Heat Conduction Model Research Articles

Mapping GENERIC Hydrodynamics into Carter’s Multifluid Theory

We show that the GENERIC model for relativistic heat conduction is a multifluid of Carter; this allows one to compute the multifluid constitutive relations directly from the GENERIC formalism. As a quick application, we prove that in the limit of infinite heat conductivity, GENERIC heat conduction reduces to the relativistic two-fluid model for superfluidity. This surprising “crossover” is a consequence of relativistic causality: if diffusion happens too fast, all the diffusing charge cumulates on the surface of the light cone, and it eventually travels at the speed of light like a wave. Our analysis is non-perturbative and carried out in a fully non-linear regime.

Soft Computing Model for Inverse Prediction of Surface Heat Flux from Temperature Responses in Short-Duration Heat Transfer Experiments

Abstract Aerodynamic experiments in high speed flow domain mainly rely on precise measurement transient surface temperatures and subsequent quantification of heat flux. These experiments are mainly simulated in high enthalpy short-duration facilities for which test flow duration are in the order of few milliseconds and the thermal loads resemble the nature of step/impulse. This study focuses on a specially designed fast-response coaxial surface junction thermal probe (CSTP) with capability of capturing transient temperature signals. The short-duration calibration experiments are realized to mimic the simulated flow conditions of high enthalpy test facilities. The classical one-dimensional heat conduction modelling has been used to deduce surface heat flux from the acquired temperature responses. It demonstrates a commendable accuracy of 2.5% when compared with known heat loads of calibration experiment. An advanced soft computing technique, the Adaptive Neuro-Fuzzy Inference System (ANFIS), is introduced for short-duration heat flux predictions. This methodology successfully recovers known (step or ramp) heat loads within a specific experimental time frame (0.2s). The results exhibit excellent agreement in prediction of trend and magnitude, carrying uncertainties of 3% for radiative and 5% for convective experiments. Consequently, the CSTP appears as a rapidly responsive transient heat flux sensor; for real-time short-duration experiments. The soft computing approach (ANFIS) offers an alternative means of heat flux estimation from temperature history irrespective of mode of heat transfer and nature of heat load, marked by its prediction accuracy, diminished mathematical intricacies, and reduced numerical requisites.

Rayleigh wave through half space semiconductor solid with temperature dependent properties

The article focuses on Rayleigh wave propagation in a homogeneous isotropic semi-conductor thermoelastic medium rotating with fixed angular frequency with temperature-dependent properties. The elastic constants depend upon the temperature function. The effects of temperature dependency parameter, time derivative, and fractional order are illustrated. By the theory of thermo-elasticity, waves result in the generation of thermal signals that propagate through the medium. A heat conduction model of three-phase lag (3PL) along with fractional order time derivative is used to analyze the thermal signals. The secular equations of Rayleigh waves are derived mathematically at the stress-free, carrier density and thermally insulated boundaries. Some specific properties like velocity, attenuation coefficient, specific heat loss and penetration depth for Rayleigh waves have been evaluated and presented graphically. The secular equations are computed numerically and depicted graphically using Matlab.

One-dimensional thermo-elastic wave analysis for dynamic thermoelasticity coupled with dual-phase-lag heat conduction model

One-dimensional thermo-elastic wave analysis for dynamic thermoelasticity coupled with dual-phase-lag heat conduction model

Sterilization Effect of Cooking Process for Guilin Rice Noodles Based on Heat Conduction Model

Sterilization Effect of Cooking Process for Guilin Rice Noodles Based on Heat Conduction Model

Amorphous-like thermal conductivity and high mechanical stability of cyclopentane clathrate hydrate.

The thermal conductivity κ of cyclopentane clathrate hydrate (CP CH) of type II was measured at temperatures down to 100 K and at pressures up to 1.3 GPa. The results show that CP CH displays amorphous-like κ characteristic of many crystalline clathrate hydrates, e.g., tetrahydrofuran (THF) CH. The magnitude of κ is 0.47 W m-1 K-1 near the melting point of 280 K at atmospheric pressure, and it is almost independent of pressure and temperature T: ln κ = -0.621-40.1/T at atmospheric pressure (in SI-units). This is slightly less than κ of type II CHs of water-miscible solvents such as THF. Intriguingly, unlike other water-rich type II clathrate hydrates of water-miscible molecules M (M·17 H2O), CP CH does not amorphize at pressures up to 1.3 GPa at 130 K and also remains stable up to 0.5 GPa at 240 K. This shows that CP CH is mechanically more stable than the previously studied water-rich type II CHs, and suggests that repulsive forces between CP and the H2O cages increase the mechanical stability of crystalline CP CH. Moreover, we show that κ of an ice-CH mixture, which often arises for CHs that form naturally, is described by the average of the parallel and series heat conduction models to within 5% for ice contents up to 22 wt%. The findings provide a better understanding of the thermal and stability properties of clathrate hydrates for their applications such as gas storage compounds.

Dynamic Thermal Response of Multiple Parallel Cracks in a Half Plane under General Transient Thermal Loading

Understanding the dynamic thermal response of materials is crucial for designing effective thermal protection systems, particularly in extreme thermal environments such as transient thermal loading, extremely low/high temperature, etc. This study investigates the dynamic thermal response of a half plane containing multiple parallel cracks under transient thermal loading using a non‐Fourier, hyperbolic heat conduction model. Our findings highlight significant deviations from traditional Fourier models, enhancing the predictive capabilities for designing thermal protection systems in extreme thermal environments. The cracks are modeled as distributions of thermal dislocations, with densities determined through Fourier and Laplace transforms. By solving the resulting singular integral equations, we calculate the temperature gradient intensity factors across multiple scenarios. Additionally, we examine the effects of thermal relaxation time, loading parameters, and crack spacing on the thermal intensity factors, both in transient and steady‐state conditions. This research confirms the robustness of the hyperbolic model and its practical implications for thermal analysis in engineering applications.

Variational Approach to Heat Conduction Modeling

Variational Approach to Heat Conduction Modeling

Calibrating a Heat Transfer Model for Baled Switchgrass Using Heat Generation

HighlightsHeat and mass transfer in baled switchgrass was modeled based on thermal conductivity and internal heat generation.Model calibration was performed through a 60-day storage evaluation of baled switchgrass in an environmental chamber.Empirical models of heat generation and DML were developed based on thermal conductivity and aerobic respiration.Model validation was performed based on an energy balance and the aerobic respiration rate of switchgrass.Abstract. This study characterizes heat transfer within baled switchgrass through the development of a two-dimensional heat conduction model and an exponential drying approach to predict moisture content. The model was simulated using the finite difference method while accounting for the effect of internal heat generation to improve prediction accuracy. Model calibration was performed using rectangular bales of switchgrass (102 x 46 x 36 cm) stored in a controlled environmental chamber for 60 days at a fixed temperature and relative humidity. The heat and mass transfer model was implemented as an inverse model to empirically estimate heat generation and dry matter loss (DML). Internal heat generation and dry matter losses were also assessed using previously published models describing the aerobic respiration rate of switchgrass. Both heat generation models were in close agreement at a nominal moisture content of 10% w.b. (R2 = 0.9542) but deviated at nominal moisture contents of 20% to 40% w.b. (R2 < 0.7543). DML simulated using the numerical model closely agreed with the DML measured in the storage evaluation (R2 > 0.9060), indicating sufficient DML estimates through the conduction model and exponential drying approach. DML simulated through the published aerobic respiration model deviated to a greater extent, particularly at the highest moisture treatment (R2 = 0.4340), indicating an insufficient consideration of the various biochemical processes occurring at elevated levels of moisture and density. The results of this study provide a framework for the development of post-harvest quality models to optimize the storage, drying, and bioconversion of baled biomass feedstocks. Keywords: Bales, Heat and mass transfer, Heat transfer model, Storage losses, Switchgrass.

Variational Approach to 2D and 3D Heat Conduction Modeling

Variational Approach to 2D and 3D Heat Conduction Modeling

Heat transport evaluation of amorphous Si, SiGe, and Ge thin films using 3ω method and minimum heat conduction model

Heat transport evaluation of amorphous Si, SiGe, and Ge thin films using 3ω method and minimum heat conduction model

HYPER-DIFFERENTIAL SENSITIVITY ANALYSIS FOR NONLINEAR BAYESIAN INVERSE PROBLEMS

We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameters. In previous works, HDSA has been used to assess the sensitivity of the solution of deterministic inverse problems to additional model uncertainties and also different types of measurement data. In the present work, we extend HDSA to the class of Bayesian inverse problems governed by PDEs. The focus is on assessing the sensitivity of certain key quantities derived from the posterior distribution. Specifically, we focus on analyzing the sensitivity of the MAP point and the Bayes risk and make full use of the information embedded in the Bayesian inverse problem. After establishing our mathematical framework for HDSA of Bayesian inverse problems, we present a detailed computational approach for computing the proposed HDSA indices. We examine the effectiveness of the proposed approach on an inverse problem governed by a PDE modeling heat conduction.

Nonlocal dual-phase-lag thermoelastic damping analysis in functionally graded sandwich microbeam resonators utilizing the modified coupled stress theory

Functionally graded (FG) sandwich structures stand as one of the most representative composite structures owing to the thermal resistance and the energy absorption property in non-unfiorm thermal environment. Additionally, accurately estimating thermoelastic damping (TED) is of great importance for the design of high-performance micro/nano-resonators. Nevertheless, the classical TED models fail on the micro/nano-scale structures due to without considering the influences of the spatial size-dependent effects related to heat transfer and elastic deformation. The nonlocal heat conduction model and modified coupled stress theory are responsible for the size-dependent effects. To address this issue, present study aims to conduct the size-dependent TED model of FG sandwich microbeam resonators for TED analysis by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are formulated, and then, the analytical solution is solved by complex frequency method. Exact and closed-form expressions for TED can be obtained through the complex frequency method. The results are validated, and the parameter effects of the nonlocal thermal parameter, the material length-scale parameter, the power-law index and the vibration modes on the TED are analyzed. The results show that the energy dissipation can be reduced by the size-dependent effects resulting in improving the quality factor of microstructures. It is expected that these results may provide a theoretical basis for predicating TED in the design of FG sandwich micro/nano-resonators with high quality factor in extreme heat transfer environment.

An implicit thermo-mechanical coupling model for heat conduction and thermal cracking in brittle materials

In this paper, an implicit thermo-mechanical coupling model is developed to simulate heat conduction and thermal cracking in brittle materials. In the thermal analysis, an implicit particle heat conduction model (PHCM) is proposed. A linear algebraic system of heat conduction equations is derived based on the temperatures of the particle system and the heat flux among adjacent particles. An analytical expression is introduced for the involved correction coefficient, with which the macroscopic thermal conductivity coefficient can be directly adopted without calibration. Furthermore, a thermal conductivity reduction coefficient is introduced to account for the thermal resistance of the cracks. In the mechanical analysis, particle discontinuous deformation analysis (PDDA), which is an implicit variant of the discrete element method, is employed. The PHCM is first verified against analytical and finite element solutions for transient heat conduction problems. The results show that the PHCM is an effective and accurate heat conduction model that readily reflects the thermal resistance of cracks. Then, the thermo-mechanical coupling model is verified by the expansion of heated specimens under different conditions. Finally, the successful application of the coupling model in the simulation of thermal shock tests demonstrates its effectiveness for thermal cracking problems.

Scale-Dependent Generalized Thermoelastic Damping in Vibrations of Small-Sized Rectangular Plate Resonators by Considering Three-Dimensional Heat Conduction

Given that thermoelastic damping (TED) is one of the main causes of energy dissipation in miniaturized structures, calculation of its exact amount is of particular importance in the design of such elements. Considering three-dimensional (3D) heat transfer along with the scale effect on both mechanical and thermal areas is one of the decisive factors in the more rigorous modeling of TED in small-sized resonators. This paper exploits the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model to establish an analytical TED relation for rectangular micro/nanoplate resonators with 3D heat conduction. At the start, the non-Fourier heat equation corresponding to 3D DPL model is derived. Then, the solution of temperature distribution is determined by employing infinite trigonometric series. Moreover, the scale-dependent frequency of the system is presented in the context of MCST. Eventually, with the help of entropy generation (EG) method, an analytical TED expression considering 3D heat conduction is established. The precision of the presented solution is examined by comparing it with a simpler model available in the literature. By choosing two common types of boundary conditions, i.e. fully-clamped (CCCC) and fully-simply (SSSS) supported plates, the influence of various factors on TED changes is comprehensively investigated in simulation section. According to the outcomes, in plates with a lower ratio of length and width to thickness, the dimension considered for heat conduction model has a noticeable impact on the variations of TED.

Establishment and analysis of a piezoelectric actuator dynamic model with temperature-dependent damping, stiffness, and piezoelectric constant

The characteristics of the piezo-stack and the flexible mechanism are both influenced by temperature, which induces the performance change of piezoelectric actuators in low-temperature. This study investigates how temperature affects the dynamics model's stiffness, damping, driving force, and friction. An axial heat conduction model based on Fourier's heat conduction law was established, and finite element analysis was carried out to study the temperature distribution of the piezo-stack. Moreover, finite element analysis was carried out at various temperatures to investigate the impact of temperature on the flexible mechanism's deformation. Based on the aforementioned study, a dynamics model with variable stiffness and damping is proposed in this paper, and the simulation results are verified. In the experiment, the effects of temperature, voltage, and frequency on the output performance of the piezoelectric actuator were investigated separately using impedance and amplitude-frequency characteristic curves to determine the resonant frequency and damping ratio of the flexible mechanism at low temperatures. Theory and experiment show that high stiffness and low piezoelectric constants at low temperatures reduce the piezoelectric actuator's output displacement, friction reduction will enhance the driving displacement of the piezoelectric actuator, and the effect of damping on output displacement is insignificant. This study offers significant theoretical value and guidance for the use of piezoelectric actuators in low-temperature situations.

Mathematical models for determining and analyzing thermal regimes in mining industry mechanism structures

Purpose. To develop linear and nonlinear mathematical models of heat conduction for isotropic heterogeneous media with internal heating. This will allow for an increased accuracy in determining temperature fields, which will subsequently impact the effectiveness of designing mechanisms, devices, and individual components of structures that have a layered structure and are subjected to heat stress. Methodology. For the development of linear and nonlinear mathematical models of the temperature field and the analysis of temperature regimes in layered media with internal thermal heating, the coefficient of thermal conductivity is described as a whole using asymmetric unit functions. This makes it possible to solve a differential equation with singular coefficients in both linear and nonlinear boundary value problems of heat conduction with appropriate boundary conditions. Findings. Quadratic equations are obtained to determine the analytical solutions of linear and nonlinear boundary problems of heat conduction for a layered plate with internal heat load. Originality. The scientific novelty lies in the given method of linearization of the nonlinear mathematical model of heat conduction and obtaining analytical solutions, in a closed form, of the corresponding linear and nonlinear boundary value problems for isotropic layered media subjected to internal heating. Practical value. The developed linear and nonlinear mathematical models for determining the temperature distribution in layered structures with internal heating make it possible to analyze heat exchange processes and ensure the thermal stability of such structures. This also makes it possible to increase the heat resistance of structures and protect them from overheating, which can lead to damage to individual components and elements of mechanisms, as well as to the entire structure as a whole. The resulting analytical solutions can be used to predict temperature fields in mine shafts, underground environments and mechanisms of mining equipment, in particular, in drilling and underground compressor stations, ventilation systems and other equipment, which improves work efficiency and reduces useful energy consumption.

Analytical solutions for thermo-elastic damping of rotational ring resonators incorporating thermal relaxations and elastic small scales

At the micro and nanoscales, thermo-elastic damping is regarded as one of the most crucial factors for promoting energy dissipation in vibrating structures. The thermo-elastic damping of a thin rotational ring resonator is explored in this paper based on three phase lag heat conduction model for thermal relaxations and nonclassical elasticity for small scale effects. Solving the heat conduction equation for radial direction heat flow and zero heat flux boundary conditions yields the temperature spread across ring cross-section. The equation takes into account only the rotating narrow ring’s in-plane vibrations. For the frequency dependent thermo-elastic damping, the combined nonlocal thermo-elasto-dynamic equations are solved. The present model is validated with the experimental and finite element data. The thermo-elastic damping of rotating rings has been found to be over predicted by classical elasticity. For a particular small scale factor, as rotational speed rises by 80%, the equivalent thermo-elastic damping of the ring resonator reduces by 43%. In addition, the effects of cross-sectional shape, nonlocal scale factor, rotating speed, modenumber, ambient temperature, and substance on thermo-elastic damping are thoroughly explored in this work. The results presented here are useful to build and construct future nanoscale resonant sensors and radio-frequency devices.

Optimization of segmented thermoelectric power generators from waste heat while considering the influence of temperature on materials

Thermoelectric technology is commonly used in waste heat utilization of automotive internal combustion engines and widely combined with solar energy units to form solar thermoelectric generator systems. The structure of the Thermoelectric Generator (TEG) needs to be optimized in order to obtain better performance for wider applications. In this paper, the influence of temperature on the height of PN-type thermoelectric arms was analyzed using an improved one-dimensional heat conduction model with the calculus method. At the same time, both the calculation formula of the maximum output power and the calculation formula of various size parameters of the TEG was derived when the influence of temperature on the performance of thermoelectric materials has been considered. In addition, the relationships among different size parameters were derived to obtain the maximum efficiency. The relationships include the most commonly used classical optimization relationship, that is, when the Seebeck coefficient, thermal conductivity and resistivity are averaged, the relationship is consistent with the classical optimization relationship. By considering the impact of temperature on the performance of thermoelectric materials, an improved calculation formula of the figure of merit (Z) was also given. The new optimization formula was compared with the classical optimization method by taking the maximum output power as the optimization index. In the case study, the temperatures of the cold end and the hot end were set at 330 K and 700 K, respectively. PbTe and PbSe were used as the materials with intermediate temperature, and Bi2Te3 was used as the material with low temperature. Through theoretical analysis, it is found that the maximum output power of the new optimization formula can be higher than that of the classical optimization formula.

Regulating thermal rectification on random networks by depositing nanoparticles

Developing an efficient strategy for regulating thermal rectification is a challenging problem. In this study, we present a heat conduction model to investigate the regulation of thermal rectification on random networks by depositing nanoparticles. We find that increasing the amount of deposited nanoparticles D or decreasing the deposition region ratio S amplifies the thermal rectification effect. Furthermore, we confirm that the thermal rectification effect of the network is more significant than that of a regular lattice with equal D. Finally, we provide a comprehensive explanation of the simulation results by analyzing the interface thermal resistance and calculating the phonon spectrum. These interesting findings have potential implications for thermal management and energy storage.