On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow (Q5961489)
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scientific article; zbMATH DE number 980897
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow |
scientific article; zbMATH DE number 980897 |
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On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow (English)
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3 February 1998
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eigenvalue problem
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asymptotic distribution of eigenvalues
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forced convection
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The eigenvalue problem NEWLINE\[NEWLINEy''+{\textstyle{1\over r}}y'+\lambda(\beta-r^2)y=0,\quad r\in[0,1], \;y(0)=1, y(1)=0NEWLINE\]NEWLINE for \(\beta\geq 1\), which arises for convection heat transfer in laminar flow through a circular tube, is considered. The technique of power series expansions is applied for obtaining asymptotic formula for large eigenvalues and a computational algorithm for small eigenvalues. The results are compared with ones obtained in the fifties. Elements of modern spectral approximation theory are not applied.
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