On the Efficiency of Cooling Surfaces with Fins Containing Internal Heat Sources

Characteristics of heat transfer in the fins (rods) that contain internal heat sources uniformly distributed within their volume are considered. The analytical relationships are obtained that allow the effectiveness of finned surface to be analyzed and evaluated. As a practical application, a problem is considered regarding the use of such fins in the design of powerful water-cooled gas-discharge radiation sources, in which the sheath can be made of leuco sapphire. It is shown that the internal heat release in the fins reduces heat removal from the cooled wall as compared to the fins without internal heat sources. At the levels of heat release that are typical for powerful gas-discharge radiation sources, the internal heat release in the fins has little effect on their efficiency. It is noted that the addition of fins to the sheaths made of leuco sapphire markedly increases the efficiency of their cooling, reduces the consumption of coolant, and consequently reduces hydraulic resistance of the flow path. However, the technology of manufacturing the sheaths with thin fins made of brittle material and difficulties of their exploitation become critically important in this case.

References

[1] Sychkov A.E. The role of efficient cooling systems in contemporary compressor units. Spetsializirovannyy inform.-analiticheskiy zhurnal "MegaPaskal" [Special. Iinform. Analyt. J. "MegaPascal"], 2009, no. 4, pp. 36-40 (in Russ.).

[2] Chichindaev A.V. Optimizatsiya kompaktnykh plastinchato-rebristykh teploobmennikov. Ch. 1. Teoreticheskie osnovy [Optimization of compact plate-fin heat exchangers. Part 1. Theoretical Foundations]. Novosibirsk, NGTU Publ., 2003. 399 p.

[3] Kuntysh V.B., Kuznetsov N.M. Teplovoy i aerodinamicheskie raschety teploobmennikov vozdushnogo okhlazhdeniya [Thermal and aerodynamic analysis of air cooled exchanger]. St. Petersburg, Energoatomizdat Publ., 1992. 280 p.

[4] Arkharov A.M., Arkharov I.A., Belyakov V.P., Smorodin A.I., eds. Kriogennye sistemy. V 2 t. T. 2. Osnovy proektirovaniya apparatov, ustanovok i system. Vtor. izd. dopoln. i pererab [Cryogenic systems. In 2 volumes. V.2. Eengineering foundation of apparatus, machine and systems]. Moscow, Mashinostroenie Publ., 1999. 720 p.

[5] Dul’nev G.N. Teplo- i massoobmen v radioelektronnoy apparature [Heat-and-mass transfer in communications electronics equipment]. Moscow, Vysshaya Shkola Publ., 1984. 248 p.

[6] Rotkop L.L., Spokoynyy Yu.E. Obespechenie teplovykh rezhimov pri konstruirovanii radioelektronnoy apparatury [Ensuring the thermal regime in designing of communications electronics equipment]. Moscow, Sovetskoe Radio Publ., 1976. 232 p.

[7] Dobrovol’skiy M.V. Zhidkostnye raketnye dvigateli [Liquid rocket engine]. Moscow, MGTU im. N.E. Baumana Publ., 2011. 486 p.

[8] Kudryavtseva N.S. Osnovy proektirovaniya effektivnykh sistem termoregulirovaniya kosmicheskikh apparatov [Engineering foundation effective systems of spacecraft temperature control]. Moscow, MAI Publ., 2012. 226 p.

[9] Mackay Donald B. Design of space powerplant. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. 332 p. (Russ. ed.: Donal’d B. Makkey. Konstruirovanie kosmicheskikh silovykh ustanovok. Moscow, Mashinostroenie Publ., 1966. 348 p.).

[10] Favorskiy O.N., Kadaner Ya.S. Voprosy teploobmena v kosmose [Problems of heat transfer in space]. Moscow, Vysshaya Shkola Publ., 1972. 280 p.

[11] Vydrik G.A., Solov’eva T.V., Kharitonov F.Ya. Prozrachnaya keramika [The transparent ceramics]. Moscow, Energiya Publ., 1980. 96 p.

[12] Vetrov V.N. Opticheskie svoystva i tekhnologiya plasticheski deformirovannykh kristallov. Diss. dokt. tekhn. nauk [Optical properties and the technology of plastically deformed crystal. Dr. tech. sci. diss.]. S.Pb, 2012. 311 p.

[13] Thermal and physical properties of aluminum and magnesium oxide Al2O3, MgO. Electronic reference book of thermal physics. Available at http://thermalinfo.ru/publ/tverdye_veshhestva/oksidy/teploemkost_oksida_aljuminija_i_magnija/21-1-0-209 (accessed 02.02.2014) (in Russ.).

[14] Polezhaev Yu.V. Be or not to be hypersonic aircraft? Inzhenerno-fizicheskiy zhurnal [Journal of Engineering Physics and Thermophysics], 2000, vol. 73, no. 1, pp. 5-10 (in Russ.).

[15] Zheleznyakova A.L., Surzhikov S.T. Numerical simulation of hypersonic flow-past for the aircraft model X-43. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2010, no. 1, pp. 3-19 (in Russ.).

[16] Eliseev V.N., Tovstonog V.A. The analysis of engineering capabilities creation of highly effective facilities with radiate heating for heat tests of aerospace equipment. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2011, no. 1, pp. 57-70 (in Russ.).

[17] Merzlikin V., Timonin V., Ojeda M.G., Sidorov O. New selectively absorbing and scattering heat-insulating coatings of the combustion chamber for low-heat-rejection diesel. SAE Technical Papers, 2007, paper 2007-24-0066, pp. 1-12. DOI: 10.4271/2007-01-1755

[18] Merzlikin V., Timonin V., Tovstonog V. Optimal spectral optical and thermo radiating characteristics of semitransparent heat-insulating coatings for low-heat-rejection diesel engines. SAE Technical Papers. 9th Int. Conf. on Eng. for Automobile-ICE2009. Capri-Naples, 2009, paper ICE09-0037, pp. 1-8 (Book Abstr. ICE2009, p. 41). DOI: 10.4271/2009-24-0116

[19] Merzlikin V.G., Bekaev A.A., Sutugin V.G., Kuznetsov Yu.A. Semitransparent heat-insulating coating with reflective oxidized sublayer. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2012, no. 4, pp. 16-29 (in Russ.).

[20] Krass, M.S., Merzlikin, V.G. Radiatsionnaya teplofizika snega i l’da [Radiative thermal physics of snow and ice]. Leningrad, Gidrometeoizdat Publ., 1990. 261 p.

[21] Merzlikin, V., Krass, M., Cheranev, S., Aloric, A. Simulation of the ocean’s spectral radiant thermal source and boundary conditions. AIP Conference Proceedings, 2013, vol. 1531, pp. 947-950. DOI: 10.1063/1.4804928

[22] Eliseev V.N. On the calculation of radiative-conductive heat exchange in a system with closed partially transparent shell. [Journal of Engineering Physics and Thermophysics], 2000, vol. 73, no. 1, pp. 107-112 (in Russ.).

[23] Zarubin V.S. On the optimum finning geometry for heat exchange surface. Izv. Vyssh. Uchebn. Zaved., Mashinostr. [Proc. Univ., Mech. Eng.], 1968, no. 3, pp. 87-92 (in Russ.).

[24] Zarubin V.S. Temperaturnye polya v konstruktsii letatel’nykh apparatov [Temperature fields in the aircraft design]. Moscow, Mashinostroenie Publ., 1966. 216 p.