Guyer Krumhansl Research Articles

Signature of electrothermal transport in 18 nm vertical junctionless gate-all-around nanowire field effect transistors

Abstract Addressing temperature hot-spots resulting from self-heating effects (SHE) poses a significant challenge in the design of emerging nanoscale transistors, such as vertical junctionless nanowire field-effect transistors (VNWFETs), due to reduced thermal conductivity. Consequently, electrothermal modeling becomes crucial for a comprehensive understanding of the underlying physical mechanisms governing carrier degradation and thermal conduction in these nanoscale devices. In this study, we present an enhanced drift-diffusion model coupled with nonlocal Guyer-Krumhansl (GK) equations to accurately capture carrier-phonon interactions and explore the electrothermal characteristics of gate-all-around (GAA) VNWFETs. Pulsed current-voltage (I–V) measurements are employed to investigate the performance of a state-of-the-art 18nm VNWFET technology. Furthermore, we report on the influences of both trapping and SHE under high-bias conditions for varying pulse widths. Our findings reveal that optimization of mobility degradation mechanisms allows for improved control over the physical behavior of carrier transport in these emerging technologies. Through careful consideration of these factors, it becomes possible to enhance the overall performance of GAA VNWFETs, particularly in mitigating temperature hot-spots and addressing challenges associated with self-heating effects.

Transient thermal fracture investigation of a cracked functionally graded layer via Guyer-Krumhansl model

Recent experimental evidence proves the Guyer-Krumhansl (G-K) model’s capability of predicting the nonclassical transient heat transfer process in heterogeneous composites. The objective of this article is to explore the dynamic thermal and fracture behaviors of a cracked orthotropic functionally graded material (FGM) layer subject to abrupt thermal shocks via the G-K equation. The thermal and elastic governing equations determined by the G-K model are transformed into the singular integral equations, which are calculated numerically to assess the non-Fourier transient temperatures and the resultant dynamic thermal stress intensity factors. Parametric comparisons are carried out for the effects of the non-Fourier thermal lagging time and thermal nonlocal length on the transient thermoelastic responses. The findings would benefit the applications of unconventional heat conduction theories and shed light on the scientific understanding of FGM’s fracture behaviors.

Thermal diffusity in copper benzene-1,3,5-tricarboxylate–reduced graphite oxide mechanical composites

Metal organic frameworks (MOFs) and particularly copper benzene-1,3,5-tricarboxylate (HKUST-1) are excellent materials for gas storage (e.g., CH4, N2, H2 adsorption) and gas separation. In this work, reduced graphene oxide (RGO)–HKUST-1 mechanical mixtures were studied in order to reveal the effect of RGO content on the pressure tolerance of the texture and heat conductivity. HKUST-1 was obtained by two different synthesis routes. Air-dried MOF and RGO were thoroughly mixed prior to the compression. Powder XRD and Raman spectroscopy were used to characterize the response of the crystal structure, while low-temperature nitrogen adsorption was used the follow the adsorption properties of the pellets. Finally, the "flash" heat pulse method was used to assess the thermal properties. The gas adsorption isotherms revealed that the adsorption capacity decreases when RGO is added. Based on Raman and XRD results, we found that the synthesis route has an effect on multiple scales. We experimentally confirmed that evaluation of the thermal diffusivity requires a model more complex than the simple Fourier equation, due to the inherent heterogeneous structure of the material. A good approximation of the Fourier coefficient of thermal diffusivity was obtained using the parameters of the Guyer–Krumhansl equation. The heat pulse experiments also revealed possible size-dependent behavior.

Two-field mixed hp-finite elements for time-dependent problems in the refined theories of thermodynamics

Modern manufacturing technologies allow heterogeneous materials with complex inner structures (e.g., foams) to be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not necessarily valid. According to various experimental observations, the Guyer–Krumhansl equation is a promising candidate for modeling such complex structures. However, practical applications need a reliable and efficient algorithm capable of handling both complex geometries and advanced heat equations. In the present paper, we derive new two-field variational formulations which treat the temperature and the heat flux as independent field variables, and we develop new, advanced hp-type mixed finite element methods, which can be reliably applied. We investigate their convergence properties for various situations, challenging in relation to stability and the treatment of fast propagation speeds. That algorithm is also proved to be outstandingly efficient, providing solutions four magnitudes faster than commercial algorithms.

Thermal and mechanical properties of AlSi7Mg matrix syntactic foams reinforced by Al2O3 or SiC particles in matrix

Materials with complex inner structure can be challenging to characterise in an effective way. The effective material parameters significantly depend on the structure, and thus on the interface properties. In the present paper, we focus on metal matrix syntactic foams, and we attempt to determine their effective thermal parameters. We supplement the results with their mechanical properties as well. For thermal characterisation, we use the heat pulse experiment to study their transient thermal response. We observed deviation from Fourier's law in multiple situations, and thus we propose an evaluation procedure for such experimental data using the Guyer–Krumhansl heat equation. We provide an iterative procedure to efficiently find the effective thermal diffusivity values provided by the Guyer–Krumhansl and Fourier equations based on the measured transient response. Furthermore, we studied the effective parameters, the specific heat, mass density, thermal conductivity and thermal diffusivity. We found that the standard estimations significantly overestimate the thermal conductivity. Furthermore, we propose a method for deducing a more reliable thermal diffusivity and thermal conductivity based on the transient temperature history, i.e., we propose to estimate Fourier's thermal diffusivity based on averaging the parameters of the Guyer-Krumhansl equation according to the observed diffusive time scales. We also found that for such metal matrix syntactic foams, even with knowing the constituents, the contact thermal resistance makes more challenging to provide a prior estimate for the effective thermal conductivity, but this difficulty can be resolved using proper effective thermal diffusivity values.

On the dynamic thermal conductivity and diffusivity observed in heat pulse experiments

Abstract Determining the thermal properties of materials with complex structures is still a major engineering challenge today. The well-known heat pulse experiment can be used to determine the thermal diffusivity by measuring the temperature history as a thermal response for a fast excitation. However, the evaluation of the measurements can be challenging, especially when dealing with non-homogeneous samples. The thermal behavior of such heterogeneous materials may exhibit a response including two-time scales. Therefore, the Fourier equation is not necessarily applicable. The simplest possible alternatives are the 2-temperature models the Guyer–Krumhansl and Jeffreys heat equations. In the present paper, we focus on the interpretation of the Jeffreys heat equation; studying its analytical solution, we present a fitting method for determining the unknown parameters. We also discuss its relation with the other two heat equations, and we offer an interpretation of how to characterize the transient response of heterogeneous materials.

Challenges in the thermal modeling of highly porous carbon foams

The heat pulse (flash) experiment is a well-known, widely used method to determine thermal diffusivity. However, for heterogeneous, highly porous materials, neither the measurement nor the evaluation methodologies are straightforward. In the present paper, we focus on two open-cell carbon foam types, differing in their porosity but having the same sample size. Recent experiments showed that a non-Fourier behavior, called ’over-diffusive’ propagation, can be present for such a complex structure. The (continuum) Guyer–Krumhansl equation stands as a promising candidate to model such transient thermal behavior. In order to obtain a reliable evaluation and thus reliable thermal parameters, we utilize a novel, state-of-the-art evaluation procedure developed recently using an analytical solution of the Guyer–Krumhansl equation. Based on our observations, it turned out that the presence of high porosity alone is necessary but not satisfactory for non-Fourier behavior. Additionally, the mentioned non-Fourier effects are porosity-dependent; however, porous samples can also follow the Fourier law on a particular time scale. These data serve as a basis to properly identify the characteristic heat transfer mechanisms and their corresponding time scales, which altogether result in the present non-Fourier behavior. Based on these, we determined the validity region of Fourier’s law in respect of time scales.

Buoyancy driven convection with a Cattaneo flux model

Abstract We review models for convective motion which have a flux law of Cattaneo type. This includes thermal convection where the heat flux law is a Cattaneo one. We additionally analyse models where the convective motion is due to a density gradient caused by a concentration of solute. The usual Fick’s law in this case is replaced by a Cattaneo one involving the flux of solute and the concentration gradient. Other effects such as rotation, the presence of a magnetic field, Guyer–Krumhansl terms, or Kelvin–Voigt theories are briefly introduced.

Proof of Straughan’s claim on Payne–Song’s and modified Guyer–Krumhansl’s equations

We prove a claim by Brian Straughan who conjectured that Payne–Song’s and modified Guyer–Krumhansl’s equations can be justified in (and derived from) the general model-building framework for the mechanics of complex bodies, so they emerge from the modelling of microstructural effects. The proof is based on taking into account micro-to-macro spatial scaling and a decomposition of the heat flux into a standard Fourier-type component and one measuring microstructural event with associated and balanced actions.

Three-field mixed hp-finite element method for the solution of the Guyer–Krumhansl heat conduction model

On the basis of numerous experimental studies the Guyer–Krumhansl heat conductivity model can be considered as one of the most promising theoretical models to simulate the low temperature processes and the thermal behavior of such complex structures as materials with inhomogeneities and interfaces, as well as porous materials. However, the classical h-version finite element methods do not provide convergent and accurate results for the solution of the Guyer–Krumhansl heat conductivity model. In recent paper, a new three-field variational formulation is derived treating the temperature, the heat flow and its current density as independent variables. Both the temperature- and the heat flow boundary condition are weakly imposed, i.e., built in the variational form.Based on this variational background, a new, hp-version mixed finite element method is constructed. The h- and p-convergence behaviors of the temperature and the heat flow are analyzed on the transient region for two representative model problems: (i) a rapid heating process with exponentially changing rate and (ii) a ramp-type heating process. The relative and absolute errors are measured in maximum norm. From the computational experiments it follows that the mixed hp-finite element method gives reliable, robust (uniformly stable) results not only for the h- but also for the p-approximation in the case of both the temperature and the heat flow.

Transient heat conduction in the cracked medium by Guyer–Krumhansl model

Transient heat conduction in the cracked medium by Guyer–Krumhansl model

Analytical Model for Thermoelastic Dissipation in Oscillations of Toroidal Micro/Nanorings in the Context of Guyer–Krumhansl Heat Equation

Thermoelastic dissipation or thermoelastic damping (TED) can restrict the quality factor of micro/nanoring resonators seriously. This paper employs the non-Fourier model of Guyer–Krumhansl (GK model) to render a size-dependent formulation and analytical solution for approximating the amount of TED in micro/nanorings with circular cross-section by inclusion of nonlocal and single-phase-lagging effects. To fulfill this objective, the equation of heat conduction in the ring is first established according to GK model. Then, by placing the temperature distribution obtained from the heat conduction equation in the TED relation defined on the basis of thermal energy approach, an expression in the form of infinite series is given for TED, which includes non-classical parameters of GK model. Finally, after checking the validity of the model through a comparative study, several simulation results are prepared to emphasize on the influence of different factors such as non-classical parameters of GK model, geometry of ring, vibrational mode and ambient temperature on TED value. Numerical examples reveal that the mentioned factors along with the two- or three-dimensional heat transfer (2D or 3D) model have major influences on TED variations.

Robust Output Regulation of a Guyer-Krumhansl Heat Equation Under Modeling Mismatches

The paper considers robust output regulation of a Guyer-Krumhansl (GK) heat conduction law under modeling mismatches. More specifically, we consider the differences of the GK model compared with a simple diffusion equation (also known as the Fourier heat conduction law) and treat them as modeling mismatches in view of robust output regulation. We will consider a simple internal model based controller to solve the output regulation problem and analyze its robustness with respect to the differences between the two heat conduction laws. Moreover, we will test the robustness of the considered controller in numerical simulations.

Mathematical analysis and numerical simulation of the Guyer–Krumhansl heat equation

The Guyer–Krumhansl heat equation has numerous important practical applications in heat conduction problems. In recent years, it turned out that the Guyer–Krumhansl model can effectively describe the thermal behavior of macroscale heterogeneous materials. Thus, the Guyer–Krumhansl equation is a promising candidate to be the next standard model in engineering. However, to support the Guyer–Krumhansl equation’s introduction into the engineering practice, its mathematical properties must be thoroughly investigated and understood. In the present paper, we show the basic structure of this particular heat equation, focusing on the differences in comparison to the Fourier heat equation obtained when (τq,μ2)→(0,0). Additionally, we prove the well-posedness of a particular, practically significant initial and boundary value problem. The stability of the solution is also investigated in the discrete space using a finite difference approach.

Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law

We investigate thoroughly a model for thermal convection of a class of viscoelastic fluids in a porous medium of Brinkman–Darcy type. The saturating fluids are of Kelvin–Voigt nature. The equations governing the temperature field arise from Maxwell–Cattaneo theory, although we include Guyer–Krumhansl terms, and we investigate the possibility of employing an objective derivative for the heat flux. The critical Rayleigh number for linear instability is calculated for both stationary and oscillatory convection. In addition a nonlinear stability analysis is carried out exactly.

Heat flow wave in suspended graphene

Based on the Guyer–Krumhansl equation, a new form of governing equation for phonon hydrodynamic transport in two-dimensional non-metallic materials is derived, which is only related to heat flux. The solution of this governing equation shows that there is a new wave phenomenon in the phonon hydrodynamic transport, which is called heat flow wave, that is, the damped oscillation of heat flux. The occurrence conditions of the heat flow wave and resonance are analytically deduced. These conditions are different from that of second sound in phonon hydrodynamic transports. The occurrence conditions of the heat flow wave indicate that a small normal scattering time is a necessary condition for the occurrence of the heat flow wave, and the shape and size of suspended graphene have a significant influence on the occurrence of the heat flow wave. It is found that the frequency of the heat flux wave is lower than that of the second sound.

Gradient models of moving heat sources for powder bed fusion applications

In this paper, we derive closed form solutions for the quasi-stationary problems of moving heat sources within the gradient theory of heat transfer. This theory can be formally deduced from the two-temperature model and it can be treated as a generalized variant of the Guyer–Krumhansl model with the fourth order governing equation. We show that considered variant of the gradient theory allows to obtain useful singularity-free solutions for the moving point and line heat sources that can be used for the refined analysis of the melt pool shape in the laser powder bed fusion processes. Derived solutions contain single additional length scale parameter that can be related to the mean size of the powder particles . Namely, we show that developed gradient models allow to describe the decrease of the melt pool depth with the increase of the powder’s particles size that was observed previously in the experiments. We also derived the dimensionless relations that can be used for the experimental identification of the model’s length scale parameter for different materials. Semi-analytical solution for the Gaussian laser beam is also derived and studied based on the Green function method within the considered theory.

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

The non-Fourier effects, such as wave-like temperature propagation and boundary temperature jumps, arise in nanosized systems due to the multiple time and space scales nature of out-of-equilibrium heat transport. The relaxation to equilibrium occurs in successive time and space scales due to couplings between different excitations, whose relaxation times have different physical meanings and may differ significantly in magnitude. The out-of-equilibrium temperature evolution is described by a hierarchy of partial differential equations of a higher order, which includes both the diffusive and wave modes of heat transport. The critical conditions of transition from wave to diffusive modes are identified. We demonstrate that the answer to the question concerning which of these modes would be detected by experimental measurements may also depend on the accuracy of the experimental setup. Comparisons between the proposed approach and other non-Fourier models, such as the Guyer–Krumhansl and Jeffreys type, are carried out. The results presented here are expected to be useful for the theoretical and experimental treatment of non-Fourier effects and particularly heat wave phenomena in complex nanosized systems and metamaterials.

Generalized thermoelasticity model for thermoelastic damping in asymmetric vibrations of nonlocal tubular shells

The present article intends to provide a size-dependent generalized thermoelasticity model and closed-form solution for thermoelastic damping (TED) in cylindrical nanoshells. With the aim of incorporating size effect within constitutive relations and heat conduction equation, nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model are exploited. Donnell–Mushtari–Vlasov (DMV) equations are also employed to model the cylindrical nanoshell. By adopting asymmetric simple harmonic form for oscillations of nanoshell and merging the motion, compatibility and heat conduction equations, the nonclassical frequency equation is extracted. By solving this eigenvalue problem and separating the real and imaginary parts of complex frequency analytically, an explicit expression is given to estimate the magnitude of TED in cylindrical nanoshells with arbitrary boundary conditions. Good agreement between the results of this study in special cases and those available in the literature affirms the validity of present formulation. In the following, for some vibration modes, a detailed parametric study is conducted to illuminate the determining role of structural and thermal nonlocal parameters in the amount of TED in simply-supported cylindrical nanoshells. The augmentation of difference between classical and nonclassical results by reduction in dimensions of nanoshell confirms the small-scale effect on TED value at nanoscales.

Local versus nonlocal constitutive theories of nonequilibrium thermodynamics: the Guyer\u2013Krumhansl equation as an example

On the example of the celebrated Grad’s 13-moment system of kinetic theory of rarefied gases and phonon hydrodynamics, it is proved that the constitutive equations of nonequilibrium thermodynamics must be nonlocal. A thermodynamic model of Guyer–Krumhansl heat-transport equation is derived within the frame of weakly nonlocal Rational Thermodynamics. The constitutive equation for the entropy flux is analyzed as well. Some nonlinear generalizations of Maxwell–Cattaneo equation are studied in view of the experiments on thermal wave propagation.