Anomalous Thermal Diffusion Research Articles

Anomalous thermal diffusion in two-layer system: The temperature profile and photoacoustic signal for rear light incidence

We analyze the influence of the generalizations of hyperbolic (Cattaneo) heat equations (GCE) on temperature profile and photoacoustic signal for the two-layer samples. The GCE extensions employ fractional-order derivatives related to the anomalous thermal diffusion in solid. We compare the superdiffusive (GCEII) and subdiffusive (GCEIII) generalizations with the classical and hyperbolic results. To show the fractional-order influence on results, we analyze opaque layers of aluminum with dye by considering only the last one with the anomalous characteristic. The promising results show that minor variations in fractional order and relaxation time can influence the photoacoustic signal.

Anomalous Heat Transport in Classical Many-Body Systems: Overview and Perspectives

In this review paper we aim at illustrating recent achievements in anomalous heat diffusion, while highlighting open problems and research perspectives. We briefly recall the main features of the phenomenon for low-dimensional classical anharmonic chains and outline some recent developments on perturbed integrable systems, and on the effect of long-range forces and magnetic fields. Some selected applications to heat transfer in material science at the nanoscale are described. In the second part, we discuss of the role of anomalous conduction on coupled transport and describe how systems with anomalous (thermal) diffusion allow a much better power-efficiency trade-off for the conversion of thermal to particle current.

Fractional GCEs behaviors merged: Prediction to the photoacoustic signal obtained with subdiffusive and superdiffusive operators

In this work, we developed a theoretical model with anomalous thermal diffusion by considering the modified Generalized Cattaneo Equations (GCEs) of Compte and Metzler, GCEI and GCEII, merged in a single operator by a linear combination in function of the fractional derivative order. This operator was compared with the generalization of Youssef for GCEIII. The range of the superdiffusive and subdiffusive regions was determined through phase velocity. In conclusion, both operators present unexpected sub- and superdiffusive intervals. Moreover, the temperature variation due to the heating by a pulsed light beam was determined. At the end, the photoacoustic signal for opaque samples was simulated varying the relaxation time and the fractional-order derivative.

Theoretical predictions for photoacoustic signal: Fractionary thermal diffusion with modulated light absorption source

We develop a theoretical framework, in the context of the anomalous thermal diffusion, for the photoacoustic signal. We obtain analytical predictions for the open photoacoustic cell technique by considering the thermal diffusion and thermoelastic bending effects. In these contexts, we consider different conditions for the thermal diffusivity, coefficient of optical absorption, the sample thickness and the amplitudes of thermal diffusion and thermoelastic bending contributions. Furthermore, opaque samples are also simulated as a special case of the optically transparent samples.

Fractal-based analysis of the void microstructure of Bi2Sr2CaCu2Ox superconducting filaments and the caused anomalous thermal diffusion

High-Tc multifilamentary composites Bi2Sr2CaCu2Ox/Ag/Ag-alloy (Bi2212) are the only round wires (RWs) to be potential candidates for fabricating high field magnets. However, the complicated microstructure of Bi2212 RWs, and especially the Bi2212 filaments, makes deep understanding of the correlation between macroscopic electrothermal behaviors and the microstructure a challenge. Building on our previous work of fractal-based analysis of the Bi2212/Ag interface, in this paper we focus on the void (gas bubble or pore) structure of individual Bi2212 filaments, taking a fractal-based analysis of the void structure and the resulting anomalous thermal diffusion. For fractal characterization of the void structure of Bi2212 filaments, we developed a fractal-based reconstruction model, and further derived a one-dimensional fractional order differential equation with the exponent α (0 < α ≤ 1), which is related to the porosity (0 ≤ ϕ ≤ 1) and fractal dimension (2 < D < 3) of the void structure of Bi2212 filaments. The calculated results show a local anomalous thermal diffusion (quite different from the diffusion in Euclidean homogeneous space corresponding to the materials without any pores), which depends on the porosity and fractal dimension of porous Bi2212 filaments. The dependence of thermal diffusion on the porosity is stronger than on the fractal dimension of the porous structure. This indicates that reducing voids/bubbles in Bi2212 filaments during the heat treatment process is significant for refining thermal diffusion.

Numerical modeling and experimental validation of fractional heat transfer induced by gas adsorption in heterogeneous coal matrix

Despite one fundamental issue in the adsorption theory of coalbed methane, little is known about the thermodynamic properties of gas adsorption in a porous coal matrix. In this work, considering the heterogeneity of pore structure and the exothermic characteristics of gas adsorption, a fractional heat conduction model with an unsteady volumetric heat source is proposed to study the heat transfer process induced by gas adsorption in a heterogeneous coal matrix. The heat conduction equation with a fractional time derivative is discretized by using an implicit numerical method based on the generalization of a standard finite-difference scheme. First, to validate the fractional heat conduction model, gas adsorption experiments on a microcalorimeter were carried out on 5 g coal samples of 0.3 mm diameter at 25 °C. The experimental heat flux with initial adsorption pressures of 3.23 bar, 5.83 bar and 9.77 bar increases rapidly from zero to peak values of 7.17 mW, 12.05 mW and 16.81 mW in less than 7 min (i.e., fast thermal diffusion stage) and then decreases slowly to zero again in approximately 2 h (i.e., slow thermal diffusion stage). It is revealed that for all tested gas pressures the fractional heat conduction model with a fractional order α=0.86 can reproduce the experimental process of heat flux with better accuracy than the Fourier law-based model (i.e., α=1), suggesting that anomalous thermal diffusion is the governing heat transfer process of gas adsorption in the coal matrix. Second, the spatial distribution and temporal evolution of temperature patterns with different model parameters are numerically simulated. It is found that the time to reach the peak temperature decreases from 760 s at the center of the coal particles to 490 s at the boundary. Finally, the parametric sensitivity of the thermodynamic properties of gas adsorption such as temperature, heat flux and integral adsorption heat is discussed in detail. Particularly, it is shown that as one of the most important thermodynamic parameters, the integral heat is very sensitive to the fractional order α. In the case of 3.23 bar, if α increases from0.75 to 1, while other model parameters remain unchanged, the integral heat could be enhanced from 1.1 J/g to 8.5 J/g.

Numerical inversion of the fractional derivative index and surface thermal flux for an anomalous heat conduction model in a multi-layer medium

• Anomalous thermal diffusion with fractional boundary in layered medium was studied. • The balance method was utilized to give an efficient finite difference scheme. • The fractional index and boundary flux were simultaneously identified. • The L–M algorithm incorporating Armijo rule and scaling technique was applied. • Numerical simulation with real experimental data was carried out. In this paper, we study an inverse problem for identifying multiple parameters of an anomalous heat conduction model with fractional derivative flux boundary conditions in a composite medium. The anomalous heat conduction equation in a layered medium is derived using the conservation of energy and the modified Fourier law with a Riemann–Liouville fractional operator. For the forward problem, we construct an effective finite difference scheme by applying the balance method to deal with the discontinuity interface. For the inverse problem, we utilize the Levenberg–Marquardt (L–M) regularization technique combined with the Armijo rule to simultaneously identify the order of the fractional derivative and the left boundary heat flux term. Finally, we use experimental data extracted from the measurement in a carbon–carbon composite material to verify the effectiveness of the proposed technique. In the experiments, we analyze the sensitivity coefficients and show the numerical results graphically. Furthermore, we introduce a diagonal scaling matrix transformation to alleviate the effect of the different parameter magnitudes on the inverse problem. The simulation results confirm that the fractional heat conduction model with estimated parameters gives a more accurate and adequate description for the heat transfer process in the carbon–carbon composite material.

Parameters estimation for a new anomalous thermal diffusion model in layered media

In this paper, we study an inverse problem of parameters estimation for a new time-fractional heat conduction model in multilayered medium. In the anomalous thermal diffusion model, we consider the fractional derivative boundary conditions and the conduction obeys modified Fourier law with Riemann–Liouville fractional operator of different order in each layer. For the direct problem, we construct an effective finite difference scheme by using the balance method to deal with the discontinuity interface. For the inverse problem, we apply the nonlinear conjugate gradient (NCG) method with different conjugated coefficients to simultaneously identify the fractional exponent in each layer. Finally, we use experimental data to verify the effectiveness of the proposed technique, in which the Jacobian matrix is achieved by a derivative-free approach. We analyze the sensitivity coefficients and the convergence behaviors of the NCG algorithm. The simulation results confirm that the fractional heat conduction model with estimated parameters gives a more accurate fitting than the classical counterpart and the NCG method is a feasible and effective technique for the inverse problem of parameters estimation in fractional model.

Fractional diffusion modeling of heat transfer in porous and fractured media

Fracture–matrix interactions strongly affect anomalous heat transfer in geological sites. This study investigates effects of the interactions between fractures and rock matrix by using the method of multiple interacting continua (MINC). The MINC generates different temperature histories for varied fracture spacings. Two analytical solutions of each porous model and fracture model are used to fit the numerical results for temperature histories due to cold-water injection. The porous model is good agreement with the result for small fracture spacing, while a solution of the fracture model fits the result for large fracture spacing. The MINC yields intermediate behaviors in between a porous medium and a single fracture. A fractional heat transfer equation (fHTE) has been developed to describe anomalous thermal diffusion in a fractured reservoir. The fHTE accounts for heat flux from fracture into matrix by using a temporal fractional derivative. The fHTE can capture numerical results for temperature histories with different fracture spacings. The fracture spacing has correlations to the fHTE best-fit parameters (i.e., the orders of fractional derivatives and the retardation parameters). The fHTE with varying time fractional derivatives can cover descriptions of subdiffusion, Fickian diffusion, and superdiffusion.

Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles

The physical approach of a small particle (virus, medical drug) to the cell membrane represents the crucial first step before active internalization and is governed by thermal diffusion. Using a fully analytical theory we show that the stretching and bending of the elastic membrane by the approaching particle induces a memory in the system, which leads to anomalous diffusion, even though the particle is immersed in a purely Newtonian liquid. For typical cell membranes the transient subdiffusive regime extends beyond 10 ms and can enhance residence times and possibly binding rates up to 50%. Our analytical predictions are validated by numerical simulations.

The Transient Heat Transfer of a Pebble Fuel Considering Anomalous Diffusion

In this article, the transient behavior of the heat transfer in the fuel element of a pebble bed modular reactor is presented. The pebble fuel is a heterogeneous system that is made up of microsphere constitutes by UO2, pyrolytic carbon, and silicon carbide mixed with graphite. To describe the anomalous thermal diffusion in this complex system, a fractional constitutive law of non-Fourier type is applied. The numerical results of the temperature distribution with fractional model were compared with the classical heat transfer model. The numerical simulations during transient behavior of the anomalous thermal diffusion process are presented in the heterogeneous pebble fuel for different anomalous diffusion exponents.

Wave convection regimes in a binary mixture in a modulated gravitational field

Nonlinear wave convection regimes are studied in a horizontal layer of an incompressible binary mixture with anomalous thermal diffusion in the gravitational field modulated with an arbitrary amplitude and finite frequency. Oscillation regimes are numerically simulated by the finite difference method for the case of a layer with impenetrable rigid boundaries, which better corresponds to experimental laboratory conditions. A qualitative difference is found in the dynamics of nonlinear quasi-periodic and subharmonic oscillations appearing in the initially stratified mixture and behaving as modulated and regular standing waves. The dependences of the intensity of convective flows on the modulation amplitude are obtained. The results of nonlinear calculations are compared with data on the boundaries of the equilibrium stability found from the linear theory. It is shown that a region of parameters exists where alternating action suppresses the convective motion.

Anomalous diffusion and thermal diffusion of light ions in a nonisothermal plasma

A turbulent state appearing upon the Cherenkov generation of slow ion acoustic waves by light ions and their induced scattering on heavy ions has been studied. The coefficients of the anomalous diffusion and thermal diffusion of light ions have been determined.

Trapped Electron Turbulence

The effect of trapped electron turbulence on the dynamics of a typical unstable mode is investigated. We establish that its principal effects are turbulence-induced additional collision frequencies for the trapped electrons and transit ions both of which are stabilizing. The resulting nonlinearly saturated fluctuation level is found to be considerably smaller than other estimates. The corresponding estimates of anomalous particle and thermal diffusion are also smaller than previous results.

On the Anomalous Thermal Diffusion Observed in the Solution of Mixed Electrolytes

On the Anomalous Thermal Diffusion Observed in the Solution of Mixed Electrolytes