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On the solution of the differential equation occurring in the problem of heat convection in laminar flow through a tube with slip—flow

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  • Xanming Wang
  • Huaijin Gu
  • Duli Yu

Abstract

A technique is developed for evaluation of eigenvalues in solution of the differential equation d 2 y / d r 2 + ( 1 / r ) d y / d r + λ 2 ( β − r 2 ) y = 0 which occurs in the problem of heat convection in laminar flow through a circular tube with silp-flow ( β > 1 ) . A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case of β > 1 , because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values of β were obtained.

Suggested Citation

  • Xanming Wang & Huaijin Gu & Duli Yu, 1996. "On the solution of the differential equation occurring in the problem of heat convection in laminar flow through a tube with slip—flow," Mathematical Problems in Engineering, Hindawi, vol. 3, pages 1-20, January.
    • Handle: RePEc:hin:jnlmpe:913017
    DOI: 10.1155/S1024123X97000495
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