High-order fluxes in heat transfer with phonons and electrons: application towavepropagation

Carlomagno, I.; Domenico, Massimiliano Di; Sellitto, A.

doi:10.1098/rspa.2021.0392

Cited by 7 publications

(2 citation statements)

References 48 publications

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“…(1.71)], where one includes a Laplacian of qi in addition to the Mariano flux. Further relevant articles on this aspect are those of Rogolino & Cimmelli [59] and Carlomagno et al [60]. The relevant nonlinear perturbation equations are then right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueui,t+ujui,j=−π,i+Δui+Rθki,ui,i=0,Pr(θ,t+uiθ,i)=Rw−qi,i+ζΔθ,Sg(qi,t+ujqi,j−ui,jqj)=RSgPr ui,3−qi−θ,i+ϵΔqi.The ϵ term in (7.1) is described by Ván & Fülöp [58] and by Mariano [<...…”

Section: Nonlinear Energy Stability For Cattaneo–christov–mariano The...mentioning

confidence: 99%

Thermal convection with a Cattaneo heat flux model

Gentile,

Straughan

2024

Proc. R. Soc. A.

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The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.

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Section: Nonlinear Energy Stability For Cattaneo–christov–mariano The...mentioning

confidence: 99%

Thermal convection with a Cattaneo heat flux model

Gentile,

Straughan

2024

Proc. R. Soc. A.

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“…Notice that Guyer-Krumhansl's equation, otherwise largely analysed (see e.g. [14][15][16][17][18][19] and references therein), involves only the common total time derivative of the heat flux, while the version (1.2) including an objective time derivative has been proposed by Morro [20,21].…”

Section: Introductionmentioning

confidence: 99%

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

Mariano

2023

Proc. R. Soc. A.

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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.

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Thermal pulse propagation beyond the Maxwell–Cattaneo theory: Application to one-dimensional nanosystems

Domenico

Sellitto

Zampoli

2022

Continuum Mech. Thermodyn.

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A non-local and non-linear thermodynamical model of heat transfer at nanoscale beyond the well-known Maxwell–Cattaneo theory is derived. The compatibility of the proposed model with second law of thermodynamics is proved. The model is subsequently used to investigate the propagation of a heat pulse in one-dimensional nanosystems in the linear case. The predicted results are compared with those arising from the Maxwell–Cattaneo theory in order to point out the possible influence both of the non-local effects, and of the relaxation effects of the higher-order fluxes. Some problems related to initial data and boundary conditions are also discussed.

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High-order fluxes in heat transfer with phonons and electrons: application towavepropagation

Cited by 7 publications

References 48 publications

Thermal convection with a Cattaneo heat flux model

Thermal convection with a Cattaneo heat flux model

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

Thermal pulse propagation beyond the Maxwell–Cattaneo theory: Application to one-dimensional nanosystems

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