avoid when choosing the excitation frequency. (3) The relationship between phase velocity and attenuation versus temperature for quasi-elastic modes is nonlinear, while that for thermal modes is approximately linear.

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions.

Damping analysis of a transversely isotropic piezothermoelastic nanobeam resonator based on the MGT thermoelasticity

The present work investigates the vibration of a piezothermoelastic nanobeam in the frame of Moore–Gibson–Thompson (MGT) thermoelasticity theory. Closed form analytical expressions for the thermoelastic damping in terms of quality factor and frequency shift for a homogeneous transversely isotropic piezothermoelastic (PTE) beam is derived by using Euler–Bernoulli beam theory and complex frequency approach. Detailed analysis of damping of vibration owing to thermal fluctuations and electric potential in the present context under three sets of boundary conditions is attempted to investigate the influence of modes of vibration, electric potential, and beam length on energy dissipation caused by thermoelastic damping in PTE beam resonators. Analytical results are illustrated with the help of graphical plots on numerical findings in the case of the nanobeam resonator of Lead Zirconate Titanate (PZT-5A) material. The investigation brings out some significant key findings and observations in view of MGT heat conduction model.

Higher-order heat conduction model in a rotating micropolar thermoelastic medium with moving heat source and electromagnetic field

Higher-order heat conduction model in a rotating micropolar thermoelastic medium with moving heat source and electromagnetic field

Numerical study of TRISO particles with random size and location distribution in cuboid and cylindrical matrix: A validation for two-regime heat conduction model

During reactor operation, the precise size values or specific size distribution of tri-structural isotropic (TRISO) fuel particles randomly dispersed within the fully ceramic microencapsulated (FCM) fuel elements are often unknown. To investigate the impact of the random distribution of positions and sizes of TRISO particles within a cuboid or cylindrical matrix on the temperature distribution of fuel elements and to establish a practical heat conduction model, TRISO fuel particles with randomly distributed positions, diameters following Gaussian or uniform distributions are generated using relevant algorithms. A cuboid and a cylindrical TRISO fuel element are modeled in ANSYS, and a three-dimensional temperature field distribution of the fuel element is obtained through numerical simulation. The probability density of the maximum temperature of the fuel element is calculated and fitted. Finally, the applicability of the two-regime heat conduction model over a broader range is validated based on the simulated data. The conclusions of this study provide reference information for predicting the temperature distribution of FCM fuel elements containing TRISO particles with random size and location distribution.

Transitions of electrical conduction mechanism in graphene flake van der Waals thin film

The electrical conduction mechanism in 2D van der Waals (vdW) thin film made of graphene flakes can be characterized by the variable range hopping (VRH) over a wide range of temperature, followed by a transition into an Arrhenius type conduction at the higher temperature. Regarding the nature of the subsequent Arrhenius type conduction, a lack of consensus exists between the nearest neighbor hopping (NNH) and the band conduction (BC). We discuss how to assess the transition in conduction mechanism based on the transient behavior of the reduced activation energy (W) and the structure of electronic density of states (DOS) of the sample. With a multi-channel conduction model, we show that the transition from VRH to BC always accompany an increase in W, which is absent in the transition from VRH to NNH. Also discussed are the peculiarities of VRH in vdW thin film and what they imply towards the properties of defects. In most vdW flake thin films, the spread of defect band in DOS is governed by the intrinsic defect energy not by the Coulomb interaction between defects. It can further be deduced that the gap in DOS near Fermi level associated with Efros-Shklovskii VRH observed in vdW film is not a Coulomb gap as found in weakly doped crystalline semiconductor, but inherent in the distribution of defect intrinsic energy. For the graphene flake thin film we synthesized, Mott VRH and BC are identified.