Conduction Model Research Articles

Thermal characteristics of a multilayered annular disk with thermosensitive features using a fractional-order heat conduction model

Thermal characteristics of a multilayered annular disk with thermosensitive features using a fractional-order heat conduction model

A Differentiable Physics-Informed Machine Learning Approach to Model Laser-based Micro-Manufacturing Process

Abstract Advanced manufacturing processes are often based on complex multiphysics phenomena that are either poorly understood or are computationally too expensive to simulate in the context of process design, control or planning. Traditionally, simplified physics models with prescribed heuristics or purely data-driven surrogate models are used as alternatives in such applications. The concept of physics-informed machine learning (PIML) has been shown to have unique advantages over both of these alternatives in various fields of complex system analysis. In this paper, a new physics-informed machine learning (PIML) approach is presented to model the geometry of the cut produced by a Magnetically-assisted Laser Induced Plasma Micro Machining (M-LIPMM) process. This PIML architecture uses a neural network to auto-adapt the parametric boundary condition and physical properties used in a simplified finite difference based physics model (of 2D heat conduction), as a function of the inputs namely the laser settings. This network also estimates the scaling and shifting parameters used by a convolutional neural network that takes the temperature profile predicted by the simplified heat conduction model to predict the width and depth of the machined cut. Trained on physical experiment data, the PIML approach compares favorably to a pure data-driven neural network model in extrapolation tests, while also providing physical insights (that the latter cannot). The PIML approach also provides an 85% better accuracy overall compared to the simplified physics model with heuristic settings.

An updated Lagrangian particle hydrodynamics (ULPH) implementation of heat conduction model for weakly-compressive fluid

An updated Lagrangian particle hydrodynamics (ULPH) implementation of heat conduction model for weakly-compressive fluid

Analysis of the dynamic responses of a piezothermoelastic microbeam resonator under dual-phase-lag heat conduction

Thermoelastic vibration responses of a piezothermoelastic (PTE) microbeam resonator have been investigated in the present work under simply supported boundary conditions. The basic governing equations for a transversely isotropic piezothermoelastic solid are formulated by assuming the Euler–Bernoulli beam theory with hyperbolic dual-phase-lag (DPL) heat conduction model. Later on, non-dimensionalization of the variables have been carried out for simplicity to obtain the set of coupled governing equations for thermal deflection, electric field, and thermal moment. Initial and boundary conditions are defined to solve for the non-dimensional thermal deflection and thermal moment by using Laplace transform technique along with the finite Fourier sine transform. Closed-form solutions of the problem are obtained. Moreover, an attempt is made to illustrate the analytical results through numerical simulations by taking a PTE material of Lead Zirconate Titanate (PZT-5A). The influence of the quadratic term of the phase-lag parameter of heal flux in the DPL model is investigated to compare the effects of phase-lags under parabolic and hyperbolic DPL models. In addition, the long-term and short-term vibration responses of thermal moment and thermal deflection are analyzed in detail to observe the impact of different factors which characterize the piezoelectric phenomena and dual-phase-lag effects. Comparative analysis of different well-known models for responses of thermal moment and thermal deflection is also presented for short- and long-time ranges. Some important observations about how piezoelectric parameters, dual-phase-lag parameters, and beam parameters affect the behavior of piezothermoelastic vibrations have been highlighted.

Thermoelastic damping in bi-layered micro/nanobeam resonators using the dual-phase-lag generalized heat conduction model

The existing analytical investigations on thermoelastic damping (TED) in laminated micro/nanobeam resonators have generally neglected the thermal axial force and rarely considered the time lagging in the heat transfer. However, laminated beams will very likely exhibit stretching-bending coupling deformation due to the deviation of the physical neutral surface from the beam mid-surface. Furthermore, the TED in layered beams has been predicted by using the energy rather than the complex frequency approach. In this presentation, TED in bi-layered micro/nanobeams is analyzed based on the Euler-Bernoulli beam theory and the dual-phase-lag (DPL) generalized heat conduction theory by considering the thermal axial force. Analytical solutions for the TED in bi-layered micro/nanobeams are developed by using both the complex frequency approach and the energy method. Numerical results are presented to examine the effects of the thermal axial force and DPL relaxation times on the TED in the laminated beam resonators for different physical and geometrical parameters, vibration modes and mechanical boundary conditions, which reveal that the thermal axial force will increase (decrease) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bi-layered beams. The maximum underestimation for the TED due to neglecting the thermal axial force will reach about 7 % in Ag/Si beam and 15 % in Cu/Si3N4 beam. The DPL effect on the TED is closely related to the material properties of the laminas and their volume fractions. For the Ag/Si beam with the thickness less than 1nm, influence of the DPL relaxation on the TED becomes significant which changes continuously from the negative contribution to the positive one with the increase in the volume fraction of the Si from 0 to 1. However, the DPL effect can be ignored in the bi-layered beams with micrometer size.

Impact of Dual Phase Lag on Natural Convection Flow in a Porous Vertical Channel in the Presence of Periodic Boundary

ABSTRACTThe dual‐phase‐lag (DPL) heat conduction model is utilized in this research to analyze the fluid flow of viscous fluid passing through a porous vertical channel with periodic boundary conditions. Periodic heating is subjected to the channel boundary. Equations regarding the model, including the momentum and energy equations, in which the DPL term is incorporated, all in dimensional form, are stated and are being transformed to their dimensionless form, then solved analytically by undetermined coefficients and variation of parameters. The actual expressions of temperature and velocity, as well as the heat transfer rate and skin friction, are determined. The effects of the DPL parameters, suction/injection, Prandtl number, heat source/sink, and Strouhal number on the dimensionless temperature and velocity profiles are demonstrated using graphs that are constructed with the aid of MATLAB. It was found during the investigation that the introduction of the DPL model, together with suction/injection in the channel, enhances the velocity and fluid temperature within the channel. Also, the decreasing effect of temperature gradient phase lag on fluid temperature and velocity conversed with that of heat flux phase lag. As an important contribution, the discovery of the effects of the phase‐lag parameters of the DPL model and suction/injection on fluid temperature and velocity would significantly help researchers advance the design of electrical and electronic systems.

Polyethylene glycol modified polysiloxane and silver decorated expanded graphite composites with high thermal conductivity, EMI shielding, and leakage-free performance

Phase change thermal interface materials (PCTIMs) have attracted significant attention due to their dual capability in temperature control and thermal buffering. However, the widespread application of PCTIMs in electronic devices is hindered by critical drawbacks such as low thermal conductivity (к), absence of electromagnetic interference shielding effectiveness (EMI SE), poor flexibility, and susceptibility to leakage. In this study, leakage-free PCTIMs were successfully fabricated with ultra-high thermal conductivity (к∥ = 23.4 W m−1 K−1, к⊥ = 8.1 W m−1 K−1), outstanding phase change functionality, exceptional EMI SE (73.2 dB), and excellent flexibility. A polyethylene glycol-modified polydimethylsiloxane (pPDMS) was synthesized through chemical grafting, demonstrating its significant potential as substrates for PCTIMs. Moreover, a designed material called silver nanoparticles-decorated expanded graphite (Ag-EG), was prepared to facilitate multidimensional material collaboration and incorporated into the pPDMS matrix to obtain Ag-EG@pPDMS composites. This integration resulted in a three-dimensional (3D) multi-layer orientation structure that enabled superior thermal conductivity in both in-plane and through-plane directions. To investigate the influence of 3D multi-layer orientation structure on Ag-EG@pPDMS, theoretical analysis was conducted using Effective Medium Theory (EMT) and Foygel thermal conduction models, which were further simulated by finite element analysis confirming substantial enhancement in material properties attributed to the 3D multi-layer orientation structure. Thermal management and electromagnetic interference (EMI) shielding applications were conducted using computers, wireless bluetooth earphones, and other electronic devices, indicating the superior thermal conductivity and EMI shielding of Ag-EG@pPDMS composites.

A unified mixed [formula omitted]-finite element framework for modeling laser pulse heating processes in the refined thermodynamics

In this paper, new multi-field variational formulations are derived for solving the following thermodynamic models: (i) ballistic-conductive system, (ii) the Guyer–Krumhansl heat conduction model and (iii) the Maxwell–Cattaneo–Vernotte model as some models of the extended irreversible thermodynamic, handling the temperature, the heat flux and the current density of heat flux as independent field variables. Based on these variational approaches as mathematical background, a family of mixed hp-version finite element methods, which is capable of reliably and efficiently modeling the temperature responses, is designed. The solutions provided by the constructed hp-FE framework are illustrated for the following two heat pulse experiments as benchmark problems: (1) sinusoid laser pulse heating process and (2) rectangular (step-like) laser pulse train. It is shown that stable, oscillation-free temperature response functions can be obtained not only for the ballistic-conductive system and the Maxwell–Cattaneo–Vernotte model but also for the under-diffuse and the over-diffuse parameter settings of the Guyer–Krumhansl heat conduction model.

Thermoelastic field analysis using differential transform under Moore-Gibson-thompson theory

Abstract Heat conduction has many applications in engineering fields. There are
various heat conduction models have been studied in the last few years.The main objective of this research is to study the effect of MGT model on thermoelastic problem . Also, offer a strong tool-the DifferentialTransform Method- for solving the governing partial differential equations with a simpler computation load than existing approaches.This paper presents the mathematical model describing the Moore–Gibson–Thompson (MGT) equation in rectangular plate. This MGT equation is modified into the heat conduction in the rectangular plate. Thermoelastic phenomena play a significant role in heat conduction, particularly in materials that experience both thermal and mechanical stresses. Thus the thermoelastic properties of rectangular plates were also studied using the two-dimensional mathematical model under MGT heat conduction.Goodier’s function and Boussinesq harmonic functions techniques have been used to obtain the thermal stresses in rectangular plates. The results have been discussed using graphs drawn by the mathematical software MATLAB.

Performance analysis of heat pipe micro-reactor with Stirling engine based on full-scope multi-physics coupled simulation

Heat pipe micro-reactors (HPMRs) with Stirling engines for power conversion are emerging as a promising surface power technology. We developed a comprehensive multi-physics solver using the open-source finite-volume code OpenFOAM to perform high-fidelity analysis of HPMR systems’ steady-state and dynamic performance. The solver couples a 3D coarse-mesh multi-group neutron diffusion model with a 3D fine-mesh thermal conduction model using a mapping approach to accurately simulate multi-physics phenomena in the reactor core. Additionally, it integrates a 2D high-temperature heat pipe model as boundary conditions for heat transfer in the core, a 1D Stirling engine model for energy conversion, and a lumped parameter radiator model for heat dissipation. Applied to the HOMER-15 reactor system, the solver aided to identify the optimal working point of the system, achieving 3 kW of electric power with a conversion efficiency of 25.2 % under 20-Hz Stirling engine frequency and 3.34-MPa pressure. The transient full-scope simulation with the solver shows that the load-follow strategy based on gas charging and venting in Stirling engines is capable to accommodate 35 % step increase of external load. When the unexpected reactivity insertion is within 0.1$, the peak temperature in the reactor core is below the allowable limit temperature. Analysis of single failure of Stirling engines indicates that the system safety and reliability can be enhanced by either incorporating an appropriate number of engines or enhancing heat transfer between Stirling engine channels.

Activation thresholds for electrical phrenic nerve stimulation at the neck: evaluation of stimulation pulse parameters in a simulation study

Abstract Objective. Phrenic nerve stimulation reduces ventilator-induced-diaphragmatic-dysfunction, which is a potential complication of mechanical ventilation. Electromagnetic simulations provide valuable information about the effects of the stimulation and are used to determine appropriate stimulation parameters and evaluate possible co-activation. Approach. Using a multiscale approach, we built a novel detailed anatomical model of the neck and the phrenic nerve. The model consisted of a macroscale volume conduction model of the neck with 13 tissues, a mesoscale volume conduction model of the phrenic nerve with three tissues, and a microscale biophysiological model of axons with diameters ranging from 5 to 14 µm based on the McIntyre–Richardson–Grill-model for myelinated axons. This multiscale model was used to quantify activation thresholds of phrenic nerve fibers using different stimulation pulse parameters (pulse width, interphase delay, asymmetry of biphasic pulses, pulse polarity, and rise time) during non-invasive electrical stimulation. Electric field strength was used to evaluate co-activation of the other nerves in the neck. Main results. For monophasic pulses with a pulse width of 150 µs, the activation threshold depended on the fiber diameter and ranged from 20 to 156 mA, with highest activation threshold for the smallest fiber diameter. The relationship was approximated using a power fit function x −3. Biphasic (symmetric) pulses increased the activation threshold by 25 to 30 %. The use of asymmetric biphasic pulses or an interphase delay lowered the threshold close to the monophasic threshold. Possible co-activated nerves were the more superficial nerves and included the transverse cervical nerve, the supraclavicular nerve, the great auricular nerve, the cervical plexus, the brachial plexus, and the long thoracic nerve. Significance. Our multiscale model and electromagnetic simulations provided insight into phrenic nerve activation and possible co-activation by non-invasive electrical stimulation and provided guidance on the use of stimulation pulse types with minimal activation threshold.

Multiband Spectrum Method for Quantifying the Ionic Contribution of Volume Strategy and Filler Strategy: Enhancing the Ionic Transport Channels for Polymeric Solid-State Batteries.

As a promising solution for solid-state batteries with high energy density and safety, understanding the mechanism of fast ion conduction in polymer-ceramic composite solid-state electrolytes (CSEs) is still a challenging task. Herein, we understand the enhanced ion conduction in CSEs using a series of ionic spectra. Ionic insight is extended to ion conduction in CSEs, resolving the mechanism of fast ion migration. With the cooperation of enhanced interface and filler ion conduction, the CSE with a conductive filler exhibits ionic conductivity higher than that of CSEs with insulating fillers. Volume and filler strategies of CSE design are proposed based on volcanic maps of conductivity. An equivalent circuit is established to describe the conduction mechanism of CSEs. Specifically, Rinterface and Rfiller are in parallel to describe the cooperation of interface and filler conduction. They are in series with Rbulk, which represents a competition between the fundamental matrix and enhanced interface conduction. The proposed conduction model is verified though the energy storage performance of solid-state batteries; a fast dynamic process promises a better rate performance and cycling stability of solid-state batteries. These results provide deep insights into fast ion conduction in ceramic-polymer CSEs, which are indispensable to develop high-performance solid-state batteries.

GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations

In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently.

Propagation, reflection, and transmission of nonlocal waves at the interface between semiconductor isotropic and diffusive porous semiconductors through a higher-order fractional derivative study

The current research paper investigates the transmission of nonlocal waves occurring at the interface between a semiconductor isotropic medium and a diffusive porous solid. A higher-order fractional-order derivative heat conduction model is utilized to account for thermal effects on wave propagation, reflection, and transmission. The interface generates five coupled and one independent transmitted wave in the lower medium, along with three coupled transmitted waves and one independent SV wave. Graphical analyses are conducted to examine the propagation speed of reflected waves in both porous and non-porous media. The impact of elastic non-locality and the fractional-order parameter on the propagation speed of all waves within the media is also assessed. The amplitude ratios are computed for the incident longitudinal displacement wave at the free boundary. The research explores the influence of physical parameters on reflection and transmission coefficients, and the results are validated through the conservation of energy. Additionally, the analysis yields deductions for certain special cases.

The heat transfer in skin tissues under the general two-temperature three-phase-lag model of heat conduction with a comparative study

In this paper, a new and more general model of heat conduction that depends on the drift velocity due to thermomass motion assumption will be established and will be applied to the skin tissue. Four different heat conduction models will be incorporated into a unified equation of heat conduction: the Pennes, Vernotte-Cattaneo, dual-phase-lag of Tzou, and the general two-temperature three-phase-lag of Youssef. The governing partial differential equations of the general two-temperature three-phase-lag model of bioheat conduction will be implemented and solved directly in the domain of the Laplace transformation. The numerical solutions of the Laplace transform will be calculated by executing the Tzou iteration formula. The ramp-type heat on the surface of the skin tissue will be considered as thermal loading. The conductive and dynamic temperature increment reactions have been studied and discussed with different values of ramp-time heat, characteristic length, and drift velocity parameters. The novelty of this work is to introduce some comparisons of the four under-studied bioheat conduction models and show the differences between them in the figures. The numerical results show that the ramp-time heat, drift velocity, and characteristic length parameters have major impacts on the increment of both dynamical and conductive temperature distributions.

Effect of oxygen vacancy engineering on hybrid conduction mechanism in Ce doped La1-xCexBaCo2O5 ceramics

The La1-xCexBaCo2O5 (x = 0.05, 0.1, 0.15, 0.2) thermosensitive ceramics with negative temperature coefficient (NTC) were synthesized using a conventional solid-phase method. X-ray diffraction analysis (XRD) revealed that La1-xCexBaCo2O5 possesses an orthorhombic perovskite structure. Scanning electron microscopy (SEM) showed a uniform and dense ceramic microstructure, with grain size initially increasing and then decreasing as the Ce content rises. X-ray photoelectron spectroscopy (XPS) data reveal the presence of oxygen vacancies and Co3+/Co2+ ion pairs within the material, showing concentrations that increase with Ce content. The resistance temperature profiles indicate the presence of a hybrid conductive mechanism in the material. In the temperature range of 2–20 K, the conductive mechanism of the material conforms to Mott's 3D VRH conduction model. When the temperature is 20–77 K, the conductive mechanism of the material is consistent with the small polariton conduction model. In addition, the mechanism of the mixed effect of oxygen vacancy concentration on the conductivity of the material is explained to elucidate the electron hopping transport conductivity mechanism of NTC thermal ceramics. First-principle calculations demonstrate that oxygen vacancies introduce new impurity energy levels and pathways for electron transport, enhancing the ceramics' electrical conductivity. These findings highlight the ceramic samples' favorable NTC characteristics and electrical conductivity across the temperature range 2–77 K, offering new possibilities for applications in extremely low-temperature NTC thermistors.

A computationally efficient anisotropic electrophysiological multiscale uterus model: From cell to organ and myometrium to abdominal surface

Background and objectivePreterm labor is a global problem affecting the health of newborns. Despite numerous studies reporting electrophysiological changes throughout pregnancy, the underlying mechanism that triggers labor remains unclear. Electrophysiological modeling can provide additional information to better understand the physiological transition from pregnancy to labor. Previous uterine electrophysiological models do not consider either the tissue thickness or fiber structure, which have both been shown to significantly impact propagation patterns. MethodsThis paper presents a parallel computational model of the uterus using the bioengineering modeling environment OpenCMISS. This model is a multiscale anisotropic model that spans different levels from cell to organ. At the cellular level, the model utilizes a mathematical representation of uterine myocytes based on multiple ion channels. In the 3D uterine model, fiber structures are added, ranging from horizontal rings in the inner layer to vertically downward fibers in the outer layer, to more accurately depict the electrophysiological activities of the uterus. Additionally, we have developed a multilayer volume conduction model based on the boundary element method to describe the propagation of electrical signals from the myometrium to the abdominal surface. ResultsOur model can not only reproduce faithfully both local non-propagated and global propagated electrical activity, but also simulate the fast wave low and fast wave high components of the electrohysterogram (EHG) on the abdominal surface. The model results support the hypothesis that the fast wave high of the EHG signal is related to uterine excitability and fast wave low is related to signal propagation. The amplitude of the simulated signal on the abdominal surface falls in the ranges of real EHG data, which is inversely proportional to the abdominal subcutaneous fat thickness, and the signal waveform highly depends on electrode position and the relative distance to the pacemaker. In addition, the propagation velocity is highly dependent on the uterus geometry and falls in the real-world data range ConclusionsOur models facilitate a better understanding of the electrophysiological changes of the uterus during pregnancy and labor, and allow for an investigation of drug effects and/or structural or anatomical abnormalities.

Size-dependent thermoelastic dissipation and frequency shift in micro/nano cylindrical shell based on surface effect and dual-phase lag heat conduction model

Size-dependent thermoelastic dissipation and frequency shift in micro/nano cylindrical shell based on surface effect and dual-phase lag heat conduction model

Multiple edge cracks in a coated semi-infinite medium due to non-Fourier thermal shock

In this wok, based on the non-Fourier C-V model, the problem for multiple edge cracks is investigated for a coating-substrate pair subjected to a sudden temperature drop at the surface of coating. The temperature and resulting thermal stresses without cracks are obtained by the method of Laplace transform. By numerically solving the singular integral equations, the thermal stress intensity factors (SIFs) are evaluated. The results from the Fourier model and C-V heat conduction model are presented for comparison. Two dimensionless quantities are proposed to account for the coupling effects of heat conduction parameters (i.e., thermal conductivity, thermal diffusivity, and thermal relaxation time). Numerical results are presented for the thermal SIF as a function of normalized quantities such as time, crack depth, material constants and crack spacing. The findings in this work are expected to provide references for maintaining the integrity of the coating-substrate pair in the extreme heat transfer applications.

Fractional-order modeling of myocardium structure effects on atrial fibrillation electrograms

Atrial fibrillation (AF) is the most common cardiac arrhythmia with mechanisms of initiation and sustaining that are not fully understood. The clinical procedure for AF contemplates the analysis of the atrial electrograms, whose morphology has been correlated with the underlying structure of the atrial myocardium. This study employs a mathematical model incorporating fractional calculus to simulate cardiac electrical conduction, accounting for tissue structural inhomogeneities using complex-valued orders. Simulations of different wavefront propagation patterns were performed, and virtual electrograms were analyzed using an asymmetry factor. Our results evinced that the shapes of the action potential and the propagating wavefront can be modulated through the fractional order under both healthy and AF conditions. Moreover, the asymmetry factor changes with variations in the fractional order. For a given propagation pattern under AF conditions, variation intervals for the asymmetry factor can be generated by forming sets of simulations with different configurations for the fractional order, representing diverse samples of atrial tissue with varying degrees of structural heterogeneity. This approach successfully reproduces the electrogram negative deflection predominance seen in AF patients, which standard integer-order models cannot predict. Our fractional-order conduction model aligns with the effects of atrial structure on the electrical dynamics observed in clinical AF. Therefore, it offers a valuable tool for studying cardiac electrophysiology, encompassing both electrical and structural interactions of the tissue within a unified model.