Heat Diffusion Model Research Articles

Modeling nanogratings erasure at high repetition rate in commercial optical glasses

Volume nanogratings (NGs) imprinted by infrared femtosecond laser in commercial optical glasses take the form of orientable subwavelength birefringent nanostructures, being composed of an assembly of nanopores. The existence of NGs strongly depends on the laser parameters and glass composition. Therefore, in this work, we tentatively model the erasure threshold of NGs in a pulse energy - repetition rate processing window. For this purpose, we combine i) a heat diffusion model to simulate the thermal treatment experienced by the glass upon laser irradiation, and ii) the Rayleigh-Plesset equation to take into account the evolution of a nanopore size during laser processing. We first determine a criterion for nanopores erasure, falling within a typical characteristic time of few tens of ns, in which the cooling of the last laser pulse absorbed by the material is progressively cooled. Then, considering a multiple pulse regime and the dependence of the deposited pulse numbers on the thermal treatment, the modeled NGs erasure threshold follows the experimental trend. Finally, considering a steady state regime for various repetition rates, and adjusting the energy deposition (absorption coefficient or beam waist) as a function of the pulse energy, the NGs existence window can perfectly match the experimental values.

Elastohydrodynamic lubrication analysis and temperature field simulation of gear system

Abstract The gearbox is one of the key components in the aero engine. In the process of high-speed operation, the internal temperature of the gearbox rises significantly, which seriously affects the service performance of transmission equipment. Based on the meshing principle and Herz contact theory, the basic meshing parameters are analyzed, and the comprehensive friction coefficient and heat flux are solved. According to the principle of convective heat transfer in a rotating disc and the frictional heat diffusion model, the CHTC (convective heat transfer coefficient) is analyzed. The FE model of the gear system is built based on ANSYS software, and the temperature distribution is analyzed by loading thermal boundary conditions with the APDL program. The calculation results indicate that the middle of the tooth tip or root of the gear has the maximum temperature. The research provides some reference values for the calculation method of the temperature field of the gear system under elastohydrodynamic lubrication.

Optical pulse-induced ultrafast antiferrodistortive transition in SrTiO3

The ultrafast dynamics of the antiferrodistortive phase transition in perovskite SrTiO3 is monitored via time-domain Brillouin scattering. Using femtosecond optical pulses, we initiate a thermally driven tetragonal-to-cubic structural transformation and detect the crystal phase through changes in the frequency of Brillouin oscillations (BO) induced by propagating acoustic phonons. Coupling the measured BO frequency with a spatiotemporal heat diffusion model, we demonstrate that, for a sample kept in the tetragonal phase, deposition of sufficient thermal energy induces a rapid transformation of the heat-affected region to the cubic phase. The initial phase change is followed by a slower reverse cubic-to-tetragonal phase transformation occurring on a timescale of hundreds of picoseconds. We attribute this ultrafast phase transformation in the perovskite to a structural resemblance between atomic displacements of the R-point soft optic mode of the cubic phase and the tetragonal phase, both characterized by anti-phase rotation of oxygen octahedra. The structural relaxation time exhibits a strong temperature dependence consistent with the prediction of the equation of motion describing collective oxygen octahedra rotation based on the energy landscape of the phenomenological Landau theory of phase transitions. Evidence of such a fast structural transition in perovskites can open up new avenues in information processing and energy storage sectors.

Thermal Analysis of Power Transformer Using 2D and 3D Finite Element Method

An accurate simulation and computational analysis of temperature distribution in large power transformers used in power plants is crucial during both the design and operational phases. This study introduces a thermal modeling analysis encompassing two- and three-dimensional (2D and 3D) approaches for power transformers. The mathematical model for heat diffusion follows the Finite Element Method (FEM) approach. Validation of the computed results involves comparing them against measurements from Hyundai’s test report for both 2D and 3D models, aiming to identify the most effective solution. Additionally, the thermal dynamics of power transformers under diverse operational conditions, specifically oil-immersed ones, are examined. The efficacy of this model is confirmed through testing on a step-up transformer at Kureimat station in Egypt, with specifications including three-phase, 50 Hz, 16.5/240 KV, nine taps, and cooling type (ONAN/ONAF1/ONAF2).

Predicting resting-state brain functional connectivity from the structural connectome using the heat diffusion model: a multiple-timescale fusion method

Objective. Understanding the intricate relationship between structural connectivity (SC) and functional connectivity (FC) is pivotal for understanding the complexities of the human brain. To explore this relationship, the heat diffusion model (HDM) was utilized to predict FC from SC. However, previous studies using the HDM have typically predicted FC at a critical time scale in the heat kernel equation, overlooking the dynamic nature of the diffusion process and providing an incomplete representation of the predicted FC. Approach. In this study, we propose an alternative approach based on the HDM. First, we introduced a multiple-timescale fusion method to capture the dynamic features of the diffusion process. Additionally, to enhance the smoothness of the predicted FC values, we employed the Wavelet reconstruction method to maintain local consistency and remove noise. Moreover, to provide a more accurate representation of the relationship between SC and FC, we calculated the linear transformation between the smoothed FC and the empirical FC. Main results. We conducted extensive experiments in two independent datasets. By fusing different time scales in the diffusion process for predicting FC, the proposed method demonstrated higher predictive correlation compared with method considering only critical time points (Singlescale). Furthermore, compared with other existing methods, the proposed method achieved the highest predictive correlations of 0.6939 ± 0.0079 and 0.7302 ± 0.0117 on the two datasets respectively. We observed that the visual network at the network level and the parietal lobe at the lobe level exhibited the highest predictive correlations, indicating that the functional activity in these regions may be closely related to the direct diffusion of information between brain regions. Significance. The multiple-timescale fusion method proposed in this study provides insights into the dynamic aspects of the diffusion process, contributing to a deeper understanding of how brain structure gives rise to brain function.

A Unified Particle-Based Solver for Non-Newtonian Behaviors Simulation.

In this article, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.

Shape optimization of the energy efficiency of building retrofitted facade

The current state of research indicates a necessity of further examination in both numerical and experimental studies related to optimizing shapes of building enclosures for the enhancement of their energy efficiency. The demand for research primarily arises due to the numerical complexities associated with optimizing shapes for this specific purpose. Consequently, the primary objective of this article is to address and bridge these gaps in the field. To achieve this, a two-dimensional steady-state heat diffusion model is assumed to represent the physical processes occurring within building facades of varying shapes. A third type boundary condition is applied to the exterior boundary, encompassing convective and incident short-wave solar radiation effects. The calculation of short-wave radiation accounts for factors such as sunlight exposure and shading, influenced by the surrounding urban environment. The internal boundary interfaces with the indoor ambient air, and thus, a Robin boundary condition is adopted. To tackle the computational demands while ensuring accuracy, the boundary element method (BEM) is employed by discretizing the domain boundary into discrete elements. Then, two heat transfer design objectives are define according to the period of investigations: ones related to enhancing heat transfer and ones focused on thermal insulation problem. Last, a real-world case study is conducted, considering a house wall under varying climate conditions throughout the year. Optimal shapes for the external wall boundary are determined with the constraint that the optimized facade utilizes the same amount of material as the reference flat one. The results demonstrate a substantial increase in energy efficiency compared to the reference flat wall case.

Thermal conductivity of SiC and PyC coatings in spherical nuclear fuel particles measured by nanosecond time domain thermoreflectance

TRi-structural ISOtropic (TRISO) nuclear particle fuels are intended for application in several designs of advanced high temperature nuclear reactors. Nanosecond time domain transient thermoreflectance has been applied to the silicon carbide (SiC) and the inner and outer pyrolytic carbon (PyC) coatings of surrogate TRISO particles, measuring mean thermal conductivities of 166 ± 18 W∙m−1K−1, 11.1 ± 1.9 W∙m−1K−1, and 8.6 ± 2.1 W∙m−1K−1, respectively, for each layer. The applicability of the analytical heat diffusion model used to fit the measured traces was examined and it was found that the boundary effect at the SiC/PyC interface becomes perceptible at a lateral distance approximately equal to the thermal penetration depth of SiC (7.1 µm). In addition, steady-state thermal modelling showed that the radial thermal resistance of the particle is dominated by the porous buffer layer. The thermal resistance will likely increase significantly upon circumferential detachment of the porous buffer carbon coating with irradiation. Implications for fuel design and reactor performance are discussed.

Time-domain thermoreflectance measurement of the thermal diffusivity of Nb thin films

Nb-coated Cu superconducting radiofrequency (SRF) cavities are of interest as a possible alternative to bulk Nb cavities for particle accelerators due to the high thermal conductivity of Cu and its lower cost than Nb. Studying the thermal diffusion properties in Nb thin films on Cu is important for developing Nb-coated Cu SRF cavities. In the present study, the thermal diffusivity of 100‒800 nm Nb films on Cu is measured by time-domain thermoreflectance (TDTR). The thermal diffusivity is obtained from a curve fit of the TDTR signal to a one-dimensional Fourier heat diffusion model over a time extending from 25 to 985 ps after laser-surface interaction. The film was examined by atomic force microscopy and scanning electron microscopy. The grain size and thermal diffusivity increase with film thickness. The thermal diffusivity reaches a value similar to that reported for bulk Nb for the 400 and 800 nm films, for which the average grain size is 47 ± 13 nm and 68 ± 18 nm, respectively. TDTR measurement for the 400-nm film taken over the temperature range of 293 to 40 K showed that the thermal diffusivity increases as the temperature is reduced. The results indicate that grain boundaries reduce the thermal diffusivity of the Nb film and, therefore, must be considered in Nb-coated Cu SRF cavities.

Intrusion tip velocity controls the emplacement mechanism of sheet intrusions

Space for intruding magma is created by elastic, viscous, and/or plastic deformation of host rocks. Such deformation impacts the geometries of igneous intrusions, particularly sills and dikes. For example, tapered intrusion tips indicate linear-elastic fracturing during emplacement, whereas fluidization of host rocks has been linked to development of elongate magma fingers with rounded tips. Although host rock fluidization has only been observed at the lateral tips of magma fingers, it is assumed to occur at their leading edges (frontal tips) and thereby control their propagation and geometry. Here, we present macro- and microstructural evidence of fluidized sedimentary host rock at the lateral tips of magma fingers emanating from the Shonkin Sag laccolith (Montana, western United States), and we explore whether fluidization could have occurred at their frontal tips. Specifically, we combine heat diffusion modeling and fracture tip velocity estimates to show that: (1) low intrusion tip velocities (≤10−5 m s−1) allow pore fluids ahead of the intrusion to reach temperatures sufficient to cause fluidization, but (2) when tip velocities are high (∼0.01−1 m s−1), which is typical for many sheet intrusions, fluidization ahead of propagating tips is inhibited. Our results suggest that intrusion tip velocity (i.e., strain rate) is a first-order control on how rocks accommodate magma. Spatially and temporally varying velocities of lateral and frontal tips suggest that deformation mechanisms at these sites may be decoupled, meaning magma finger formation may not require host rock fluidization. It is thus critical to consider strain rate and three-dimensional intrusion geometry when inferring dominant magma emplacement mechanisms.

Physics-based thermal noise effect reduction in sonic IR crack length estimation

ABSTRACT Using heat diffusion models in sonic infrared (IR) inspection technology that captures arbitrary frictional heat generation function along a crack lends itself to estimation of crack length using thermal images alone. This study introduces novel physics-based approach that relies on the governing heat diffusion model linearity and superposition of point heat sources along crack to reduce thermal noise effect in crack length estimation. It utilises thermal images and their timestamps in sonic IR inspection to deliver spatiotemporal average representation of the aforementioned point heat sources to reduce thermal noise effect in crack length estimation. The proposed methodology is tested against two-dimensional and three-dimensional finite element simulations with an arbitrary frictional heat generation function along crack. Virtual random thermal noise levels ranging between 50 and 200 mK, which are higher than IR cameras Noise Equivalent Temperature Difference values, are added to simulated results to reflect realistic and drastic thermal noise levels. Spatiotemporal averaging using combined sets of different thermal images captured at various times in single sonic IR inspection delivered about 16% total uncertainty in the estimation of a crack length at 95% confidence level based on 60 experiments. Similar uncertainty level is obtained using independently reported sonic IR experimental data.

Evaluation of bioconvection for sinusoidally moving Jeffrey nanoparticles in view of temperature dependent thermal conductivity and Cattaneo-Christov heat diffusion model

With impressive thermal outcomes, the nanofluids present multidisciplinary applications in the cooling processes, thermal systems, extrusion processes, heat storage devices and many more. The aim of current research is to inspect thermal impact of Jeffrey fluid with tiny particles under the assumptions of variable thermal conductivity. The problem is supported with applications of chemical reaction, activation energy and magnetic force. For heat and mass transfer phenomenon, Cattaneo-Christov diffusion theories have been implemented. The formulated model is solved by using the homotopy analysis method (HAM) with excellent accuracy. The graphical analysis is performed with specified range of parameters like 0.2⩽H⩽0.8, 0.1⩽ϖ⩽1.7, 0.0⩽N⩽1.5, 0.0⩽Π⩽3.1, 0.3⩽γ⩽0.6, 0.6⩽Ψ⩽3.2, 0.5⩽Ω⩽2.0, 0.0⩽Σ⩽1.5, 0.2⩽Nt⩽1.7, 1.0⩽Pr⩽1.9, 0.5⩽Sc⩽1.4,0.3⩽β⩽1.5, 0.1⩽ε⩽1.0, 0.2⩽Nb⩽1.7. The assessment of flow parameters is graphically evaluated. It is observed that both velocity profiles periodically enhance for Deborah number while temperature, microorganisms and concentration distributions decelerate. The greater estimates of variable thermal conductivity and heat generation improve the temperature distribution while conflicting scenario ensures for thermic relaxation constant.

Fractionalizing, coupling and methods for the coupled system of two-dimensional heat diffusion models

<abstract><p>The present manuscript gives an overview of how two-dimensional heat diffusion models underwent a fractional transformation, system coupling as well as solution treatment. The governing diffusion models, which are endowed with Caputo's fractional-order derivatives in time $ t $, are suitably coupled using the (1) convection phenomenon, (2) interfacial coupling by considering the mechanism of a double-layered bar, and the (3) nonlinear coupling due to temperature-dependent thermal diffusivities. Semi-analytical and analytical methods are considered for the solution treatment. Moreover, we seek a computational environment to graphically illustrate the systems' response to different fractional orders in each case through the determined diffusional fields. Besides, we supply certain concluding notes at the end.</p></abstract>

Boundary heat diffusion classifier for a semi-supervised learning in a multilayer network embedding

The scarcity of high-quality annotations in many application scenarios has recently led to an increasing interest in devising learning techniques that combine unlabeled data with labeled data in a network. In this work, we focus on the label propagation problem in multilayer networks. Our approach is inspired by the heat diffusion model, which shows usefulness in machine learning problems such as classification and dimensionality reduction. We propose a novel boundary-based heat diffusion algorithm that guarantees a closed-form solution with an efficient implementation. We experimentally validated our method on synthetic networks and five real-world multilayer network datasets representing scientific coauthorship, spreading drug adoption among physicians, two bibliographic networks, and a movie network. The results demonstrate the benefits of the proposed algorithm, where our boundary-based heat diffusion dominates the performance of the state-of-the-art methods.

Correlation of the cell disintegration index with Luikov's heat and mass transfer parameters for drying of pulsed electric field (PEF) pretreated plant materials

Currently, the modelling of drying processes of plant tissues pre-treated by pulsed electric field (PEF) is following experimentally identified curves or separate heat and mass transfer and diffusion models with different levels of accuracy. This research had two major objectives: mathematical modeling and control of drying process of different vegetables pretreated by PEF during convective drying. The mathematical modeling was based on Luikov's heat and mass transfer model along with properties of different vegetables. Computer modelling was done using the difference method for predicting moisture and the temperature potentials of untreated and PEF-treated vegetables. The formulation and the solution procedures were applied to simulate the simultaneous heat and mass transfer in selected vegetables subjected to the convective drying. Suggested model had a good correlation with experimental results. Moreover, cell disintegration index can be used as a controllable parameter in heat and mass transfer models to predict drying behavior of potato, onion, and carrot tissues. Obtained drying models can be used as a mathematical tool to predict drying behavior for various types of agricultural products pre-treated by pulsed electric field. • Pulsed electric field (PEF) pre-treatment reduced the drying time. • Obtained methodology is a good tool for the analysis and modelling of PEF assisted drying. • Cell disintegration index is in relationship with the kinetics coefficients of Luikov's model. • Cell disintegration index can be used to predict drying behavior of plant tissues.

Numerical treatment of microscale heat transfer processes arising in thin films of metals

The microscale heat transport equation (MHTE) is an important model in the microtechnology. The MHTE differs from the classical model of heat diffusion since it includes temperatures derivatives of second- and third-order with respect to time, and space and time, respectively. This paper studies the application of the localized radial basis function partition of unity (LRBF-PU) method for finding the MHTE solution. The proposed algorithm discretizes the unknown solution in two phases. First, the discretization of time dimension is obtained through the finite difference with second order accuracy. In addition, the unconditional stability and the convergence of the temporal semi-discretization are analysed with the help of the discrete energy method in an appropriate Sobolev space. Second, the discretization of the spatial dimension is accomplished with the help of the LRBF-PU. One of the main disadvantages of global collocation techniques is the high computational cost caused by the associated dense algebraic system. Using the proposed strategy, one can divide the original domain into a number of sub-domains through a kernel approximation over every sub-domain. The LRBF-PU method avoids the ill-conditioning driven by global collocation RBF-based methods and decreases the related computational cost. Numerical examples highlight the robustness and accuracy of the LRBF-PU.

Comparison of Holocene temperature reconstructions based on GISP2 multiple-gas-isotope measurements

Nitrogen and argon stable isotope data obtained from ancient air in ice cores provide the opportunity to reconstruct past temperatures in Greenland. In this study, we use a recently developed fitting-algorithm based on a Monte Carlo inversion technique coupled with two firn densification and heat diffusion models to fit several Holocene gas-isotope data measured at the GISP2 ice core and infer temperature variations.We present for the first time the resulting temperature estimates when fitting δ15N, δ40Ar, and δ15Nexcess as individual targets. While the comparison between the reconstructions using δ15N and δ40Ar shows high agreement, the use of δ15Nexcess for temperature reconstruction is problematic because the statistical and systematic data uncertainty is higher and has a particular impact on multi-decadal to multi-centennial signals.Our analyses demonstrate that T(δ15N) provides the most robust estimate. The T(δ15N) estimate is in better agreement with Buizert et al. (2018) than with the temperature reconstruction of Kobashi et al. (2017). However, all three reconstruction strategies lead to different temperature realizations.

Understanding Thermal Lagging Behaviors in Thermoelectric Elements With the Dual-Phase-Lag Model

Abstract This study investigates the heat transport mechanism in semiconductor elements within a homogeneous thermoelectric cooling system using the dual-phase-lag (DPL) model. The thermal lagging behavior is analyzed and explored during the energy transport process. The coupled energy and constitutive partial differential equations are solved simultaneously to reduce the complexity of the high-order spatial and time derivatives. This approach simplifies the mathematical solution process and reduces numerical instabilities when compared to the conventional methodology in which either the temperature or heat flux is solved individually with a single equation. The effect of the thermal lagging behavior on energy transport is examined and compared to results by using the Cattaneo–Vernotte model. Furthermore, the phase-lag behavior on the temperature and heat flux profiles is investigated in detail. This study provides perceptive information for engineering applications in which the microscale heat transport phenomenon plays a significant role during the design process. Adding the dual-phase-lag model to the traditional heat diffusion model is a complementary option for engineers in the thermoelectric industry.

Thin Film Flow of Tangent Hyperbolic Fluid with Nonlinear Mixed Convection Flow and Entropy Generation

This paper examined the three-dimensional steady thin film flow of tangent hyperbolic fluid with nonlinear mixed convection flow and entropy generation past a stretching surface under the influence of magnetic field. For the flow problem, the Cattaneo–Christov heat and mass diffusion model was employed to examine heat and mass transfer characteristics and impacts of the normally directed magnetic field. To transform nonlinear PDEs into ODEs, the variable transformation technique was used. The bvp4c algorithm was implemented to solve these ODEs. The behavior of every leading parameter on the velocities, temperature, concentration profile, entropy generation, and Bejan number was reported with tabular and figurative form. The results show that as the values of Br increase, the entropy generation enhances, but the Bejan number decreases. Moreover, as the values of B increase, the opposite characteristics are observed in entropy generation and Bejan number graphs. Furthermore, the skin friction coefficient number, local Nusselt number, and Sherwood number are graphically discussed for the active involved parameters. The best agreement is recorded when we compare this paper with the previous literature for various values of M .

Numerical investigations on solid-fueled ramjet inlet thermodynamic properties effects on generating self-sustained combustion instability

In this work, combustion instability of the solid-fueled ramjet (involving diffusion-dominant combustion process) is investigated using a numerical model. Effects of inlet thermodynamic properties, such as inlet temperature Tin, Mach number Ma and mass flow rate m˙a on generating combustion instability are evaluated. The 2-dimensional (2D) model is first validated with 3-dimensional (3D) model and the experimental data. Further validations are conducted on chemical reaction model, heat transfer model and diffusion models and comparing the acoustic signature of a Ramjet combustor and mode-shapes with the experimental data available. It is then used to identify stable and unstable acoustic modes exited by unsteady heat release in the combustor. Large-scale temperature waves are observed to be convected downstream. To clarify the mechanism of such limit cycles, Rayleigh criterion is utilized by analyzing the phase difference between the acoustic pressure and unsteady heat release rate. In addition, attempts are made to determine Rayleigh index and the oscillations' growth rate. Finally, it is found that the inlet temperature plays little roles on affecting the limit cycle intensity. This is quite different from m˙a and Ma. Larger m˙a and/or Ma, more intensified limit cycle oscillations. In general, the model provides a useful low-computational-cost numerical platform to investigate thermoacoustic instability in a Ramjet combustor.