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Solution of Characteristic Problems

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Theory of Periodic Conjugate Heat Transfer

Part of the book series: Mathematical Engineering ((MATHENGIN,volume 5))

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Abstract

The main objective of the analysis presented in this chapter consists in finding solutions allowing calculating the factor of conjugation (FC), whose definition is given by (2.13)[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. After substitution of the equations for the temperature oscillations (2.9a), (2.9b) together with (2.11) for the THTC in the boundary condition (BC) (2.10), multiplication of the infinite Fourier series in the left-hand side of (2.10) and orthogonalization [16], it is possible in principle to determine both complex conjugate eigenvalues of this boundary problem A n , A n ∗ and the FC.

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Notes

  1. 1.

    The theory of positive chain fractions is based on three fundamental theorems that are proved in [20] using the method of mathematical induction. A generalization of one of these fundamental theorems for a case of the chain fraction with an arbitrary sign is given in Appendix C.

References

  1. Y.B. Zudin, D.A. Labuntsov, Peculiarities of heat transfer at periodic asymmetrical regime. Works of Moscow Power Engineering Institute 377, 35–39 (1978) (in Russian)

    Google Scholar 

  2. Y.B. Zudin, Analysis of heat-transfer processes of periodic intensity. Dissertation. Moscow Power Engineering Institute (1980) (in Russian)

    Google Scholar 

  3. D.A. Labuntsov, Y.B. Zudin, Heat-Transfer Processes of Periodic Intensity (Energoatomizdat, Moscow, 1984) (in Russian)

    Google Scholar 

  4. Y.B. Zudin, A method of heat-exchange calculation in the presence of periodic intensity fluctuations. High Temp. 29, 921–928 (1991)

    Google Scholar 

  5. Y.B. Zudin, Calculation of effect for supplying heat to the wall on the averaged heat exchange coefficient. Thermophys. Aeromech. 1, 117–119 (1994)

    Google Scholar 

  6. Y.B. Zudin, Design of the wall heat effect on averaged convective heat transfer in processes of heat exchange with periodic intensity. Appl. Ener. Russ. J. Fuel Power Heat Syst. 33, 76–81 (1995)

    Google Scholar 

  7. Y.B. Zudin, Pulse law of true heat transfer coefficient pulsations. Appl. Ener. Russ. J. Fuel Power Heat Syst. 34, 142–147 (1996)

    Google Scholar 

  8. Y.B. Zudin, Theory on Heat-Transfer Processes of Periodic Intensity. Habilitationsschrift (Moscow Power Engineering Institute, Moscow, 1996) (in Russian)

    Google Scholar 

  9. Y.B. Zudin, Effect of the thermophysical properties of the wall on the heat transfer coefficient. Therm. Eng. 45(3), 206–209 (1998)

    Google Scholar 

  10. Y.B. Zudin, Temperature waves on a wall surface. Russ. Dokl. Phys. J. Acad. Sci. 43(5), 313–314 (1998)

    Google Scholar 

  11. Y.B. Zudin, The effect of the method for supplying heat to the wall on the averaged heat-transfer coefficient in periodic rate heat-transfer processes. Therm. Eng. 46(3), 239–243 (1999)

    Google Scholar 

  12. Y.B. Zudin, Harmonic law of fluctuations of the true heat transfer coefficient. Thermophys. Aeromech. 6, 79–88 (1999)

    Google Scholar 

  13. Y.B. Zudin, Self-oscillating process of heat exchange with periodic intensity. J. Eng. Phys. Thermophys. 72, 635–641 (1999)

    Article  Google Scholar 

  14. Y.B. Zudin, Processes of heat exchange with periodic intensity. Therm. Eng. 47(6), 124–128 (2000)

    Google Scholar 

  15. Y.B. Zudin, Averaging of the heat-transfer coefficient in the processes of heat exchange with periodic intensity. J. Eng. Phys. Thermophys. 73, 643–647 (2000)

    Article  Google Scholar 

  16. E.M. Stein, R. Shakarchi, Fourier Analysis: An Introduction (Princeton University Press, Princeton, 2003)

    MATH  Google Scholar 

  17. P.V. Tsoi, V.P. Tsoi, A method of representing nonstationary temperature fields in the best approximations. High Temp. 40, 456–468 (2002)

    Article  Google Scholar 

  18. H.D. Baehr, K. Stephan, Heat and Mass Transfer (Springer, Berlin, 1998)

    MATH  Google Scholar 

  19. C. Dietz, M. Henze, S.O. Neumann J. von Wolfersdorf, B. Weigand, Numerical and experimental investigation of heat transfer and fluid flow around a vortex generator using explicit algebraic models for the turbulent heat flux. Proceedings of the 17th International Symposium on Airbreathing Engines, September 4–9, Munich, Germany, Paper ISABE-2005–1197, (2005)

    Google Scholar 

  20. A.Ya. Khinchin, Continued Fractions (Dover, New York, 1997)

    Google Scholar 

  21. R. Sauer, I. Szabo, Mathemati sche Hilfsmittel des Ingenieurs, Teil 1–4 (Springer, Berlin, 1969)

    Google Scholar 

  22. L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis (P. Noordho, Groningen, 1958)

    MATH  Google Scholar 

  23. M. Abramovitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1974)

    Google Scholar 

  24. I.N. Bronstein, K.A. Semendjajew, G. Musiol, H. Mühlig, Taschenbuch der Mathematik (Verlag Harry Deutsch, Frankfurt, 2005)

    Google Scholar 

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Authors and Affiliations

  1. Russian State Atomic Energy Corporation Russian Nuclear-Power Machine Building, Research Institute, u. Kosmonavta Volkova 6a, 125171, Moskva, Russia

    Professor Dr.-Ing. habil. Yuri B. Zudin

Authors
  1. Professor Dr.-Ing. habil. Yuri B. Zudin
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Correspondence to Yuri B. Zudin .

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Zudin, Y.B. (2012). Solution of Characteristic Problems. In: Theory of Periodic Conjugate Heat Transfer. Mathematical Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21421-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-21421-9_3

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  • Print ISBN: 978-3-642-21420-2

  • Online ISBN: 978-3-642-21421-9

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