<abstract xmlns="http://www.w3.org/1999/xhtml">

By using a procedure of classical irreversible thermodynamics with internal variable (CIT-IV), some possible interactions among heat conduction and viscous-anelastic flows for rheological media are studied. In particular, we introduce as internal variables a second rank tensor 
<inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ijmce-2024-0011_ineq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>ε</mi><mrow><mi>α</mi><mi>β</mi></mrow><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></math>
<tex-math>\varepsilon _{\alpha \beta }^{(1)}</tex-math>
</alternatives>
</inline-formula>
 that is contribution to inelastic strain and a vector <italic>ξα</italic> that influences the thermal transport phenomena and we derive the phenomenological equations for these variables in the anisotropic and isotropic cases. The stress-strain equations, the general flows and the temperature equation in visco-anelastic processes are obtained and when the medium is isotropic, we obtain that the total heat flux <bold>J</bold>(<italic>q</italic>) can be split in two parts: a first contribution <bold>J</bold>(0), governed by Fourier law, and a second contribution <bold>J</bold>(1), obeying Maxwell-Cattaneo-Vernotte (M-C-V) equation.
</abstract>

By using a procedure of classical irreversible thermodynamics with internal variable (CIT-IV), some possible interactions among heat conduction and viscous-anelastic flows for rheological media are studied. In particular, we introduce as internal variables a second rank tensor 



εαβ(1)
\varepsilon _{\alpha \beta }^{(1)}


 that is contribution to inelastic strain and a vector ξα that influences the thermal transport phenomena and we derive the phenomenological equations for these variables in the anisotropic and isotropic cases. The stress-strain equations, the general flows and the temperature equation in visco-anelastic processes are obtained and when the medium is isotropic, we obtain that the total heat flux J(q) can be split in two parts: a first contribution J(0), governed by Fourier law, and a second contribution J(1), obeying Maxwell-Cattaneo-Vernotte (M-C-V) equation.

Derivations of the stress-strain relations for viscoanelastic media and the heat equation in irreversible thermodynamic with internal variables

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

By using a procedure of classical irreversible thermodynamics with internal variable (CIT-IV), some possible interactions among heat conduction and...

Derivations of the stress-strain relations for viscoanelastic media and the heat equation in irreversible thermodynamic with internal variables

Article Category: Original Study

Published Online: Jan 10, 2024

Page range: 141 - 154

Received: Sep 27, 2023

Accepted: Nov 03, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0011

Keywords
Non-equilibrium thermodynamic, rheology, viscoanelastic media, heat flow

© 2024 Vincenzo Ciancio, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Derivations of the stress-strain relations for viscoanelastic media and the heat equation in irreversible thermodynamic with internal variables

Article Category: Original Study

Published Online: Jan 10, 2024

Page range: 141 - 154

Received: Sep 27, 2023

Accepted: Nov 03, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0011

KeywordsNon-equilibrium thermodynamic, rheology, viscoanelastic media, heat flow

© 2024 Vincenzo Ciancio, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Non-equilibrium thermodynamic, rheology, viscoanelastic media, heat flow