Mathematical Problems in Engineering

Mathematical Problems in Engineering / 1996 / Article

Open Access

Volume 3 |Article ID 913017 | https://doi.org/10.1155/S1024123X97000495

Xanming Wang, Huaijin Gu, Duli Yu, "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, vol. 3, Article ID 913017, 20 pages, 1996. https://doi.org/10.1155/S1024123X97000495

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

Received07 Mar 1996

Abstract

A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2+(1/r)dy/dr+λ2(βr2)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.

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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