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Peer-reviewedCC BY 4.0Fractal and Fractional

Beyond the Reduced Temperature Equation: Energy–Flux Dynamics in Fractional Heat Transport

  • Slobodanka P. Galovic1
  • Miroslava I. Jordovic-Pavlovic2
  • Marica N. Popovic3
  1. 1Vinca Institute of Nuclear Sciences—National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovica Alsa 12-14, 11001 Belgrade, Serbia
  2. 2Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, 36000 Kraljevo, Serbia
  3. 3Institute of Physics—National Institute of the Republic of Serbia, University of Belgrade, Pregrevica 118, 11030 Belgrade, Serbia
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Abstract

Fractional heat-transport models provide a framework for describing anomalous thermal dynamics beyond the classical Fourier description. However, reducing a coupled energy–flux formulation to a temperature equation can conceal information about how the thermal field is dynamically coupled to the heat flux. Different energy–flux realizations may therefore lead to the same reduced fractional temperature equation while retaining different field–flux relations. We investigate the consequences of this non-uniqueness for externally driven photothermal transport over the order range 0 ≤ α ≤ 1. We show that distinct energy–flux realizations can share the same reduced propagation equation while possessing different characteristic thermal impedances, resulting in distinct photothermal amplitude and phase responses under the same external excitation. Thus, the reduced fractional propagation equation alone does not uniquely characterize the response of an externally driven thermal system. More broadly, our results show that specifying a fractional transport model requires not only the choice of the fractional operator, but also its role within the coupled energy–flux formulation. The analysis therefore makes explicit information that is lost upon reduction to a field-only equation and shows how externally driven thermal response can distinguish realizations that are equivalent at the level of the reduced temperature equation.

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Cite

BibTeXRIS
BibTeX
@article{galovic2026beyond,
  title = {{Beyond the Reduced Temperature Equation: Energy–Flux Dynamics in Fractional Heat Transport}},
  author = {Slobodanka P. Galovic and Miroslava I. Jordovic-Pavlovic and Marica N. Popovic},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10100693},
  url = {https://www.mdpi.com/2504-3110/10/10/693},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Beyond the Reduced Temperature Equation: Energy–Flux Dynamics in Fractional Heat Transport
AU  - Slobodanka P. Galovic
AU  - Miroslava I. Jordovic-Pavlovic
AU  - Marica N. Popovic
PY  - 2026
DA  - 2026/10/03
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10100693
UR  - https://www.mdpi.com/2504-3110/10/10/693
AB  - Fractional heat-transport models provide a framework for describing anomalous thermal dynamics beyond the classical Fourier description. However, reducing a coupled energy–flux formulation to a temperature equation can conceal information about how the thermal field is dynamically coupled to the heat flux. Different energy–flux realizations may therefore lead to the same reduced fractional temperature equation while retaining different field–flux relations. We investigate the consequences of this non-uniqueness for externally driven photothermal transport over the order range 0 ≤ α ≤ 1. We show that distinct energy–flux realizations can share the same reduced propagation equation while possessing different characteristic thermal impedances, resulting in distinct photothermal amplitude and phase responses under the same external excitation. Thus, the reduced fractional propagation equation alone does not uniquely characterize the response of an externally driven thermal system. More broadly, our results show that specifying a fractional transport model requires not only the choice of the fractional operator, but also its role within the coupled energy–flux formulation. The analysis therefore makes explicit information that is lost upon reduction to a field-only equation and shows how externally driven thermal response can distinguish realizations that are equivalent at the level of the reduced temperature equation.
SN  - 2504-3110
ER  -