arXiv subjects

Róbert Kovács

Publications and source records attributed to Róbert Kovács.

At least 19 recordsLinked to original sources

arXiv2026

Origin of effective non-Fourier heat conduction phenomena in heterogeneous materials

Phenomenological models of non-Fourier heat conduction often lack a strict microstructural foundation, leading to ambiguities when modeling complex heterogeneous materials. In this study, we derive a continuum heat equation beyond Fourier's law using spatial volume averaging for a two-component system. We analytically prove that the experimentally observed static and dynamic thermal diffusivity arise directly from the distinct material properties, concluding that heterogeneous media are inherently over-diffusive. The resulting heat equation is thermodynamically compatible, and the microstructural origin allows the calculation of non-Fourier transport coefficients. Furthermore, we demonstrate that finite-sample boundaries introduce higher-order spatial non-localities, thereby explaining the size dependence of over-diffusion. We validate the model against experimental data across metal and carbon foams, rocks, and metal-organic frameworks.

physics.app-ph↗

arXiv2026

Thermodynamically consistent initialization of the Maxwell--Cattaneo---Vernotte heat conduction model: Analytical solutions and engineering applications

This paper investigates the numerical initialization of the one-dimensional Maxwell--Cattaneo--Vernotte (MCV) heat conduction model, addressing the critical mathematical challenge of defining the initial time derivative for non-equilibrium states. In modern high-frequency thermal engineering applications, traditional time-integration schemes and commercial finite-element solvers frequently introduce severe numerical artifacts when handling non-Fourier models. This study systematically evaluates three initialization strategies: a zero derivative, a spatially uniform non-zero derivative, and an exact space-dependent derivative. Using an explicit staggered finite-difference scheme, the transient responses to an exponentially distributed initial temperature field under adiabatic boundary conditions are compared against an analytical solution using the Galerkin method. The results demonstrate that assuming a zero or spatially uniform initial derivative introduces significant unphysical oscillatory deviations, leading to heat-flux prediction errors as the relaxation time increases. Conversely, mapping the exact space-dependent derivative onto the staggered grid preserves the local thermodynamic structure of the initial state, yielding robust transient responses that match the analytical benchmark without meaningful computational overhead. These findings establish a thermodynamically consistent initialization technique that can be extended to non-local models as well.

physics.app-ph↗

arXiv2025

The piston effect in supercritical fluids investigated via a reversible-irreversible vector field splitting-based explicit time integration scheme

In the vicinity of the liquid--vapor critical point, supercritical fluids behave strongly compressibly and, in parallel, thermophysical properties have strong state dependence. These lead to various peculiar phenomena, one of which being the piston effect where a sudden heating induces a mechanical pulse. The coupling between thermal and mechanical processes, in the linear approximation, yields a non-trivially rich thermoacoustics. The numerous applications of supercritical fluids raise the need for reliable yet fast and efficient numerical solution for thermoacoustic time and space dependence in this sensitive domain. Here, we present a second-order accurate, fully explicit staggered space-time grid finite difference method for such coupled linear thermoacoustic problems. Time integration is based on the splitting of the state space vector field representing the interactions that affect the dynamics into reversible and irreversible parts, which splitting procedure leads to decoupled wave and heat equations. The former is a hyperbolic partial differential equation, while the latter is a parabolic one, therefore, different time integration algorithms must be amalgamated to obtain a reliable, dispersion error-free, and dissipation error-free numerical solution. Finally, the thermoacoustic approximation of the supercritical piston effect is investigated via the developed method.

math.NA↗

arXiv2025

Discovering correlations between metal foam thermal characteristics and non-Fourier behavior

Due to their low density and large specific surface area, metal foams are increasingly used as cellular materials that combine excellent structural and thermal properties. Their cellular structure makes them particularly suitable for use in heat exchangers, insulation, and fire protection layers. The heat transport that takes place within them is a complex phenomenon characterized by the simultaneous presence of heat conduction, heat transfer, and heat radiation, making their modeling a significant challenge. The aim of the research is to develop a one-dimensional, time-dependent, discrete numerical model capable of describing the effective thermal behavior of metal foams. The model takes into account heat conduction through the solid phase, conductive heat transfer in the closed cavities, thermal radiation between the pore walls, and by-passing heat conduction around the cavity. The results highlight that geometric features such as cavity size and arrangement have a significant impact on temperature distribution and confirm that classical Fourier-based models are not accurately applicable to porous materials, but the Guyer--Krumhansl equation is an adequate candidate. Furthermore, we correlated the static and dynamic thermal diffusivity with the metal foam parameters, showing a significant sensitivity to the cavity thermal attributes.

physics.app-ph↗

arXiv2024

Investigating the whirling heat current density in the Guyer--Krumhansl equation

Among the numerous heat conduction models, the Guyer--Krumhansl equation has a special role. Besides its various application possibilities in nanotechnology, cryotechnology, and even in case of modeling heterogeneous materials, it poses additional mathematical challenges compared to the Fourier or Cattaneo {(a.k.a. Maxwell--Cattaneo--Vernotte)} equations. Furthermore, the Guyer--Krumhansl equation is the first heat conduction model, which includes the curl of the heat flux density in the evolution equation. In the present paper, we place our focus on the consequences of the existence of such whirling heat current density by solving the two-dimensional Guyer--Krumhansl equation with a space and time-dependent heat pulse boundary condition. The discretization poses further challenges in regard to the boundary condition for which we propose a particular extrapolation method. Furthermore, with the help of the Helmholtz decomposition, we show the analogy with the linearized acoustics of Newtonian fluids, which reveals how the heat flux density plays the role of the velocity field. Our solutions also reveal an unexpected temperature evolution caused by the whirling heat flux density, namely, the temperature can locally be decreased for a short time in a case when the curl of the heat flux density dominates the heat conduction process.

physics.app-ph↗

arXiv2024

Four spacetime dimensional simulation of rheological waves in solids and the merits of thermodynamics

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts - instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions.

physics.class-ph↗

arXiv2023

Challenges in the thermal modeling of highly porous carbon foams

The heat pulse experiment is a well-known method for determining thermal diffusivity. However, neither the measurement nor the evaluation methodologies are straightforward for heterogeneous, highly porous materials. In the present paper, we focus on two open-cell carbon foam types, differing in their porosity but having the same size. Recent experiments showed that a non-Fourier behaviour, called 'over-diffusive' propagation, is probably present for such a complex structure. The (continuum) Guyer-Krumhansl equation stands as a promising candidate to model such transient thermal behaviour. 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 behaviour. Additionally, the mentioned non-Fourier effects are porosity-dependent. However, porous samples can also follow the Fourier law. These data serve as a basis to correctly identify the characteristic heat transfer mechanisms and their corresponding time scales, which altogether result in the present non-Fourier behaviour. Keywords: flash experiments, non-Fourier heat conduction, highly porous carbon foams.

physics.class-ph↗

arXiv2023

Heat equations beyond Fourier: from heat waves to thermal metamaterials

In the past decades, numerous heat conduction models beyond Fourier have been developed to account for the large gradients, fast phenomena, wave propagation, or heterogeneous material structure, such as being typical for biological systems, superlattices, or thermal metamaterials. It became a challenge to orient among the models, mainly due to their various thermodynamic backgrounds and possible compatibility issues. Additionally, in light of the recent findings on the field of non-Fourier heat conduction, it is not even straightforward how to interpret and utilize a non-Fourier heat equation, primarily when one aims to thermally design the material structure to construct the new generation of thermal metamaterials. Adding that numerous modeling strategies can be found in the literature accompanying different interpretations even for the same heat equation makes it even more difficult to orient ourselves and find a comprehensive picture of this field of research. Therefore, this review aims to ease the orientation among advanced heat equations beyond Fourier by discussing properties concerning their possible practical applications in light of experiments. We start from the simplest model with basic principles and notions, then proceed toward the more complex models related to coupled phenomena such as ballistic heat conduction. We do not enter the often complicated technical details of each thermodynamic framework but do not aim to compare each approach. However, we still briefly present their background to highlight their origin and the limitations acting on the models. Additionally, the field of non-Fourier heat conduction has become quite segmented, and that paper also aims to provide a common ground, a comprehensive mutual understanding of the basics of each model, together with what phenomenon they can be applied to.

cond-mat.stat-mech↗

arXiv2022

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

Thanks to modern manufacturing technologies, heterogeneous materials with complex inner structures (e.g., foams) can 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 stands as a promising candidate to model such complex structures. However, the practical applications need a reliable and efficient algorithm that is capable of handling both complex geometries and advanced heat equations. In the present paper, we present the development of a $hp$-type finite element technique, which can be reliably applied. We investigate its convergence properties for various situations, being 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.

math.NA↗

arXiv2022

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

The Guyer-Krumhansl heat equation has numerous important practical applications in both low-temperature and room temperature heat conduction problems. In recent years, it turned out that the Guyer-Krumhansl model can effectively describe the thermal behaviour 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 $(τ_{q}, μ^{2})\rightarrow (0,0)$}. 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.

math.AP↗

arXiv2022

The role of the initial states for non-Fourier heat equations

There are several models for heat conduction - non-Fourier equations - in the literature that are important for various practical problems. These models manifest themselves in partial differential equations, and the application of which requires developing efficient and reliable solution methods. In the present paper, we focus on the analytical solutions of two non-Fourier models, specifically on the Maxwell-Cattaneo-Vernotte and Guyer-Krumhansl equations, as they share an established thermodynamic background, and find numerous applications. Although initial conditions are usually homogeneous in space in many situations, real applications can easily point beyond such a simple initial state. Therefore, we aim to investigate the consequences of nonhomogeneous initial conditions, emphasising the physical requirements to keep the solution physically admissible. We conclude the calculations with a method for determining the initial time derivatives in consistence with thermodynamics, avoiding contradictions.

physics.class-ph↗

arXiv2021

A case study of non-Fourier heat conduction using Internal Variables and GENERIC

Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law and its various extensions -- the Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type, Ginzburg-Landau (Allen-Cahn) type and ballistic-diffusive -- heat conduction equations are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction, and open new ways for numerical simulations of heat-conduction problems.

physics.class-ph↗

arXiv2021

Size effects and beyond-Fourier heat conduction in room-temperature experiments

It is a long-lasting task to understand heat conduction phenomena beyond Fourier. Besides the low-temperature experiments on extremely pure crystals, it has turned out recently that heterogeneous materials with macro-scale size can also show thermal effects that cannot be modelled by the Fourier equation. This is called over-diffusive propagation, different from low-temperature observations, and is found in numerous samples made from metal foam, rocks, and composites. The measured temperature history is indeed similar to what Fourier's law predicts but the usual evaluation cannot provide reliable thermal parameters. This paper is a report on our experiments on several rock types, each type having multiple samples with different thicknesses. We show that size-dependent thermal behaviour can occur for both Fourier and non-Fourier situations. Moreover, based on the present experimental data, we find an empirical relation between the Fourier and non-Fourier parameters, which may be helpful in later experiments to develop a more robust and reliable evaluation procedure.

physics.class-ph↗

arXiv2021

Continuum modeling perspectives of non-Fourier heat conduction in biological systems

The thermal modeling of biological systems has increasing importance in developing more advanced, more precise techniques such as ultrasound surgery. One of the primary barriers is the complexity of biological materials: the geometrical, structural, and material properties vary in a wide range, and they depend on many factors. Despite these difficulties, there is a tremendous effort to develop a reliable and implementable thermal model. In the present paper, we focus on the continuum modeling of heterogeneous materials with biological origin. There are numerous examples in the literature for non-Fourier thermal models. However, as we realized, they are associated with a few common misconceptions. Therefore, we first aim to clarify the basic concepts of non-Fourier thermal models. These concepts are demonstrated by revisiting two experiments from the literature in which the Cattaneo-Vernotte and the dual phase lag models are utilized. Our investigation revealed that using these non-Fourier models is based on misinterpretations of the measured data, and the seeming deviation from Fourier's law originates in the source terms and boundary conditions.

physics.class-ph↗

arXiv2021

Novel evaluation method for non-Fourier effects in heat pulse experiments

The heat pulse (flash) experiment is a well-known and widely accepted method to measure the thermal diffusivity of a material. In recent years, it is observed that the thermal behavior of heterogeneous materials can show deviation from the classical Fourier equation, resulting in a different thermal diffusivity and requiring further thermal parameters to identify. Such heterogeneity can be inclusions in metal foams, layered structure in composites, or even cracks and porous parts in rocks. Furthermore, the next candidate, the so-called Guyer-Krumhansl equation, is tested on these experiments with success. However, these recent evaluations required a computationally intensive fitting procedure using countless numerical solutions, even when a good initial guess for the parameters is found by hand. This paper presents a Galerkin-type discretization for the Guyer-Krumhansl equation, which helped us find a reasonably simple analytical solution for time-dependent boundary conditions. Utilizing this analytical solution, we developed a new evaluation technique to immediately estimate all the necessary thermal parameters using the measured temperature history.

physics.app-ph↗

arXiv2020

Open mathematical aspects of continuum thermodynamics: hyperbolicity, boundaries and nonlinearities

Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view.

cond-mat.stat-mech↗

arXiv2020

Non-equilibrium theories of rarefied gases: internal variables and extended thermodynamics

Limits of classical constitutive laws such as Fourier and Navier-Stokes equations are discovered since decades. However, the proper extensions -- generalizations of these are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based Rational Extended Thermodynamics (RET) and non-equilibrium thermodynamics with internal variables (NET-IV). First, the paper starts with the case of rigid heat conductors summarizing the result achieved so far. Then a typical example of compressible bodies is shown by presenting the first generalization for rarefied gases, called Meixner's theory. It is further extended using generalized entropy current in the framework of NET-IV. It is shown how its structure is related to RET and how the compatibility between them can be acquired.

cond-mat.stat-mech↗

arXiv2020

Analytical and numerical modelling of ballistic heat conduction observed in heat pulse experiments

Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a thermo-mechanical model in which the generalized heat equation - the so-called Maxwell-Cattaneo-Vernotte equation - is coupled to thermal expansion. At the same time, the other one uses internal variables. For the first one, we developed a numerical solution and tested on the heat pulse experiment performed by McNelly et al.~on NaF samples. For the second one, we found an analytical solution that emphasizes the role of boundary conditions. This analytical method is used to validate the earlier developed numerical code.

cond-mat.stat-mech↗