On the solution of the differential equation occurring in the problem of heat convection in laminar flow through a tube with slip—flow
A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2+(1/r)dy/dr+λ2(β−r2)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 inv...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
1996-01-01
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Series: | Mathematical Problems in Engineering |
Subjects: | |
Online Access: | http://dx.doi.org/10.1155/S1024123X97000495 |
Summary: | A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2+(1/r)dy/dr+λ2(β−r2)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. |
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ISSN: | 1024-123X 1563-5147 |