Based on the new analytical solution of the problem of wave heat transfer, the dynamics of motion, interaction, and reflection of isolated temperature waves (solitons) in limited regions under the action of isolated temperature pulses of rectangular shape and the mechanism of refl ection of temperature solitons from the opposite boundary are investigated. In accord with this mechanism, fi rst the entire energy of a soliton is absorbed and then a reversetravelling temperature wave originates with the same space carrier as in the direct wave. During interaction of subsequent solitons with the refl ected ones, their energies are fi rst added up and then are separated into opposite directions (as a result of dissipation), preserving the kinematic characteristics. Since the time of action of isolated waves is proportional to several relaxation times and the depth of heating is equal to the limited number of nanometers, such investigations are of great interest also for the case in relativistic mechanics where high-power radiations interact with the surfaces of solid bodies.
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References
A. V. Luikov, Heat Conduction Theory [in Russian], Vysshaya Shkola, Moscow (1967).
A. G. Shashkov, A. V. Bubnov, and S. Yu. Yanovskii, Wave Phenomena of Heat Conduction [in Russian], URSS, Moscow (2004).
V. F. Formalev, S. A. Kolesnik, and E. L. Kuznetsova, Nonstationary heat transfer in an anisotropic semispace under conditions of heat exchange with the surrounding medium of assigned temperature, Teplofi z. Vys. Temp., 54, No. 6, 876–882 (2016).
V. F. Formalev, S. A. Kolesnik, and E. L. Kuznetsova, On wave heat transfer on times comparable with relaxation time in the case of intense convective-conductive heat transfer, Teplofi z. Vys. Temp., 56, No. 3, 412–416 (2018).
V. F. Formalev, S. A. Kolesnik, and E. L. Kuznetsova, Wave heat transfer in the orthotropic semispace under the action of nonstationary point source of thermal energy, Teplofi z. Vys. Temp., 56, No. 5, 799–804 (2018).
V. F. Formalev, S. A. Kolesnik, and E. L. Kuznetsova, Nonstationary heat transfer in a plate with general-form anisotropy on the effect of pulse heat sources, Teplofi z. Vys. Temp., 55, No. 5, 778–784 (2017).
V. F. Formalev and S. A. Kolesnik, Heat transfer in a half-space with transversal anisotropy under the action of a lumped heat source, J. Eng. Phys. Thermophys., 92, No. 1, 52–59 (2019).
É. M. Kartashov, Mathematical models of heat conduction with a two-phase lag, J. Eng. Phys. Thermophys., 89, No. 2, 346–356 (2016).
A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov, Aggravated Regimes in Problems for Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1987).
V. F. Formalev and S. A. Kolesnik, Temperature-dependent anisotropic bodies thermal conductivity tensor components identification method, Int. J. Heat Mass Transf., 123, 994–998 (2018).
V. F. Formalev and S. A. Kolesnik, On the inverse boundary heat conduction problems in recovery of heat fluxes toward anisotropic bodies with nonlinear characteristics of heat transfer, Teplofi z. Vys. Temp., 55, No. 4, 564–569 (2017).
V. F. Formalev, On thermal shock waves in nonlinear solid media, Teplofi z. Vys. Temp., 50, No. 6, 799–803 (2012).
O. N. Shablovskii and D. G. Krol′, Phenomenological estimation of time of the thermal relaxation on explosive crystallization of amorphous silicon fi lms, Tepl. Prots. Tekh., No. 5, 203–208 (2010).
O. N. Shablovskii, Thermal hysteresis in nonlinear media, J. Eng. Phys. Thermophys., 59, No. 1, 949–950 (1990).
V. L. Kolpashchikov and A. I. Shnip, Linear thermodynamic theory of heat conduction with memory, J. Eng. Phys. Thermophys., 46, No. 6, 732–739 (1984).
V. L. Kolpashchikov and A. I. Shnip, Linear defi ning equations on heat-conduction theory with fi nite thermal-perturbation velocity, J. Eng. Phys. Thermophys., 34, No. 2, 245–248 (1978).
A. N. Tikhonov and A. A. Samarskii, Equations on Mathematical Physics [in Russian], Nauka, Moscow (1972).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 1, pp. 11–17, January–February, 2020.
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Formalev, V.F., Kartashov, É.M. & Kolesnik, S.A. On the Dynamics of Motion and Reflection of Temperature Solitons in Wave Heat Transfer in Limited Regions. J Eng Phys Thermophy 93, 10–15 (2020). https://doi.org/10.1007/s10891-020-02085-9
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DOI: https://doi.org/10.1007/s10891-020-02085-9