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Phonon hydrodynamics originated from the macroscopic energy and momentum balance equations (called Guyer-Krumhansl equations) proposed by Guyer and Krumhansl by solving the linearized Boltzmann transport equation for studying second sound in the normal-process collision dominated phonon transports in an isotropic nonmetallic crystal with a dispersionless frequency spectrum. However, the low-dimensional dielectric materials and semiconductors are anisotropic, and the different branches in their phonon frequency spectrum usually have different group velocities. For such materials, we derive the macroscopic energy and momentum balance equations from the linear Boltzmann transport equation to describe the phonon hydrodynamic transport, and solve the longstanding debate about whether the energy balance equation contains the second-order spatial derivatives of temperature. Finally, by solving the modified Guyer-Krumhansl equations, we find the minimum and maximum values of the length required by the occurrence of second sound in suspended single-layer graphene with the rectangular shape. [ABSTRACT FROM AUTHOR]

Over the last twenty-five years, the search for generalized equations that allow us to better understand the phenomenon of heat conduction has become an active frontier both in transport theory, and in non-equilibrium thermodynamics, due to the growing interest in nanotechnologies, thermal metamaterials and fast devices. Here we review how some mathematical analogies between generalized heat-transport equations and well-known equations in hydrodynamics, electronics and optics have been helpful to infer new forms of heat transfer arising in extended thermodynamics and to inspire the consideration of new phenomena. We also examine in each case the thermodynamic basis of the respective formulation. [ABSTRACT FROM AUTHOR]

The Guyer–Krumhansl equation for the heat flux is a phenomenological bridge between Fourier heat transport (for size of the system much bigger than the mean free path of heat carriers) and hydrodynamic heat transport (for size of the system comparable to the mean free path of heat carriers). The corresponding phonon hydrodynamics is analogous to Newtonian hydrodynamics, but with the velocity replaced by the heat flux, the pressure gradient replaced by the temperature gradient and the shear viscosity replaced by the square of the mean-free path divided by the thermal conductivity. In this paper, we propose a nonlinear generalization of the Guyer–Krumhansl equation and phonon hydrodynamics based on an analogy with the power-law model of non-Newtonian fluids leading to a non-diffusive behaviour of heat transport. On the basis of this model, we obtain the corresponding nonlinear effective thermal conductivity of the model, depending on the radius of the channel and on the temperature gradient. The present proposal could be useful in the light of recent analyses of Poiseuille phonon hydrodynamics which suggest a non-Newtonian behaviour. [ABSTRACT FROM AUTHOR]

In the past few decades, numerous heat conduction models extending beyond Fourier's have been developed to account for large gradients, fast phenomena, wave propagation, and heterogeneous material structures typical of biological systems, superlattices, and thermal metamaterials. Navigating through these models has become challenging due to their varying thermodynamic backgrounds and potential compatibility issues. Furthermore, recent discoveries in the field of non-Fourier heat conduction have complicated the interpretation and utilization of specific non-Fourier heat equations, especially when designing materials for the new generation of thermal metamaterials. The situation is further compounded by the existence of numerous modeling strategies in the literature, each offering different interpretations of even the same heat equation. This complexity makes it increasingly difficult to gain a comprehensive understanding of this research field. Therefore, this review aims to facilitate the navigation of advanced heat equations beyond Fourier by discussing their properties and potential practical applications in the context of experiments. We begin with the simplest models and their fundamental principles, progressing toward more complex, coupled phenomena, such as ballistic heat conduction. We do not delve into the often intricate technical details of each thermodynamic framework or aim to compare each approach from a methodological perspective. Instead, we focus on reviewing models primarily from the Rational Extended Thermodynamics, Extended Irreversible Thermodynamics, and Non-Equilibrium Thermodynamics with Internal Variables frameworks. Additionally, we discuss relevant models from kinetic theory, fractional derivatives, thermomass, and phase lag approaches. We provide background information on these models to highlight their origins, any limitations they may have, and the corresponding stability conditions, if applicable. Furthermore, as the field of non-Fourier heat conduction has become quite segmented, this paper also seeks to establish a common foundation, promoting a comprehensive mutual understanding of the fundamentals of each model and the phenomena to which they can be applied. [ABSTRACT FROM AUTHOR]

Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Past experimental and theoretical works exploring nanoscale heat transport in semiconductors addressed known deviations from Fourier's law modeling by including effective parameters, such as a size-dependent thermal conductivity. However, recent experiments have qualitatively shown behavior that cannot be modeled in this way. Here, we combine advanced experiment and theory to show that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be described using a general hydrodynamic heat transport model, contrary to previous understanding of heat flow in bulk silicon. We use a comprehensive set of extreme ultraviolet scatterometry measurements of nondiffusive transport from transiently heated nanolines and nanodots to validate and generalize our ab initio model, that does not need any geometry-dependent fitting parameters. This allows us to uncover the existence of two distinct time scales and heat transport mechanisms: an interface resistance regime that dominates on short time scales and a hydrodynamic-like phonon transport regime that dominates on longer time scales. Moreover, our model can predict the full thermomechanical response on nanometer length scales and picosecond time scales for arbitrary geometries, providing an advanced practical tool for thermal management of nanoscale technologies. Furthermore, we derive analytical expressions for the transport time scales, valid for a subset of geometries, supplying a route for optimizing heat dissipation.

In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local differential terms (gradients, Laplacians) or integral terms with memory kernels. In contrast to this typical situation, which has led to substantial progress in several fields, we ask ourselves whether in some cases it would be convenient to start from non-local internal variables with non-local evolution equations. We examine this point by considering three main lengths: the observation scale R defining the elementary volumes used in the description of the system, the mean free path l of the microscopic elements of the fluid (particles, phonons, photons, and molecules), and the overall characteristic size L of the global system. We illustrate these ideas by considering three-dimensional rigid heat conductors within the regime of phonon hydrodynamics in the presence of thermal vortices. In particular, we obtain a generalization of the Guyer–Krumhansl equation, which may be of interest for heat transport in nanosystems or in systems with small-scale inhomogeneities. [ABSTRACT FROM AUTHOR]

The super-ballistic temperature dependence of thermal conductivity, facilitated by collective phonons, has been widely studied. It has been claimed to be unambiguous evidence for hydrodynamic phonon transport in solids. Alternatively, hydrodynamic thermal conduction is predicted to be as strongly dependent on the width of the structure as is fluid flow, while its direct demonstration remains an unexplored challenge. In this work, we experimentally measured thermal conductivity in several graphite ribbon structures with different widths, from 300 nm to 1.2 µm, and studied its width dependence in a wide temperature range of 10–300 K. We observed enhanced width dependence of the thermal conductivity in the hydrodynamic window of 75 K compared to that in the ballistic limit, which provides indispensable evidence for phonon hydrodynamic transport from the perspective of peculiar width dependence. This will help to find the missing piece to complete the puzzle of phonon hydrodynamics, and guide future attempts at efficient heat dissipation in advanced electronic devices. [ABSTRACT FROM AUTHOR]

Understanding the energy transport properties of hot energy carriers is of great importance for a diverse range of topics from nanoelectronics and photochemistry to the discovery of quantum materials. While much progress has been made in the study of hot carrier dynamics using ultrafast far-field time-resolved spectroscopies, it remains a great challenge to understand hot carrier transport and interaction dynamics at the nanoscale. Existing theoretical models yield only qualitative predictions that are difficult to validate against experiments. Here we present a theoretical framework that extends the study of near-field thermal radiation into the ultrafast time domain, enabling sensitive local probing and quantitative study of nanoscale hot electron and phonon transport effects that have been challenging to quantify. The proposed technique of near-field hot carrier nanoscopy directly links the features of different nonequilibrium effects to near-field thermal absorption and scattering by a scanning nanotip. Our model predicts ultrafast thermal radiation in response to photoexcitation, as well as elucidates the nanoscopic radiation properties of a number of hot carrier dissipation pathways, including nonlinear electron supercollision, second sound, and nonlocal phonon transport. This work is expected to guide experiments to identify the fundamental constraints unlocking thermal wave (second sound) propagation and address the roles of competing hydrodynamic and ballistic phonon effects at the nanoscale.

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. [ABSTRACT FROM AUTHOR]

We employ thermoreflectance thermal imaging to directly measure the steady-state two-dimensional (2D) temperature field generated by nanostructured heat sources deposited on silicon substrate with different geometrical configurations and characteristic sizes down to 400nm. The analysis of the results using Fourier's law not only breaks down as size scales down, but it also fails to capture the impact of the geometry of the heat source. The substrate effective Fourier thermal conductivities fitted to wire-shaped and circular-shaped structures with identical characteristic lengths are found to display up to 40% mismatch. Remarkably, a hydrodynamic heat transport model reproduces the observed temperature fields for all device sizes and shapes using just intrinsic Si parameters, i.e., a geometry and size-independent thermal conductivity and nonlocal length scale. The hydrodynamic model provides insight into the observed thermal response and of the contradictory Fourier predictions. We discuss the substantial Silicon hydrodynamic behavior at room temperature and contrast it to InGaAs, which shows less hydrodynamic effects due to dominant phonon-impurity scattering. [ABSTRACT FROM AUTHOR]

Recent observation of second sound in graphite at a temperature above 100 K has aroused a great interest in the study of thermal waves in non-metallic solid materials. In this article, based on the Guyer–Krumhansl model, we investigate the second sound and thermal resonance phenomena in phonon hydrodynamics. The occurrence condition for the second sound is derived. It shows that the smaller the relaxation time of N-scattering of the non-metallic solid with a large relaxation time of R-scattering, the more likely the second sound will occur. For the phonon transport in the non-metallic solid excited by an oscillatory heat source with a single frequency, the occurrence condition for thermal resonance and a formula for calculating the external heat source frequency at resonance are also derived. It is found that the low-dimensional materials with small size are prone to the occurrence of second sound and thermal resonance. These phenomena open up new avenues for thermal management and energy conversion. [ABSTRACT FROM AUTHOR]

Thermal wave, namely wavelike behavior of heat propagation in transient heat conduction, enjoys much attention due to the recent investigations into phonon hydrodynamics in low-dimensional materials. In this paper, an improved phonon Monte Carlo (MC) simulation algorithm is developed based on the Callaway's dual relaxation time approximation model, which can deal with the coupling of normal and resistance scattering processes. Via the method, more thermal wave evidences are observed from the microscopic view of phonons, including overshooting and diffraction. Furthermore, the ballistic and hydrodynamic thermal waves are deeply studied. Two kinds of dissipation are found to exist in thermal waves, namely spatial dissipation and resistance dissipation. The former keeps the conservation of phonon momentum, but it lengthens the wavelength and decreases the peak temperature. The latter destroys the phonon momentum and keeps the original profile, lowering the peak temperature. Finally, phonon transport phenomena in Ziman hydrodynamic regime and diffusive regime are investigated, by introducing the scattering probability. The propagation tendency of thermal energy is found to decrease with the increasing scattering probability. The investigations into phonon hydrodynamics help to understand the heat transport characteristics and improve thermal management in low-dimensional materials. [ABSTRACT FROM AUTHOR]

The hydrodynamic behavior of phonons is of particular interest and importance owing to the strong demand for highly thermal conductive materials. Thermal transport in hydrodynamic regime becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena. In this work, we present a direct numerical study of nonlocal phonon thermal transport in graphene ribbon with vicinity geometry based on the phonon Boltzmann transport equation with first-principles inputs. We demonstrate the viscosity-dominated hydrodynamic transport behaviors with two abnormal thermal transport phenomena: heat current whirlpools and negative nonlocal effect, which originate from phonon viscosity. Phonon viscosity produces the vorticity of shear flows, leading to the backflow of the heat current and the generation of negative nonlocal vicinity response. The system average temperature and the ribbon width as well as the relative positions of the heat sources play a pivotal role in the occurrence of heat current whirlpools and negative nonlocal temperature response. The present work provides solid evidence for phonon hydrodynamic transport in graphene and a potential avenue for experimental detection in the future., (© 2023 IOP Publishing Ltd.)

A mathematical model is presented for thermal transport in nanowires with rectangular cross sections. Expressions for the effective thermal conductivity of the nanowire across a range of temperatures and cross-sectional aspect ratios are obtained by solving the Guyer–Krumhansl hydrodynamic equation for the thermal flux with a slip boundary condition. Our results show that square nanowires transport thermal energy more efficiently than rectangular nanowires due to optimal separation between the boundaries. However, circular nanowires are found to be even more efficient than square nanowires due to the lack of corners in the cross section, which locally reduce the thermal flux and inhibit the conduction of heat. By using a temperature-dependent slip coefficient, we show that the model is able to accurately capture experimental data of the effective thermal conductivity obtained from Si nanowires, demonstrating that phonon hydrodynamics is a powerful framework that can be applied to nanosystems even at room temperature. [ABSTRACT FROM AUTHOR]

The heat flux across a nanowire is computed based on the Guyer-Krumhansl equation. Slip conditions with a slip length depending on both temperature and nanowire radius are introduced at the outer boundary. An explicit expression for the effective thermal conductivity is derived and compared to existing models across a given temperature range, providing excellent agreement with experimental data for Si nanowires. [ABSTRACT FROM AUTHOR]

A novel lattice Boltzmann scheme is proposed for phonon transport based on the phonon Boltzmann equation. Through the Chapman–Enskog expansion, the phonon lattice Boltzmann equation under the gray relaxation time approximation recovers the classical Fourier's law in the diffusive limit. The numerical parameters in the lattice Boltzmann model are therefore rigorously correlated to the bulk material properties. The new scheme does not only eliminate the fictitious phonon speed in the diagonal direction of a square lattice system in the previous lattice Boltzmann models, but also displays very robust performances in predicting both temperature and heat flux distributions consistent with analytical solutions for diverse numerical cases, including steady-state and transient, macroscale and microscale, one-dimensional and multi-dimensional phonon heat transport. This method may provide a powerful numerical tool for deep studies of nonlinear and nonlocal heat transports in nanosystems. [ABSTRACT FROM AUTHOR]

Nanostructuring on length scales corresponding to phonon mean free paths provides control over heat flow in semiconductors and makes it possible to engineer their thermal properties. However, the influence of boundaries limits the validity of bulk models, while first-principles calculations are too computationally expensive to model real devices. Here we use extreme ultraviolet beams to study phonon transport dynamics in a 3D nanostructured silicon metalattice with deep nanoscale feature size and observe dramatically reduced thermal conductivity relative to bulk. To explain this behavior, we develop a predictive theory wherein thermal conduction separates into a geometric permeability component and an intrinsic viscous contribution, arising from a new and universal effect of nanoscale confinement on phonon flow. Using experiments and atomistic simulations, we show that our theory applies to a general set of highly confined silicon nanosystems, from metalattices, nanomeshes, porous nanowires, to nanowire networks, of great interest for next-generation energy-efficient devices.

Phonon hydrodynamics is an effective macroscopic method to study heat transport in dielectric solid and semiconductor. It has a clear and intuitive physical picture, transforming the abstract and ambiguous heat transport process into a concrete and evident process of phonon gas flow. Furthermore, with the aid of the abundant models and methods developed in classical hydrodynamics, phonon hydrodynamics becomes much easier to implement in comparison to the current popular approaches based on the first-principle method and kinetic theories involving complicated computations. Therefore, it is a promising tool for studying micro- and nanoscale heat transport in rapidly developing micro and nano science and technology. However, there still lacks a comprehensive account of the theoretical foundations, development and implementation of this approach. This work represents such an attempt in providing a full landscape, from physical fundamental and kinetic theory of phonons to phonon hydrodynamics in view of descriptions of phonon systems at microscopic, mesoscopic and macroscopic levels. Thus a systematical kinetic framework, summing up so far scattered theoretical models and methods in phonon hydrodynamics as individual cases, is established through a frame of a Chapman–Enskog solution to phonon Boltzmann equation. Then the basic tenets and procedures in implementing phonon hydrodynamics in nanoscale heat transport are presented through a review of its recent wide applications in modeling thermal transport properties of nanostructures. Finally, we discuss some pending questions and perspectives highlighted by a novel concept of generalized phonon hydrodynamics and possible applications in micro/nano phononics, which will shed more light on more profound understanding and credible applications of this new approach in micro- and nanoscale heat transport science. [ABSTRACT FROM AUTHOR]

Heat flow along two-dimensional strips as a function of the Knudsen number is examined in two different versions of heat-transport equations with non-local terms, with or without heat slip flow. In both of them, a parabolic heat profile corresponding to the Poiseuille phonon flow may appear in some domains of temperature, or of the Knudsen number, in the transition from the Fourier regime to the ballistic one. The influence of the slip heat flow on such a transition is discussed. [ABSTRACT FROM AUTHOR]

Longitudinal and transverse modes of thermal disturbances in isotopically pure alkali-halide crystals are derived from phonon hydrodynamics. Guyer-Krumhansl (GK) model of phonon scattering is first recovered by relating the first and second viscosity to the relaxation times. Helmholtz potentials are then introduced to split the two modes from the heat flux vector. It has been found that the scalar potential coincides with the heat equation in the dual-phase-lag model, while the vector potential describes dispersive transverse phonons and introduces a new type of equation in microscale heat transfer. [ABSTRACT FROM AUTHOR]

Abstract: The silicon nanosystems have shown a great potential for high efficient energy conversion devices due to the strong size effect on thermal conductivity. An accurate and convenient prediction model for such size effect is highly desired. In this paper a macroscopic heat conduction model for nano-systems is presented based on the phonon gas dynamics, in which heat conduction is regarded as phonon gas flow in a porous medium. The resistant term in the momentum equation of the phonon gas flow consists of two parts. One is the Darcy's term, representing the volume resistance and another is the Brinkman term, representing the surface resistance. The latter is usually negligible compared with the former for the medium at the normal scale, while the relative importance of the Brinkman term increases and consequently, the thermal conductivity decreases with size reduction. The effective phonon gas viscosity is extracted from the experiments and found to be proportional to the system size in nanoscale based on the rarefied gas dynamics. In this way an explicit expression for the size dependent thermal conductivity of silicon nanosystems is obtained, which agrees well with the experimental results for both nano-wires and films. [Copyright &y& Elsevier]

Abstract: This paper analyzes the propagation of the waves of weak discontinuity in a phonon gas described by the four-moment maximum entropy phonon hydrodynamics involving a nonlinear isotropic phonon dispersion relation. For the considered hyperbolic equations of phonon gas hydrodynamics, the eigenvalue problem is analyzed and the condition of genuine nonlinearity is discussed. The speed of the wave front propagating into the region in thermal equilibrium is first determined in terms of the integral formula dependent on the phonon dispersion relation and subsequently explicitly calculated for the Dubey dispersion-relation model: . The specification of the parameters and for sodium fluoride (NaF) and semimetallic bismuth (Bi) then makes it possible to compare the calculated dependence of the wave-front speed on the sample’s temperature with the empirical relations of Coleman and Newman (1988) describing for NaF and Bi the variation of the second-sound speed with temperature. It is demonstrated that the calculated temperature dependence of the wave-front speed resembles the empirical relation and that the parameters and obtained from fitting respectively the empirical relation and the original material parameters of Dubey (1973) are of the same order of magnitude, the difference being in the values of the numerical factors. It is also shown that the calculated temperature dependence is in good agreement with the predictions of Hardy and Jaswal’s theory (Hardy and Jaswal, 1971) on second-sound propagation. This suggests that the nonlinearity of a phonon dispersion relation should be taken into account in the theories aiming at the description of the wave-type phonon heat transport and that the Dubey nonlinear isotropic dispersion-relation model can be very useful for this purpose. [Copyright &y& Elsevier]

Abstract: We study heat transport in bulk/nanoporous/bulk silicon devices; we show that, despite bulk/nanoporous devices may act as thermal rectifiers, the non-linear aspects of their joint thermal conductance are not strong enough to lead to a negative differential thermal resistance, necessary to allow bulk/nanoporous/bulk Si devices to act as thermal transistors. Furthermore, we explicitly study the effective thermal conductivity of the mentioned devices for several temperatures, geometries, porosities, and pore size. [Copyright &y& Elsevier]

A phonon-hydrodynamics approach is used to analyze the influence of porosity and of pore size on the reduction of the thermal conductivity in porous silicon. Different geometrical arrangements of the pores have been considered. For any given value of the porosity, the theoretical results show that for increasing Knudsen number (i.e., decreasing pore size) the effective thermal conductivity decreases whatever the geometrical arrangement of the pores is. [ABSTRACT FROM AUTHOR]

The Chapman-Enskogmethod is generalized for accounting the effect of kineticmodes on hydrodynamic evolution. Hydrodynamic states of phonon system of insulators have been studied in a small drift velocity approximation. For simplicity, the investigation was carried out for crystals of the cubic class symmetry. It has been found that in phonon hydrodynamics, local equilibrium is violated even in the approximation linear in velocity. This is due to the absence of phonon momentum conservation law that leads to a drift velocity relaxation. Phonon hydrodynamic equations which take dissipative processes into account have been obtained. The results were compared with the standard theory based on the local equilibrium validity. Integral equations have been obtained for calculating the objects of the theory (including viscosity and heat conductivity). It has been shown that in low temperature limit, these equations are solvable by iterations. Steady states of the system have been considered and an expression for steady state heat conductivity has been obtained. It coincides with the famous result by Akhiezer in the leading low temperature approximation. It has been established that temperature distribution in the steady state of insulator satisfies a condition of heat source absence. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this work is to analyze the shape dependence of the effective thermal conductivity of nanowires, based on the model of phonon hydrodynamics. In particular, we consider elliptical and rectangular nanowires, and we compare their respective thermal conductivities with those of circular nanowires and of wide thin plates. [Copyright &y& Elsevier]

Abstract: We present a theoretical analysis of thermal rectification in a porous Si/bulk Si device, taking into account ballistic effects in phonon-pore collisions when phonon mean free path is much longer than the radius of the pores. Starting from an approximate analytical expression for the effective thermal conductivity of porous Si, we obtain the thermal rectifying coefficient of the device as a function of porosity, pore size, temperature interval, and relative lengths of porous and bulk samples. [Copyright &y& Elsevier]

The lattice Boltzmann Peierls Callaway (LBPC) method is a recent development of the versatile lattice Boltzmann formalism aimed at a numerical experiment on mesoscale thermal transport in a multiphase phonon gas. Two aspects of mesoscopic thermal transport are discussed: the finite phonon mean free path and the interface thermal resistance. Based on the phonon momentum screening length measured in the LBPC computational apparatus, the validity of the Umklapp collision relaxation time in the Callaway collision operator is examined quantitatively. The discrete nature of the spatio-temporal domain in the LBPC method, along with the linear approximation of the exponential screening mechanism in the Callaway operator, reveals a large discrepancy between the effective phonon mean free path and the analytic phonon mean free path when the relaxation time is small. The link bounce back interface phonon collision rule is used to realize the interface thermal resistance between phonon gases with dissimilar dispersion relations. Consistent with the Callaway collision operator for the bulk phonon dynamics, the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution uniquely defined by the energy conservation principle. The interface thermal resistance is linearly proportional to the relaxation time of the proposed phonon interface collision rule. [ABSTRACT FROM AUTHOR]

The dispersion relation of heat waves along nanowires is obtained, displaying the influence of the roughness of the walls. This knowledge may be useful for the development of new experimental techniques based on heat waves, complementary to current steady-state measurements, for the exploration of phonon-wall collisions in smooth and rough walls. [ABSTRACT FROM AUTHOR]

• For the phonon transport in the two-dimensional nonmetallic materials the inflow boundary condition should be prescribed. • Phonon flows caused only by heat flux may occur in two-dimensional nonmetallic materials. • The inflow boundary condition plays a significant role in making the thermal conductivity of suspended graphene extremely high. Phonon hydrodynamics originated from the Guyer-Krumhansl heat conduction model. However, there is still no reasonable explanation for the high thermal conductivity of suspended graphene by using the Guyer-Krumhansl heat conduction model. In this article, based on the Guyer-Krumhansl equation we find that the inflow boundary condition specifying the non-zero heat flux at the inlet of the rectangular two-dimensional nonmetallic materials can induce phonon transport. Results show that the combined action of the phonon flow caused by the inflow boundary condition and the Poiseuille phonon flow induced by the temperature difference can make the effective thermal conductivity of two-dimensional nonmetallic materials (such as suspended graphene) much higher than the bulk thermal conductivity. [ABSTRACT FROM AUTHOR]

Novel techniques have been created for studying phonon kinetics. A supersonic conduction electron flux is used to produce a phonon flux. Transverse electron focusing (TEF) is applied for checking the electron gas affected by phonons. A turbulent regime of phonon flow-phonon flux step broadening-reveals itself as step broadening of non-equilibrium electron flux. [ABSTRACT FROM AUTHOR]

Phonon hydrodynamics is an exotic phonon transport phenomenon that challenges the conventional understanding of diffusive phonon scattering in crystalline solids. It features a peculiar collective motion of phonons with various unconventional properties resembling fluid hydrodynamics, facilitating non Fourier heat transport. Hence, it opens up several new avenues to enrich the knowledge and implementations on phonon physics, phonon engineering, and micro and nanoelectronic device technologies. This review aims at covering a comprehensive development as well as the recent advancements in this field via experiments, analytical methods, and state-of-the-art numerical techniques. The evolution of the topic has been realized using both phenomenological and material science perspectives. Further, the discussions related to the factors that influence such peculiar motion, illustrate the capability of phonon hydrodynamics to be implemented in various applications. A plethora of new ideas can emerge from the topic considering both the physics and the material science axes, navigating toward a promising outlook in the research areas around phonon transport in non-metallic solids., (© 2022 IOP Publishing Ltd.)

In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann equation with the resistive scattering term as an equivalent source term, we recover a phonon hydrodynamic equation which is reduced to the Guyer-Krumhansl heat transport equation and the Fourier's law in the limit of dominant normal scattering and dominant resistive scattering respectively. The transition of heat transport from diffusive regime to hydrodynamic regime is modeled extensively by the present numerical scheme, which produces results in good agreement with the benchmark solutions and experimental measurement. Two well-known phonon hydrodynamic phenomena including the phonon Poiseuille flow and second sound propagation are well captured by the lattice Boltzmann scheme. This work will promote the numerical modeling and deeper understanding of the non-Fourier heat transport induced by phonon normal scattering. [ABSTRACT FROM AUTHOR]

Machine learning techniques are used to explore the intrinsic origins of the hydrodynamic thermal transport and to find new materials interesting for science and engineering. The hydrodynamic thermal transport is governed intrinsically by the hydrodynamic scale and the thermal conductivity. The correlations between these intrinsic properties and harmonic and anharmonic properties, and a large number of compositional (290) and structural (1224) descriptors of 131 crystal compound materials are obtained, revealing some of the key descriptors that determines the magnitude of the intrinsic hydrodynamic effects, most of them related with the phonon relaxation times. Then, a trained black-box model is applied to screen more than 5000 materials. The results identify materials with potential technological applications. Understanding the properties correlated to hydrodynamic thermal transport can help to find new thermoelectric materials and on the design of new materials to ease the heat dissipation in electronic devices., (© 2022 IOP Publishing Ltd.)

Recent experiment and theoretical results show that thermal wave is more likely to occur in the low dimensional nonmetallic materials, such as graphene. In this article, based on the Guyer-Krumhansl model we derive the occurrence condition of the overshooting phenomenon in suspended graphene. This condition indicates that at the temperature 100 K if the size of suspended graphene is within the required range of about micro to millimeter, phonon transport is in the under-damped free oscillation regime and the overshooting can occur. Furthermore, we find that the overshooting phenomenon induced by the interference of thermal waves can cause the temperature in the heat conduction medium three times more than that of the temperature at the boundary, and the effective thermal conductivity of suspended graphene is more than six times of its bulk counterpart. Finally, an experimental plan to demonstrate the overshooting phenomenon (or second sound) in suspended graphene is proposed. • The occurrence condition for overshooting phenomenon in suspended graphene is derived. • Thermal wave interference makes temperature three times more than that of the temperature at the boundary. • Thermal conductivity of graphene can be increased more than six times of its bulk counterpart by overshooting. • An experimental plan to show the overshooting phenomenon in suspended graphene is proposed. [ABSTRACT FROM AUTHOR]

• The Knudsen minimum occurs when the ratio of thickness to width of thin graphite is less than 0.26. • The non-slip boundary condition leads to a smaller thermal conductivity of thin graphite than its bulk one. • Under the non-local boundary condition thermal conductivity of thin graphite increasing as decreasing its thickness. The recent experimental results reveal that thermal conductivity of thin graphite increases with the decrease of thickness. The exact mechanism of this phenomenon still remains elusive. Here, based on the one-dimensional Guyer-Krumhansl model and the non-local boundary condition, we show that decreasing thickness of thin graphite enhances its thermal conductivity. Whether Knudsen minimum phenomenon arises in phonon transport of thin graphite is also an unsolved scientific problem. By using the Guyer-Krumhansl model with the non-slip boundary condition in the width direction and the non-local boundary condition in the thickness direction for thin graphite, we find that the Knudsen minimum phenomenon can occur when the ratio of the thickness to width is less than 0.26. [ABSTRACT FROM AUTHOR]