Integral Method of Boundary Characteristics: Neumann Condition

  • V. A. Kot

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.


heat-conduction equation integral method of heat balance thermal-disturbance front 


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  1. 1.
    T. R. Goodman, Application of integral methods to transient nonlinear heat transfer, Adv. Heat Transf., Academic Press, New York (1964), Vol. 1, pp. 51–122.Google Scholar
  2. 2.
    A. S. Wood, A new look at the heat balance integral method, Appl. Math. Model., 25, No. 10, 815–824 (2001).CrossRefzbMATHGoogle Scholar
  3. 3.
    J. Hristov, The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and exercises, Thermal Sci., 13, No 2, 27–48 (2009).CrossRefGoogle Scholar
  4. 4.
    S. L. Mitchell and T. G. Myers, Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions, Int. J. Heat Mass Transf., 53, No. 17, 3540–3551 (2010).CrossRefzbMATHGoogle Scholar
  5. 5.
    D. Langford, The heat balance integral method, Int. J. Heat Mass Transf., 16, No. 12, 2424–2428 (1973).CrossRefGoogle Scholar
  6. 6.
    T. G. Myers, Optimizing the exponent in the heat balance and refined integral methods, Int. Commun. Heat Mass Transf., 36, No 2, 143–147 (2009).CrossRefGoogle Scholar
  7. 7.
    T. R. Goodman, The heat-balance integral — further considerations and refinements, Trans. ASME, Ser. C, No. 1, 83–93 (1961).Google Scholar
  8. 8.
    F. M. Fedorov, Boundary Method for Solving Applied Problems of Mathematical Physics [in Russian], Nauka, Novosibirsk (2000).Google Scholar
  9. 9.
    E. V. Stefanyuk, Additional Boundary Conditions in Boundary-Value Heat-Conduction Problems [in Russian], Samara State Tech. Univ., Samara (2004).Google Scholar
  10. 10.
    V. A. Kot, Method of boundary characteristics, J. Eng. Phys. Thermophys., 88, No. 6, 1390–1408 (2015).CrossRefGoogle Scholar
  11. 11.
    V. A. Kot, Boundary characteristics for the generalized heat-conduction equation and their equivalent representations, J. Eng. Phys. Thermophys., 89, No. 4, 985–1007 (2016).CrossRefGoogle Scholar
  12. 12.
    V. A. Kot, The boundary function method. Fundamentals, J. Eng. Phys. Thermophys., 90, No. 2, 366–391 (2017).CrossRefGoogle Scholar
  13. 13.
    H. S. Carslow and J. C. Jaeger, Conduction of Heat in Solids, 2nd edn., Oxford University Press, Oxford, UK (1992).Google Scholar
  14. 14.
    G. D. Gureev and M. D. Gureev, Influence of the time form of a laser pulse on the change in the surface temperature at the heating stage, Vestn. Samarsk. Gos. Tekh. Univ., Ser.: Fiz.-Mat. Nauk, No. 1 (16), 130–135 (2008).Google Scholar
  15. 15.
    N. N. Rykalin, Calculations of Thermal Processes in Welding [in Russian], Mashinostroenie, Moscow (1951).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of BelarusMinskBelarus

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