THERMAL SCIENCE

International Scientific Journal

Aloisi Somer

,

Andressa Novatski

,

Marcelo K. Lenzi

,

Luciano R. Da Silva

,

Ervin K. Lenzi

FRACTIONAL DUAL-PHASE-LAG HEAT CONDUCTION WITH PERIODIC HEATING AND PHOTO-THERMAL RESPONSE

ABSTRACT
We apply an extension of dual-phase-lag in thermal systems to predict the photoacoustic signal for transmission configuration and characteristics of the open photoacoustic cell technique. For this, we consider a particular case from Jeffrey’s equation as an extension of the generalized Cattaneo equations. In this context, we obtain the temperature distribution under the effects of fractional differential operators, allowing the calculation of the Photoacoustic signal for the transmission set-up. The results show a rich class of behaviors related to the anomalous diffusion connected to these fractional operators.
KEYWORDS
anomalous diffusion, Fractional Dynamics, Generalized Cattaneo Equation
PAPER SUBMITTED: 2023-02-01
PAPER REVISED: 2023-02-22
PAPER ACCEPTED: 2023-03-04
PUBLISHED ONLINE: 2023-04-22
DOI REFERENCE: https://doi.org/10.2298/TSCI230201086S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [2537 - 2547]
REFERENCES
  1. A. Pekalski, Diffusion Processes: Experiment, Theory, Simulations, Diffusion Processes: Experiment,Theory, Simulations, Springer, 1994.
  2. L. Vlahos, H. Isliker, Y. Kominis, K. Hizanidis, Normal and anomalous diffusion: A tutorial, arXiv preprint arXiv:0805.0419 (2008).
  3. A. Pekalski, K. Sznajd-Weron, Anomalous Diffusion: From Basics to Applications, Springer, 1999.
  4. J. Klafter, A. Blumen, M. F. Shlesinger, Stochastic pathway to anomalous diffusion, Phys. Rev. A 35 (1987) 3081.
  5. Y. Liang, S. Wang, W. Chen, Z. Zhou, R. L. Magin, A survey of models of ultraslow diffusion in heterogeneous materials, Appl. Mech. Rev. 71 (2019) 040802.
  6. A. Block, M. Liebel, R. Yu, M. Spector, Y. Sivan, F. J. García de Abajo, N. F. van Hulst, Tracking ultrafast hot-electron diffusion in space and time by ultrafast thermomodulation microscopy, Science Advances 5 (2019) eaav8965.
  7. M. Mozafarifard, D. Toghraie, Time-fractional subdiffusion model for thin metal films under femtosecond laser pulses based on caputo fractional derivative to examine anomalous diffusion process, Int. J. Heat. Mass. Tran. 153 (2020) 119592.
  8. C. Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3 (1948) 83-101.
  9. W. Zhang, X. Cai, S. Holm, Time-fractional heat equations and negative absolute temperatures, Comput. Math. Appl. 67 (2014) 164 - 171.
  10. Y. R. Koh, M. Shirazi-HD, B. Vermeersch, A. M. S. Mohammed, J. Shao, G. Pernot, J.-H. Bahk, M. J. Manfra, A. Shakouri, Quasi-ballistic thermal transport in Al0.1Ga0.9n thin film semiconductors, Appl. Phys. Lett. 109 (2016) 243107.
  11. A. Compte, R. Metzler, The generalized Cattaneo equation for the description of anomalous transport processes, J. Phys. A: Math. and Gen. 30 (1997) 7277-7289.
  12. S. Galovic, Z. Šoškic, M. Popovic, D. Cevizovic, Z. Stojanovic, Theory of photoacoustic effect in media with thermal memory, J. Appl. Phys. 116 (2014) 024901
  13. Z. Šoškic, S. Ciric ostíc, S. Galovic, An extension to the methodology for characterization of thermalproperties of thin solid samples by photoacoustic techniques, Int. J. Therm. Sci. 109 (2016) 217-230.
  14. K. Djordjevic, D. Milicevic, S. Galovic, E. Suljovrujic, S. Jacimovski, D. Furundzic, M. Popovic, Photothermal response of polymeric materials including complex heat capacity, Int. J. Thermophys. 43 (2022) 68.
  15. A. Somer, A. Novatski, E. K. Lenzi, Theoretical predictions for photoacoustic signal: Fractionary thermal diffusion with modulated light absorption source, Eur. Phys. J. Plus. 134 (2019) 18.
  16. A. Somer, A. Novatski, F. C. Serbena, E. K. Lenzi, Fractional gces behaviors merged: prediction to the photoacoustic signal obtained with subdiffusive and superdiffusive operators, J. Appl. Phys. 128 (2020) 075107.
  17. D. Markushev, D. Markushev, S. Aleksi c, D. Pantic, S. Galovic, D. Lukic, J. Ordonez-Miranda, Enhancement of the thermoelastic component of the photoacoustic signal of silicon membranes coated with a thin tio2 film, J. Appl. Phys. 131 (2022) 085105.
  18. M. Popovic, D. Markushev, M. Nesic, M. Jordovic Pavlovic, S. Galovic, Optically induced temperature variations in a two-layer volume absorber including thermal memory effects, J. Appl. Phys. 129 (2021) 015104.
  19. A. Rosencwaig, A. Gersho, Theory of the photoacoustic effect with solids, J. Appl. Phys. 47 (1976) 64-69.
  20. L. F. Perondi, L. C. M. Miranda, Minimal-volume photoacoustic cell measurement of thermal diffusivity: effect of the thermoelastic sample bending, J. Appl. Phys. 62 (1987) 2955-2959.
  21. A. Somer, F. Camilotti, G. Costa, C. Bonardi, A. Novatski, A. Andrade, V. Kozlowski Jr, G. Cruz, The thermoelastic bending and thermal diffusion processes influence on photoacoustic signal generation using open photoacoustic cell technique, J. Appl. Phys. 114 (2013) 063503.
  22. D. Todorovic, M. D. Rabasovic, D. Markushev, Photoacoustic elastic bending in thin film - substrate system, J. Appl. Phys. 114 (2013) 213510.
  23. M. Nesic, S. Galovic, Z. Soskic, M. Popovic, D. M. Todorovic, Photothermal Thermoelastic Bending for Media with Thermal Memory. Int. J. Thermophys. 33, 2203-2209 (2012)
  24. E. Awad, T. Sandev, R. Metzler, A. Chechkin, From continuous-time random walks to the fractional jeffreys equation: Solution and properties, Int. J. Heat. Mass. Tran. 181 (2021) 121839.
  25. E. Awad, R. Metzler, Crossover dynamics from superdiffusion to subdiffusion: Models and solutions, Fract. Calc. Appl. Anal. 23 (2020) 55-102.
  26. H.-Y. Xu, X.-Y. Jiang, Time fractional dual-phase-lag heat conduction equation, Chinese Phys. B 24 (2015) 034401.
  27. A. Somer, A. Novatski, G. K. da Cruz, C. B. K. da Cruz, F. C. Serbena, E. K. Lenzi, Simultaneous fit of the photoacoustic signal amplitude and phase for aisi 316 with fractional analysis (2022).
  28. D. Tzou, A unified field approach for heat conduction from macro- to micro-scales, Previews of Heat and Mass Transfer 21 (1995) 196.
  29. S. Singh, P. Saccomandi, R. Melnik, Three-phase-lag bio-heat transfer model of cardiac ablation, Fluids 7 (2022) 180.
  30. A. Hobiny, F. Alzahrani, I. Abbas, Analytical estimation of temperature in living tissues using the tplbioheat model with experimental verification, Mathematics 8 (2020) 1188.
  31. R. Kumar, R. Tiwari, A. Singhal, S. Mondal, Characterization of thermal damage of skin tissue subjected to moving heat source in the purview of dual phase lag theory with memory-dependent derivative, Wave Random Complex (2021) 1-18.
  32. Z. Shomali, R. ovács, P. Ván, I. V. udinov, J. Ghazanfarian, Lagging heat models in thermodynamics and bioheat transfer: a critical review, Continuum Mech. Therm. 34 (2022) 637-679.
  33. E. K. Lenzi, R. S. Mendes, K. S. Fa, L. S. Moraes, L. R. da Silva, L. S. Lucena, Nonlinear fractional diffusion equation: Exact results, J. Math. Phys. 46 (2005) 083506.
  34. L. R. Evangelista, E. K. Lenzi, Fractional Diffusion Equations and Anomalous Diffusion, Cambridge University Press, 2018.
  35. L. R. Evangelista, E. K. Lenzi, An Introduction to Anomalous Diffusion and Relaxation, Springer Nature, 2023.
  36. G. Rousset, F. Lepoutre, L. Bertrand, Influence of thermoelastic bending on photoacoustic experiments related to measurements of thermal diffusivity of metals, J. Appl. Phys. 54 (1983) 2383-2391.
  37. D. Jou, J. Casas-Vázquez, G. Lebon, Extended Irreversible Thermodynamics, Springer, 1996.
  38. A. Somer, M. N. Popovic, G. K. da Cruz, A. Novatski, E. K. Lenzi, S. P. Galovic, Anomalous thermal diffusion in two-layer system: The temperature profile and photoacoustic signal for rear light incidence (2022).
  39. S. Galovic, D. Kostoski, Photothermal wave propagation in media with thermal memory, J. Appl. Phys. 93 (2003) 3063-3070.
  40. M. N. Popovic, M. V. Nesic, M. Zivanov, D. D. Markushev, S. P. Galovic, Photoacoustic response of a transmission photoacoustic configuration for two-layer samples with thermal memory, Opt. Quant. Electron. 50 (2018) 330.
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Fractional dual-phase-lag heat conduction with periodic heating and photo-thermal response

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