Three-Layer Problem on Heat Exchange in a Medium with Counterflows
With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterflows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that i...
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| Published in: | Journal of engineering physics and thermophysics Vol. 97; no. 3; pp. 535 - 544 |
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| Abstract | With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterflows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterflows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat flow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterflows of liquid, in it there arises a heat flow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The effective coefficient of heat conductivity of medium, generated in it by the counterflows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these flows. An immovable layer in a medium, separating the counterflows of liquid, increases the generation of heat in the medium, and the heat flow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment. |
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| AbstractList | With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterflows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterflows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat flow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterflows of liquid, in it there arises a heatflow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The effective coefficient of heat conductivity of medium, generated in it by the counterflows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these flows. An immovable layer in a medium, separating the counterflows of liquid, increases the generation of heat in the medium, and the heat flow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment. Keywords: heat exchange, counterflows, effective heat conductivity, temperature gradient. With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterflows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterflows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat flow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterflows of liquid, in it there arises a heatflow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The effective coefficient of heat conductivity of medium, generated in it by the counterflows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these flows. An immovable layer in a medium, separating the counterflows of liquid, increases the generation of heat in the medium, and the heat flow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment. With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterflows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterflows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat flow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterflows of liquid, in it there arises a heat flow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The effective coefficient of heat conductivity of medium, generated in it by the counterflows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these flows. An immovable layer in a medium, separating the counterflows of liquid, increases the generation of heat in the medium, and the heat flow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment. |
| Audience | Academic |
| Author | Filippov, A. I. |
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| Cites_doi | 10.1016/j.ijheatmasstransfer.2021.122128 10.31857/S004036440003638-5 10.1016/j.ijheatmasstransfer.2021.122500 10.1007/BF02662149 10.1002/zamm.19260060404 10.1016/j.ijheatmasstransfer.2021.122260 10.1007/s11182-015-0526-5 10.1007/s11182-013-0011-y 10.1016/j.mvr.2021.104241 |
| ContentType | Journal Article |
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| Keywords | temperature gradient counterflows heat exchange effective heat conductivity |
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| References | FilippovAIAkhmetovaOVKovalskiiAAMethod of coefficient-by-coefficient averaging in the problem on the laminar flow of a gas in a wellPrikl. Mekh. Tekh. Fiz.20185917182 Jayati Tripathi, B. Vasu, O. Anwar Bég, B. Reddy Mounika, and Rama Subba Reddy Gorla, Numerical simulation of the transport of nanoparticles as drug carriers in hydromagnetic blood flow through a diseased artery with vessel wall permeability and rheological effects, Microvascular Res., 139, 104–241 (2022). KrasniqiDSelimajRKrasniqiMFilkoskiRVThermal dynamic analysis of parallel and counter flow heat exchangersInt. J. Mech. Eng. Technol.201896723729 Zhang Enwei, Wang Xiaoliang, and Liu Qingquan, Numerical investigation on the temporal and spatial statistical characteristics of turbulent mass transfer above a two-dimensional wavy wall, Int. J. Heat Mass Transf., 184, Article ID 122260 (2022). A. I. Filippov, A. F. Sadriev, E. V. Mukhametzyanov, and A. I. Leontiev, Polyharmonic transcillator of a travelling wave, Izv. Vyssh. Uchebn. Zaved., Fiz., 56, No. 2, 39–44 (2013). NigmatulinRIFilippovAIKhismatullinASTranscillator transfer of heat in a liquid with gas bubblesTeplofiz. Aéromekh.2012195595612 V. I. Baikov, N. V. Pavliukevich, A. K. Fedotov, and A. I. Shnip, Thermophysics, Vol. 2 [in Russian], Izd. A. V. Luikov ITMO, NAN Belarusi, Minsk (2014). I. A. Charnyi, Heating of the near-bottom zone of a well in the process of pumping of hot water into it, Neft. Khoz., Nos. 2–3, 18–23 (1953). FilippovAIShabarovABAkhmetovaOVTemperature field of a turbulent flow in a well with a dependence of the heat capacity on the temperatureTeplofiz. Vys. Temp.201856457858410.31857/S004036440003638-5 A. I. Filippov, A. R. Karimov, and A. K. Galimova, Transcillator effect in a medium with a two-dimensional stationary cellular flow, Izv. Vyssh. Uchebn. Zaved., Fiz., 58, No. 4, 58–64 (2015). Yeo Ilhwan and Lee Seunghyun, 2D computational investigation into transport phenomena of subcooled and saturated flow boiling in large length to diameter ratio micro-channel heat sinks, Int. J. Heat Mass Transf., 183, Article ID 122128 (2022). Li Yun and Wu Huiying, Experiment investigation on flow boiling heat transfer in a bidirectional counter-flow microchannel heat sink, Int. J. Heat Mass Transf., 187, Article ID 122500 (2022). M. A. Pudovkin, V. A. Chugunov, and A. N. Salamatin, Problem on Heat Exchange as Applied to the Theory of Drilling of Wells [in Russian], Izd. Kazansk. Gos. Univ., Kazan’ (1977). ChekaliukEBThermodynamics of an Oil Pool1965MoscowNedra[in Russian] A. Anzelius, Über Erwärmung vermittels durchströmender Medien, Z. Angw. Math. Mech., August (1926). ZeldovichYa. BExact solution of the problem on the diffusion in a periodic velocity field and turbulent diffusionDokl. Akad. Nauk SSSR19822664821826678165 FilippovAIKotelnikovVAMinlibaevMRThe phenomenon of vibration transfer in two-component oscillating interacting systemsJ. Eng. Phys. Thermophys.199770348749210.1007/BF02662149 DankoVPDiianovaSNAbazianAGInvestigation of the hydrodynamic regimes of operation of apparatus with a moving packingPrikl. Mekh. Tekh. Fiz.2018594110116 2921_CR6 EB Chekaliuk (2921_CR7) 1965 2921_CR4 2921_CR5 2921_CR3 AI Filippov (2921_CR16) 2018; 59 2921_CR1 VP Danko (2921_CR2) 2018; 59 D Krasniqi (2921_CR9) 2018; 9 AI Filippov (2921_CR15) 2018; 56 RI Nigmatulin (2921_CR17) 2012; 19 Ya. B Zeldovich (2921_CR11) 1982; 266 2921_CR10 AI Filippov (2921_CR12) 1997; 70 2921_CR13 2921_CR14 2921_CR8 2921_CR18 |
| References_xml | – reference: NigmatulinRIFilippovAIKhismatullinASTranscillator transfer of heat in a liquid with gas bubblesTeplofiz. Aéromekh.2012195595612 – reference: FilippovAIAkhmetovaOVKovalskiiAAMethod of coefficient-by-coefficient averaging in the problem on the laminar flow of a gas in a wellPrikl. Mekh. Tekh. Fiz.20185917182 – reference: Li Yun and Wu Huiying, Experiment investigation on flow boiling heat transfer in a bidirectional counter-flow microchannel heat sink, Int. J. Heat Mass Transf., 187, Article ID 122500 (2022). – reference: ZeldovichYa. BExact solution of the problem on the diffusion in a periodic velocity field and turbulent diffusionDokl. Akad. Nauk SSSR19822664821826678165 – reference: ChekaliukEBThermodynamics of an Oil Pool1965MoscowNedra[in Russian] – reference: A. Anzelius, Über Erwärmung vermittels durchströmender Medien, Z. Angw. Math. Mech., August (1926). – reference: I. A. Charnyi, Heating of the near-bottom zone of a well in the process of pumping of hot water into it, Neft. Khoz., Nos. 2–3, 18–23 (1953). – reference: KrasniqiDSelimajRKrasniqiMFilkoskiRVThermal dynamic analysis of parallel and counter flow heat exchangersInt. J. Mech. Eng. Technol.201896723729 – reference: DankoVPDiianovaSNAbazianAGInvestigation of the hydrodynamic regimes of operation of apparatus with a moving packingPrikl. Mekh. Tekh. Fiz.2018594110116 – reference: V. I. Baikov, N. V. Pavliukevich, A. K. Fedotov, and A. I. Shnip, Thermophysics, Vol. 2 [in Russian], Izd. A. V. Luikov ITMO, NAN Belarusi, Minsk (2014). – reference: FilippovAIShabarovABAkhmetovaOVTemperature field of a turbulent flow in a well with a dependence of the heat capacity on the temperatureTeplofiz. Vys. Temp.201856457858410.31857/S004036440003638-5 – reference: Zhang Enwei, Wang Xiaoliang, and Liu Qingquan, Numerical investigation on the temporal and spatial statistical characteristics of turbulent mass transfer above a two-dimensional wavy wall, Int. J. Heat Mass Transf., 184, Article ID 122260 (2022). – reference: M. A. Pudovkin, V. A. Chugunov, and A. N. Salamatin, Problem on Heat Exchange as Applied to the Theory of Drilling of Wells [in Russian], Izd. Kazansk. Gos. Univ., Kazan’ (1977). – reference: A. I. Filippov, A. F. Sadriev, E. V. Mukhametzyanov, and A. I. Leontiev, Polyharmonic transcillator of a travelling wave, Izv. Vyssh. Uchebn. Zaved., Fiz., 56, No. 2, 39–44 (2013). – reference: Jayati Tripathi, B. Vasu, O. Anwar Bég, B. Reddy Mounika, and Rama Subba Reddy Gorla, Numerical simulation of the transport of nanoparticles as drug carriers in hydromagnetic blood flow through a diseased artery with vessel wall permeability and rheological effects, Microvascular Res., 139, 104–241 (2022). – reference: A. I. Filippov, A. R. Karimov, and A. K. Galimova, Transcillator effect in a medium with a two-dimensional stationary cellular flow, Izv. Vyssh. Uchebn. Zaved., Fiz., 58, No. 4, 58–64 (2015). – reference: FilippovAIKotelnikovVAMinlibaevMRThe phenomenon of vibration transfer in two-component oscillating interacting systemsJ. Eng. Phys. Thermophys.199770348749210.1007/BF02662149 – reference: Yeo Ilhwan and Lee Seunghyun, 2D computational investigation into transport phenomena of subcooled and saturated flow boiling in large length to diameter ratio micro-channel heat sinks, Int. J. Heat Mass Transf., 183, Article ID 122128 (2022). – volume: 266 start-page: 821 issue: 4 year: 1982 ident: 2921_CR11 publication-title: Dokl. Akad. Nauk SSSR – volume: 59 start-page: 71 issue: 1 year: 2018 ident: 2921_CR16 publication-title: Prikl. Mekh. Tekh. Fiz. – volume: 59 start-page: 110 issue: 4 year: 2018 ident: 2921_CR2 publication-title: Prikl. Mekh. Tekh. Fiz. – volume-title: Thermodynamics of an Oil Pool year: 1965 ident: 2921_CR7 – volume: 9 start-page: 723 issue: 6 year: 2018 ident: 2921_CR9 publication-title: Int. J. Mech. Eng. Technol. – ident: 2921_CR1 doi: 10.1016/j.ijheatmasstransfer.2021.122128 – volume: 19 start-page: 595 issue: 5 year: 2012 ident: 2921_CR17 publication-title: Teplofiz. Aéromekh. – volume: 56 start-page: 578 issue: 4 year: 2018 ident: 2921_CR15 publication-title: Teplofiz. Vys. Temp. doi: 10.31857/S004036440003638-5 – ident: 2921_CR3 doi: 10.1016/j.ijheatmasstransfer.2021.122500 – volume: 70 start-page: 487 issue: 3 year: 1997 ident: 2921_CR12 publication-title: J. Eng. Phys. Thermophys. doi: 10.1007/BF02662149 – ident: 2921_CR8 – ident: 2921_CR10 – ident: 2921_CR5 doi: 10.1002/zamm.19260060404 – ident: 2921_CR6 – ident: 2921_CR4 doi: 10.1016/j.ijheatmasstransfer.2021.122260 – ident: 2921_CR14 doi: 10.1007/s11182-015-0526-5 – ident: 2921_CR13 doi: 10.1007/s11182-013-0011-y – ident: 2921_CR18 doi: 10.1016/j.mvr.2021.104241 |
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| SubjectTerms | Anisotropic media Anisotropy Asymptotic methods Classical Mechanics Complex Systems Conduction heating Conductive heat transfer Convective heat transfer Counterflow Electric properties Engineering Engineering Thermodynamics Equivalence Heat and Mass Transfer Heat Conduction and Heat Transfer in Technological Processes Heat exchange Heat transfer Heat transmission Industrial Chemistry/Chemical Engineering Laws, regulations and rules Newton Theory Thermal conductivity Thermodynamics |
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| Title | Three-Layer Problem on Heat Exchange in a Medium with Counterflows |
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