Second-sound beyond Maxwell–Cattaneo: Nonlocal effects in hyperbolic heat transfer at the nanoscale

Sellitto, A.; Zampoli, Vittorio; Jordan, P.M.

doi:10.1016/j.ijengsci.2020.103328

Cited by 17 publications

(11 citation statements)

References 43 publications

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“…The equation for the heat flux may, in principle, assume various forms. In the first case, one may follow, for example, Christov & Jordan [46], Jou et al [47], Sellitto et al [48], and write…”

Section: Cattaneo Models and Thermal Convectionmentioning

confidence: 99%

“…For another example, right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueviT,i ≡∑i=13vi∂T∂xi =u∂T∂x+v∂T∂y+w∂T∂z.Since the fluid is incompressible normal∂vinormal∂xi=0.The equation for the balance of energy may be written as normal∂Tnormal∂t+vinormal∂Tnormal∂xi=−normal∂Qinormal∂xi.The equation for the heat flux may, in principle, assume various forms. In the first case, one may follow, for example, Christov & Jordan [46], Jou et al [47], Sellitto et al [48], and write τ(∂Qi∂t+vj∂Qi∂…”

Section: Cattaneo Models and Thermal Convectionmentioning

confidence: 99%

See 1 more Smart Citation

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: Cattaneo Models and Thermal Convectionmentioning

confidence: 99%

Section: Cattaneo Models and Thermal Convectionmentioning

confidence: 99%

Thermal convection with a Cattaneo heat flux model

Gentile,

Straughan

2024

Proc. R. Soc. A.

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“…• The Θ e (ζ) vs. ζ profile under Case (iii) admits a pair of temperature-rate waves (see, e.g., Refs. [20,31,32]), i.e., jumps in Θ e (ζ); see Remark 5.…”

Section: Case (Iv)mentioning

confidence: 99%

“…• A thermal shock (see, e.g., Refs. [31,32]), i.e., a jump in T e (ζ), must occur under Case (iv); see Remark 6.…”

Section: Case (Iv)mentioning

confidence: 99%

On the structure of isothermal acoustic shocks under classical and artificial viscosity laws: Selected case studies

Carillo¹,

Jordan²

2022

Preprint

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Assuming Newton's law of cooling, the propagation and structure of isothermal acoustic shocks are studied under four different viscosity laws. Employing both analytical and numerical methods, 1D traveling wave solutions for the velocity and density fields are derived and analyzed. For each viscosity law considered, expressions for both the shock thickness and the asymmetry metric are determined. And, to ensure that isothermal flow is achievable, upper bounds on the associated Mach number values are derived/computed using the isothermal version of the energy equation.

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“…We do this here and employ what is now known as Cattaneo -Christov theory for the heat flux. Second sound, or the phenomenon whereby heat travels as a wave, is a highly prominent subject at present and is particularly relevant in connection with nanoscale effects, see Sellitto et al [89].…”

Section: Non -Isothermal Poroacoustic Wavesmentioning

confidence: 99%

Jordan–Cattaneo waves: Analogues of compressible flow

Straughan

2020

Wave Motion

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Second-sound beyond Maxwell–Cattaneo: Nonlocal effects in hyperbolic heat transfer at the nanoscale

Cited by 17 publications

References 43 publications

Thermal convection with a Cattaneo heat flux model

Thermal convection with a Cattaneo heat flux model

On the structure of isothermal acoustic shocks under classical and artificial viscosity laws: Selected case studies

Jordan–Cattaneo waves: Analogues of compressible flow

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