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MATHEMATICAL LOW-REYNOLDS MODELING OF HEAT EXCHANGE IIN TURBULENT FLOW IN FLAT CHANNELS WITH TURBULATORS SYMMETRICALLY LOCATED ON BOTH SIDES

https://doi.org/10.21822/2073-6185-2018-45-2-70-93

Abstract

Objectives The aim of the study was to simulate the heat transfer in flat channel with turbulators, symmetrically located on its both sides, depending on the channel's geometric parameters and the coolant flow modes followed by the verification of the obtained calculated data by the existing experiment.

Methods The calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations, closed with the help of the Menter shear stress transport model, by factored finite-volume method, as well as the energy equation on multiscale intersecting structured grids (Fast COmposite Mesh method, FCOM).

Results A theoretical mathematical calculation model for intensified heat exchange in turbulent flow for a flat channel with turbulators, symmetrically located on both sides, depending on the channel's geometric parameters and coolant flow modes was generated. The calculation results of the intensified heat exchange in flat channels with double turbulators, depending on the determining parameters, are in very good agreement with the existing experimental material and have an undeniable advantage over the latter, since the assumptions made in their derivation cover a much wider range of determining parameters than the limitations of the experiments (Pr = 0.7 ч 100; Re = 103ч 106; h / dЭ= 0.005 ч 0.2; t / h= 1 ч 200).

 ConclusionAccording to the calculation results based on the developed model, it is possible to optimise the heat exchange intensification in flat channels with double turbulators, as well as to control the process of heat exchange intensification. The comparative calculations of the intensified hydraulic resistance and heat exchange for flat channels with two-sided symmetrical flow turbulators with corresponding data for round channels with turbulators were carried out and analysed. From the point of view of heat exchange intensification, all other conditions being equal, the reduction of a flat channel with two-sided symmetrical turbulators with respect to a round tube with turbulators takes place because a smaller increase in heat exchange is achieved with a greater increase in hydraulic resistance. It was established by calculation that the relative hydraulic resistance ξП/ ξT for channels with turbulators is always higher than for smooth channels; however, the relative heat exchange NuП/ NuT for channels with turbulators can be higher than for smooth channels. Therefore, there is an enhanced redistribution of the temperature drop over the channel section with an intensified heat exchanger. The developed theoretical method based on the solution of the Reynolds equations by the factored finite-volume method, combined with the energy equation on multiscale intersecting structured grids and closed by means of the Menter shear stress transport model, makes it possible, with reasonable accuracy, to calculate heat exchange coefficients and hydraulic resistance in flat channels of practically any forms of double symmetrically located flow turbulators.

About the Author

I. E. Lobanov
Moscow Aviation Institute (National Research University)
Russian Federation

4 Volokolamskoe shosse, Moscow 125993

Igor' E.Lobanov - Dr. Sci. (Technical), Leading researcher, Problematic scientific-research Laboratory – 204.





References

1. Kalinin E.K., Dreytser G.A., KoppI .Z. idr. Effektivnye poverkhnosti teploobmena. M.: Energoatomizdat; 1998. 408 s. [Kalinin E.K., Dreytser G.A., Kopp I.Z. et al. Effective heat-exchange suraces. Moscow: Energoatomizdat; 1998. 408 p. (in Russ.)]

2. Kalinin E.K., Dreitser G.A., Yarkho S.A. Intensifikatsiya teploobmena v kanalakh. M.: Mashinostroenie; 1972. 220 s. [Kalinin E.K., Dreitser G.A., Yarkho S.A. Intensification of heat transfer in the channels. M.: Mashinostroenie; 1972. 220 p. (in Russ.)]

3. Han J.C., Park J.S., Ibrahim M.Y. Measurement of heat transfer and pressure drop in rectangular channel with turbulence promoters. NASA Contactor Rep. 4015. Texas AEM University College Station. 1986. 200 p.

4. Han J.C., Park J.S. Developing heat transfer in rectangular channels with rib turbulators. Int. J. HeatMassTransfer. 1988; 31(1):183 - 195.

5. Pavlovskii V.G., Dedusenko Yu.M. Teploobmen i gidravlicheskoe soprotivlenie v korotkom ploskoparallel'nom kanale s iskusstvenno sherokhovatymi stenkami. Inzhenerno-fizicheskii zhurnal. 1969;XVII(6):1098 - 1101. [Pavlovskii V.G., Dedusenko Yu.M. Heat transfer and hydraulic resistance in a short plane-parallel channel with artificially rough walls. Journal of Engineering Physics and Thermophysics. 1969;XVII(6):1098 - 1101 (in Russ.)]

6. Pavlovskii V.G. Opredelenie teplovoi effektivnosti turbulizatsii vozdushnogo potoka v gidrodinamicheskom nachal'nom uchastke ploskoparallel'nogo kanala. Depon. VINITI AN SSSR. 1969. № 630. [Pavlovskii V.G. Determination of the thermal efficiency of the turbulence of the air flow in the hydrodynamic initial section of the plane-parallel channel. Depsied in VINITI AN SSSR. 1969. № 630. (in Russ.)]

7. Sukomel A.S., Velichko V.I., Abrosimov Yu.G. Teploobmen i trenie pri turbulentnom techenii gaza v korotkikh kanalakh. M.: Energiya; 1979. 216 s. [Sukomel A.S., Velichko V.I., Abrosimov Yu.G. Heat transfer and friction in turbulent gas flow in short channels. M.: Energiya; 1979. 216 p. (in Russ.)]

8. Velichko V.I., Pronin V.A. Raschet teplootdachi v ploskom kanale s otryvom i prisoedineniem vozdushnogo potoka. Mezhvuzovskii tematicheskii sbornik nauchnykh trudov “Intensifikatsiya teplomassoobmena v energeticheskikh ustanovkakh”. M.: MEI; 1985;54:84 - 91. [Velichko V.I., Pronin V.A. Calculation of heat transfer in a flat channel with separation and addition of air flow. Interuniversity thematic collection of scientific papers “Intensification of heat and mass transfer in power plants”. M.: MEI; 1985;54:84 - 91. (in Russ.)]

9. Migai V.K. K teorii teploobmena v turbulentnom potoke s otryvom. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza. 1967;2:170 - 174. [Migai V.K. To the theory of heat transfer in a turbulent flow with separation. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza. 1967;2:170 - 174. (in Russ.)]

10. Migai V.K., Firsova E.V. Teploobmen i gidravlicheskoe soprotivlenie v puchkakh trub. L.: Nauka; 1986. 195 s. [Migai V.K., Firsova E.V. Heat transfer and hydraulic resistance in pipe stacks. L.: Nauka; 1986. 195 p. (in Russ.)]

11. Lobanov I.E., Myakochin A.S., Nizovitin A.A. Modelirovanie intensifitsirovannogo teploobmena pri turbulentnom techenii v trubakh s turbulizatorami na baze uravneniya balansa turbulentnoi pul'satsionnoi energii. Vestnik MAI. 2007;14(4):13 - 22. [Lobanov I.E., Myakochin A.S., Nizovitin A.AModeling of intensified heat transfer in turbulent flow in pipes with turbulators based on the balance equation of turbulent pulsating energy. Vestnik MAI. 2007;14(4):13 - 22. (in Russ.)]

12. Lobanov I.E., Dreitser G.A. Matematicheskoe modelirovanie predel'nogo teploobmena za schet turbulizatsii potoka pri turbulentnom techenii v ploskikh kanalakh s odnostoronnimi turbulizatorami. Tekhnika i tekhnologiya. 2010;5:19 - 31. [Lobanov I.E., Dreitser G.A. Mathematical modeling of limiting heat transfer due to flow turbulence under turbulent flow in flat channels with one-side turbulators. Engineering & Technologies. 2010; 5:19 - 31. (in Russ.)]

13. Lobanov I.E., Paramonov N.V. Matematicheskoe modelirovanie predel'nogo teploobmena za schet turbulizatsii potoka pri turbulentnom techenii v ploskikh kanalakh s turbulizatorami na odnoi poverkhnosti. Tezisy dokladov 9 Mezhdunarodnoi konferentsii “Aviatsiya i kosmonavtika – 2010”. SPb.: Masterskaya pechati; 2010. S. 170—171. [Lobanov I.E., Paramonov N.V. Mathematical modeling of limiting heat transfer due to flow turbulence under turbulent flow in flat channels with turbulators located on one surface. Abstracts of the 9th International Conference “Aviation and Cosmonautics – 2010”. SPb.: Masterskaya pechati; 2010. P. 170 - 171. (in Russ.)]

14. Lobanov I.E., Fleytlikh B.B. Modelirovanie intensifitsirovannogo teploobmena pri turbulentnom techenii v ploskikh kanalakh s periodicheskipoverkhnostnoraspolozhennymi turbulizatoramipotokanabazesemisloynoymodeliturbulentnogopogranichnogosloya. Fundamental'nye i prikladnye problemy tekhniki i tekhnologii. 2011;2(286):42-50. [Lobanov I.E., Fleytlikh B.B. Modeling of intensified heatexchange under the turbulent flow in the flat channels with flow turbulisators, periodically situated on the surface, based on 7-layer model of turbulent boundary layer. Fundamental and Applied Problems of Technics and technology. 2011;2(286):42-50. (in Russ.)]

15. Lobanov I.E., Fleytlikh B.B. Modelirovanie intensifitsirovannogo teploobmena pri turbulentnom techenii v ploskikh kanalakh s periodicheski poverkhnostno raspolozhennymi turbulizatorami potoka na baze semisloynoy modeli turbulentnogo pogranichnogo sloya. Tezisy Mezhdunarodnoy nauchnoy shkoly “Problemy gazodinamiki i teploobmena v energeticheskikh tekhnologiyakh”. Moskva; 2011. S. 50-52. [Lobanov I.E., Fleytlikh B.B. Modeling of intensified heat-exchange under the turbulent flow in the flat channels with flow turbulisators, periodically situated on the surface, based on 7-layer model of turbulent boundary layer. Abstracts of International scientific school “Problems of gas dynamics and heat-exchange in energetic technologies ”. Moscow; 2011. P. 50-52. (in Russ.)]

16. Lobanov I.E. Teoriya teploobmena pri turbulentnom techenii v ploskikh kanalakh s poverkhnostnoras polozhennym i odnostoronnimi turbulizatorami potoka na baze semisloynoy modeli turbulentnogo pogranichnogosloya. Moskovskoe nauchnoe obozrenie. 2012;4(1):7-12. [Lobanov I.E. Theory of heat exchange under turbulent flow in flat channels with with single-sided flow turbulisators, situated on the surface, based on 7-layer model of turbulent boundary layer. Moskovskoe nauchnoe obozrenie. 2012;4(1):7-12. (in Russ.)]

17. Lobanov I.E. Analiticheskoe reshenie zadachi ob intensifitsirovannom teploobmene pri turbulentnom techenii v ploskikh kanalakh s periodicheskipoverkhnostnoraspolozhennymiturbulizatorami potokanabazesemisloynoymodeliturbulentnogopogranichnogosloya. Nauchnoe obozrenie. 2012;2:375-387. [Lobanov I.E. Analytical solution of the problem of intensified heat exchange under turbulent flow in flat channels with flow turbulisators, periodically situated on the surface, based on 7-layer model of turbulent boundary layer. Science review. 2012;2:375-387. (in Russ.)]

18. Lobanov I.E. Teploobmen pri turbulentnom techenii vploskikh kanalakh s ravnomernoraspolozhennym i poverkhnostnymi odnostoronnimi turbulizatorami potoka. Vestnik mashinostroeniya. 2012;8:13-17. [Lobanov I.E. Heat exchange under turbulent flow in flat channels with evenly situated surface single-sided flow turbulisators. Russian Engineering Research. 2012;8:13-17. (in Russ.)]

19. Lobanov I.E. Modelirovanie intensifitsirovannogo teploobmena pri turbulentnom techenii v ploskikh kanalakh s periodicheskimi poverkhnostno raspolozhennymi turbulizatorami potoka na baze semisloinoi modeli turbulentnogo pogranichnogo sloya s korrelyatsiei s kol'tsevym kanalom. Moskovskoe nauchnoe obozrenie. 2012;12(1):11 - 19. [Lobanov I.E. Modeling of intensified heat transfer in turbulent flow in flat channels with periodic superficially located flow turbulators based on a seven-layer model of a turbulent boundary layer with correlation with a ring channel. Moskovskoe nauchnoe obozrenie. 2012;12(1):11 - 19. (in Russ.)]

20. Lobanov I.E. Analiticheskoe reshenie zadachi ob intensifitsirovannom teploobmene v ploskikh kanalakh s odnostoronnimi poverkhnostnymi turbulizatorami potoka. Otraslevye aspekty tekhnicheskikh nauk. 2013;2:4 - 13. [Lobanov I.E. Analytical solution of the problem of intensified heat exchange in flat channels with one-side surface flow turbulators. Otraslevye aspekty tehniceskih nauk. 2013; 2:4 - 13. (in Russ.)]

21. Lobanov I.E. Matematicheskoe modelirovanie predel'nogo teploobmena pri iskusstvennoi turbulizatsii potoka v ploskikh kanalakh s turbulizatorami na obeikh storonakh. Al'manakh sovremennoi nauki i obrazovaniya. 2010;7(38):62 - 71. [Lobanov I.E. Mathematical modeling of limiting heat transfer during artificial flow turbulence in flat channels with turbulators on both sides. Al'manakh sovremennoi nauki i obrazovaniya. 2010;7(38):62 - 71. (in Russ.)]

22. Lobanov I.E. Matematicheskoe modelirovanie predel'nogo teploobmena za schet turbulizatsii potoka pri turbulentnom techenii v ploskikh kanalakh s turbulizatorami na obeikh poverkhnostyakh. Tezisy dokladov 9 Mezhdunarodnoi konferentsii “Aviatsiya i kosmonavtika - 2010”. S-Pb.: Masterskaya pechati; 2010. S. 202 - 203. [Lobanov I.E. Mathematical modeling of the limit heat transfer due to flow turbulence under turbulent flow in flat channels with turbulators on both surfaces. Abstracts of the 9th International Conference “Aviation and Cosmonautics – 2010”. S-Pb.: Masterskaya pechati; 2010. P. 202 - 203. (in Russ.)]

23. Dreitser G.A., Isaev S.A., Lobanov I.E. Raschet konvektivnogo teploobmena v trubakh s periodicheskimi vystupami. Problemygidrodinamikiiteploobmenavenergeticheskikhustanovkakh. M.: Izd. MEI; 2003;1:57-60. [Dreytser G.A., Isaev S.A., Lobanov I.E. Calculation of convective heat exchange in pipes with periodical protrusions. The problems of hydro-dynamics and heat exchange in energetic facilities. Moscow: Izd. MEI; 2003;1:57-60. (in Russ.)]

24. Dreitser G.A., Isaev S.A., Lobanov I.E. Raschet konvektivnogo teploobmena v trube s periodicheskimi vystupami. Vestnik MAI. 2004;11(2):28 - 35. [Dreitser G.A., Isaev S.A., Lobanov I.E. Calculation of convective heat transfer in a pipe with periodic protrusions. Vestnik MAI. 2004;11(2):28 - 35. (in Russ.)]

25. Dreitser G.A., Isaev S.A., Lobanov I.E. Raschet konvektivnogo teploobmena v trube s periodicheski raspolozhennymi poverkhnostnymi turbulizatorami potoka. Teplofizika vysokikh temperatur. 2005;43(2):223 - 230. [Dreitser G.A., Isaev S.A., Lobanov I.E. Calculation of convective heat transfer in a pipe with periodically located surface flow turbulators. High Temperature. 2005;43(2):223 - 230. (in Russ.)]

26. Kalinin E.K., Lobanov I.E. Problemy issledovaniya teploobmennykh protsessov pri techeniyakh odnofaznykh sred na etape uspeshnogo razvitiya chislennogo modelirovaniya. Tezisy dokladov i soobshchenii VI Minskogo mezhdunarodnogo foruma po teplomassoobmenu. Minsk. 2008;1:101 - 103. [Kalinin E.K., Lobanov I.E. Problems of investigating heat transfer processes during single-phase medium flows at the stage of successful development of numerical simulation. Abstarcts of the VI Minsk International Forum on Heat and Mass Transfer. Minsk. 2008;1:101 - 103. (in Russ.)]

27. Kalinin E.K., Lobanov I.E. Problemy issledovaniya teploobmennykh protsessov pri techeniyakh odnofaznykh sred na etape uspeshnogo razvitiya chislennogo modelirovaniya. Trudy VI Minskogo mezhdunarodnogo foruma po teplomassoobmenu. Sektsiya № 1. Konvektivnyi teplomassoobmen. Minsk; 2008. Doklad № 1—27. S. 1—10. [Kalinin E.K., Lobanov I.E. Problems of investigating heat transfer processes during single-phase medium flows at the stage of successful development of numerical simulation. Proceedings of the VI Minsk International Forum on Heat and Mass Transfer. Section 1. Convective heat and mass transfer. Minsk; 2008. Report № 1 - 27. P. 1 - 10. (in Russ.)]

28. Isaev S.A., Myakochin A.S., Nizovitin A.A., Lobanov I.E., Boyarkina O.A. Vikhrevaya intensifikatsiya konvektivnogo teploobmena pri turbulentnom techenii vozdukha i masla v trubakh i kanalakh s periodicheskimi elementami diskretnoi sherokhovatosti. Trudy Pyatoi Rossiiskoi natsional'noi konferentsii po teploobmenu. V 8 tomakh. Tom 6. Intensifikatsiya teploobmena. Radiatsionnyi i slozhnyi teploobmen. M.: MEI; 2010. S. 84—87. [Isaev S.A., Myakochin A.S., Nizovitin A.A., Lobanov I.E., Boyarkina O.A. Vortex intensification of convective heat transfer in turbulent flow of air and oil in pipes and channels with periodic elements of discrete roughness. Proceedings of the Fifth Russian National Conference on Heat Transfer. In 8 volumes. Volume 6. Heat exchange intensification. Radiation and complex heat transfer. Moscow: MEI; 2010. P. 84 - 87. (in Russ.)]

29. Isaev S.A., Baranov P.A., Gotovskii M.A., Myakochin A.S., Nizovitin A.A., Lobanov I.E. Intensifikatsiya teploobmena v trubakh s ob"emnymi i poverkhnostnymi vikhregeneratorami dlya neodnorodnykh teplonositelei. Tezisy dokladov Chetvertoi mezhdunarodnoi konferentsii “Teplomassoobmen i gidrodinamika v zakruchennykh potokakh”. M.: Izdatel'skii dom MEI; 2011. S. 66. [Isaev S.A., Baranov P.A., Gotovskii M.A., Myakochin A.S., Nizovitin A.A., Lobanov I.E. Intensification of heat exchange in pipes with volumetric and surface vortex generators for inhomogeneous heat carriers. Abstracts of the reports of the Fourth International Conference “Heat and mass exchange and hydrodynamics in vortex flows”. Moscow: Izdatel'skii dom MEI; 2011. P. 66. (in Russ.)]

30. Isaev S.A., Baranov P.A., Gotovskii M.A., Myakochin A.S., Nizovitin A.A., Lobanov I.E. Intensifikatsiya teploobmena v trubakh s ob"emnymi i poverkhnostnymi vikhregeneratorami dlya neodnorodnykh teplonositelei. Sbornik dokladov Chetvertoi mezhdunarodnoi konferentsii “Teplomassoobmen i gidrodinamika v zakruchennykh potokakh”. M., 2011. Sektsiya 2. Doklad № 20. S. 1 - 34. [Isaev S.A., Baranov P.A., Gotovskii M.A., Myakochin A.S., Nizovitin A.A., Lobanov I.E. Intensification of heat exchange in pipes with volumetric and surface vortex generators for inhomogeneous heat carriers. Collected papers of the Fourth International Conference “Heat and mass transfer and hydrodynamics in swirling flows”. Moscow, 2011. Section 2. Report № 20. P. 1 - 34. (in Russ.)]

31. Lobanov I.E. Teoreticheskoe issledovanie struktury vikhrevykh zon mezhdu periodicheskimi, poverkhnostno raspolozhennymi turbulizatorami potoka pryamougol'nogo poperechnogo secheniya. Izvestiya vuzov. Aviatsionnaya tekhnika. 2011; 4:64 - 66. [Lobanov I.E. Theoretical study of the structure of vortex zones between periodic, superficially located flow turbulators of a rectangular cross-sectional flow. Izv. VUZ. Aviatsionnaya Tekhnika. 2011;4:64 - 66. (in Russ.)]

32. Lobanov I.E., Kalinin E.K. Teoreticheskoe issledovanie, sopostavlenie s eksperimentom linii toka i sostavlyayushchikh kineticheskoi energii turbulentnykh pul'satsii v vikhrevykh strukturakh v trubakh s turbulizatorami. Otraslevye aspekty tekhnicheskikh nauk. 2011;12:4 - 15. [Lobanov I.E., Kalinin E.K. Theoretical study, comparison with experiment of streamlines and components of the kinetic energy of turbulent pulsations in vortex structures in pipes with turbulators. Otraslevye aspekty tekhnicheskikh nauk. 2011;12:4 - 15. (in Russ.)]

33. Lobanov I.E. Modelirovanie struktury vikhrevykh zon mezhdu periodicheskimi poverkhnostno raspolozhennymi turbulizatorami potoka pryamougol'nogo poperechnogo secheniya. Matematicheskoe modelirovanie. 2012;24(7):45 - 58. [Lobanov I.E. Modeling of the structure of vortex zones between periodic superficially placed flow turbulators of a rectangular cross-sectional flow. Mathematical Models and Computer Simulations. 2012;24(7):45 - 58. (in Russ.)]

34. Lobanov I.E. Matematicheskoe modelirovanie struktury vikhrevykh zon mezhdu periodicheskimi poverkhnostno raspolozhennymi turbulizatorami potoka polukruglogo i kvadratnogo poperechnogo secheniya. Otraslevye aspekty tekhnicheskikh nauk. 2012;9:11 - 30. [Lobanov I.E. Mathematical modeling of the structure of vortex zones between periodic superficially located flow turbulators of a semicircular and square cross-sectional flow. Otraslevye aspekty tekhnicheskikh nauk. 2012;9:11 - 30. (in Russ.)]

35. Lobanov I.E. Matematicheskoe modelirovanie intensifitsirovannogo teploobmena pri turbulentnom techenii v kanalakh. Dissertatsiya na soiskanie uchenoy stepeni doktora tekhnicheskikh nauk. Moskva; 2005. 632 s. [Lobanov I.E. Mathematical modeling of intensified heat-exchange under the turbulent flow in the channels. Doctor of technical sciences dissertation. Moscow; 2005. 632 p. (in Russ.)]

36. Lobanov I.E., ShteynL.M. Perspektivnye teploobmennye apparatysintensifitsirovannym teploobmenom dlya metallurgicheskogoproizvodstva. (Obshchayateoriyaintensifitsirovannogoteploobmenadlyateploobmennykhapparatov, primenyaemykhv sovremennom metallurgicheskom proizvodstve.) V 4-khtomakh. TomI. Matematicheskoe modelirovanie intensifitsirovannogoteploobmenapriturbulentnomtecheniivkanalakhsprimeneniemosnovnykhanaliticheskikhichislennykhmetodov. M.: Izdatel'stvo Assotsiatsii stroitel'nykh vuzov; 2009. 405 s. [Lobanov I.E., Shteyn L.M. Perspective heat-exchange apparatus with intensified heat-exchange for metallurgical production. (General theory of intensified heat-exchange for heat-exchange apparatus used in modern metallurgical production). In 4 volumes. Volume I. Mathematical modeling of intensified heat-exchange under the turbulent flow in channels using major analytical and numeric methods. Moscow: Izdatel'stvo Assotsiatsii stroitel'nykh vuzov; 2009. 405 p. (in Russ.)]

37. Bystrov Yu.A., Isaev S.A., Kudryavtsev H.A.i dr. Chislennoe modelirovanie vikhrevoi intensifikatsii teploobmena v paketakh trub. S-Pb: Sudostroenie; 2005. 398 s. [Bystrov Yu.A., Isaev S.A., Kudryavtsev H.A.etal. Numerical simulation of vortex intensification of heat exchange in pipe stacks. S-Pb: Sudostroenie; 2005. 398 p. (in Russ.)]

38. Ashrafian A., AnderssonH.I. RoughnessEffectsinTurbulentChannelFlow. Turbulence, HeatTransferandMassTransfer 4. NewYork, Wellington (UK): Begell House Inc.; 2003. Р. 425 - 432.

39. Lobanov I.E., Paramonov N.V. Matematicheskoe modelirovanie intensifitsirovannogo teploobmena pri techenii v kanalakh na osnove slozhnykh modelei turbulentnogo pogranichnogo sloya. M.: Izdatel'stvo MAI; 2011. 160 s. [Lobanov I.E., Paramonov N.V. Mathematical modeling of intensified heat transfer during flow in channels based on complex models of the turbulent boundary layer. M.: Izdatel'stvo MAI; 2011. 160 p. (in Russ.)]

40. Lobanov I.E. Modelirovanie intensifitsirovannogo teploobmena i ego stratifikatsii pri turbulentnom techenii v trubakh s turbulizatorami v shirokom diapazone geometricheskikh i rezhimnykh parametrov. Otraslevye aspekty tekhnicheskikh nauk. 2012;8:3 - 22. [Lobanov I.E. Modeling of intensified heat exchange and its stratification under turbulent flow in pipes with turbulators in a wide range of geometric and regime parameters. Otraslevye aspekty tehniceskih nauk. 2012;8:3 - 22 (in Russ.)]


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Lobanov I.E. MATHEMATICAL LOW-REYNOLDS MODELING OF HEAT EXCHANGE IIN TURBULENT FLOW IN FLAT CHANNELS WITH TURBULATORS SYMMETRICALLY LOCATED ON BOTH SIDES. Herald of Dagestan State Technical University. Technical Sciences. 2018;45(2):70-93. (In Russ.) https://doi.org/10.21822/2073-6185-2018-45-2-70-93

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