This note is concerned with the dynamics of 1D temperature waves generated by time modulation of a boundary heat flux. It demonstrates how a certain temporal transfer function of both parabolic and low frequency hyperbolic interfacial temperature waves happens to be frequency semi-invariant with a vibrating boundary heat flux. It is proved that only high frequency hyperbolic interfacial temperature waves can have a fully frequency-invariant temporal transfer function relative to such a vibrating boundary. The frequency response of an associated complex transfer function is also studied and demonstrated to behave, at low frequencies, as fixed lag compensator. Only according to hyperbolic theory of heat conduct, this compensator converts, at high frequencies, to a fixed gain amplifier.
Révisé le :
Accepté le :
Première publication :
Mots clés : Temporal transfer function, Temperature wave, Frequency invariance, Complex transfer function, Interfacial solutions, Hyperbolic heat conduction
CC-BY 4.0
@article{CRMECA_2023__351_S3_A8_0,
author = {Nassar Haidar},
title = {Frequency response of certain temporal and complex transfer functions for the {Interfacial} {1D} temperature wave},
journal = {Comptes Rendus. M\'ecanique},
publisher = {Acad\'emie des sciences, Paris},
year = {2023},
doi = {10.5802/crmeca.197},
language = {en},
note = {Online first},
}
TY - JOUR AU - Nassar Haidar TI - Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave JO - Comptes Rendus. Mécanique PY - 2023 PB - Académie des sciences, Paris N1 - Online first DO - 10.5802/crmeca.197 LA - en ID - CRMECA_2023__351_S3_A8_0 ER -
Nassar Haidar. Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave. Comptes Rendus. Mécanique, Online first (2023), pp. 1-13. doi : 10.5802/crmeca.197.
[1] Automatic Feedback Control System Synthesis, McGraw-Hill, NY, USA, 1955
[2] Modern Control System Theory & Application, Addison Wesley World Student Series, Addison-Wesley Publishing Group, 1978
[3] Theory of Automatic Control (A. Ed. Netushil, ed.), Mir Publishers, 1978 | Zbl
[4] Justification of input/output methods for systems with unbounded control & observation, IEEE Trans. Autom. Control, Volume 44 (1999) no. 1, pp. 81-95 | DOI | MR | Zbl
[5] Introduction to the Theory of Heat Conduction in Solids, Macmillan & Co, London, 1921 | Zbl
[6] Conduction of Heat in Solids, Oxford University Press, 1959
[7] Heat and Mass Transfer, Mir Publishers, Moscow, 1980 | Zbl
[8] Investigation of the thermophysical properties of polymers by the temperature wave technique, J. Therm. Anal. Calorim., Volume 38 (1992) no. 5, pp. 1139-1149 | DOI
[9] Photothermal applications to the thermal analysis of solids, J. Therm. Anal. Calorim., Volume 37 (1991), pp. 1065-1101 | DOI
[10] Scanning thermal wave microscopy (STWM), J. Heat Transfer, Volume 125 (2003) no. 1, pp. 156-163 | DOI
[11] Long pulsed alexandrite laser-assisted hair removal at 5, 10 and 20 millisecond pulse durations, Lasers Surg. Med., Volume 24 (1999) no. 5, pp. 332-337 | DOI
[12] A New Approach to Guided Wave Ray Tomography for Temperature-Robust Damage Detection Using Piezoelectric Sensors, Sensors, Volume 18 (2018) no. 10, 3518 | DOI
[13] Sinusoidal heating method to noninvasively measure tissue perfusion, IEEE Trans. Biomed. Eng., Volume 49 (2002) no. 8, pp. 867-877 | DOI
[14] Neutron density waves versus temperature waves, Int. J. Adv. Nucl. React. Des. Technol., Volume 3 (2021), pp. 206-212 | DOI
[15] Energy propagation of thermal waves, Eur. J. Phys., Volume 27 (2006) no. 6, pp. 1349-1355 | DOI | Zbl
[16] Diffusion waves and their uses, Phys. Today, Volume 53 (2000) no. 8, pp. 29-34 | DOI
[17] On physical and mathematical wave fronts in temperature waves, Transylv. J. Math. Mech., Volume 14 (2022) no. 2, pp. 139-158
[18] Explicit state and output boundary controllers for PDEs, J. Autom. Control, Volume 13 (2003) no. 2, pp. 1-9 | DOI
[19] Transfer functions for infinite-dimensional systems, Syst. Control Lett., Volume 52 (2004) no. 3-4, pp. 247-255 | DOI | MR | Zbl
[20] A general tranfer function representation for a class of hyperbolic distributed parameter systems, Int. J. Math. Comput. Sci., Volume 23 (2013) no. 2, pp. 291-307 | DOI | MR
[21] Heat waves, Rev. Mod. Phys., Volume 61 (1989) no. 1, pp. 41-73 | DOI | MR | Zbl
[22] Addendum to the paper “Heat waves”, Rev. Mod. Phys., Volume 62 (1990) no. 2, pp. 375-391 | Zbl
[23] Polarization of temperature waves in a dual heat flux vector space, Part. Diff. Eqns. Appl. Math., Volume 4 (2021), 100155 | DOI
[24] Exact solution of Guyer–Krumhansl type heat equation by operational method, Int. J. Heat Mass Transfer, Volume 96 (2016), pp. 132-144 | DOI
[25] The use of modulated temperature programs in thermal methods, J. Therm. Anal. Calorim., Volume 64 (2001), pp. 7-14 | DOI
[26] Evaluation of heat capacity measurements by temperature-modulated differential scanning calorimetry, J. Therm. Anal. Calorim., Volume 102 (2010) no. 3, pp. 1135-1140 | DOI
[27] Realization of thermal inertia in frequency domain, Entropy, Volume 16 (2014) no. 2, pp. 1101-1121 | DOI
[28] Transition regime in the ultrafast laser heating of solids, J. Appl. Phys., Volume 127 (2020), 073101 | DOI
[29] Behavior of temperature waves in solids in the description of heat conduction by a hyperbolic equation, Tech. Phys. Lett., Volume 21 (1995) no. 6, pp. 485-488
[30] Non-Fourier heat conduction in a slab subjected to periodic surface heating, J. Korean Phys. Soc., Volume 36 (2000) no. 4, pp. 209-214
[31] Fractional ultrafast laser-induced magneto-thermoelastic behavior in perfect conducting metal films, J. Therm. Stress., Volume 28 (2014) no. 1, pp. 64-82 | DOI
[32] Sur une forme de l’équation de la chaleur éliminant la paradoxe d’une propagation instantanée, C. R. Acad. Sci. Paris, Volume 246 (1958), pp. 431-433 | Zbl
[33] Les paradoxes de la théorie continue de l’équation de la chaleur, C. R. Acad. Sci. Paris, Volume 246 (1958) no. 22, pp. 3154-3155 | Zbl
[34] Exterior calculus note on the additive separation of variables 3D solution to a dynamical neutron diffusion BVP, Diff. Eqns. Control Process., Volume 2019 (2019) no. 4, pp. 53-72 | MR | Zbl
[35] The response of nanobeams with temperature-dependent properties using state-space method via modified couple stress theory, Symmetry, Volume 12 (2020) no. 8, 1276 | DOI
[36] et al. New analytical method based on dynamic response of planar mechanical elastic systems, Bound. Value Probl., Volume 2020 (2020) no. 1, 104 | DOI | MR | Zbl
[37] The size-dependent thermoelastic vibrations of nanobeams subjected to harmonic excitation and rectified sine wave heating, Mathematics, Volume 8 (2020) no. 7, 1128 | DOI
[38] Generalized solutions in elasticity of micropolar bodies with voids, Rev. Acad. Canar. Cienc., Volume 8 (1996) no. 1, pp. 101-109 | MR | Zbl
Cité par Sources :
Commentaires - Politique