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Extended Stokes series: laminar flow through a heated horizontal pipe

Published online by Cambridge University Press:  26 April 2006

Milton Van Dyke
Milton Van Dyke
Affiliation:
Department of Mechanical Engineering, Stanford University. Stanford. CA 94305, USA
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Abstract

Morton's series for fully developed laminar flow through a uniformly heated horizontal pipe is simplified by assuming high Prandtl number, and then extended by computer to 31 terms in powers of a parameter that is the product of the Prandtl, Rayleigh, and Reynolds numbers. As in the analogous problems, treated previously, of flow through a loosely coiled pipe and a slowly rotating pipe, convergence is limited by a conjugate pair of square-root singularities on the imaginary axis. For the global heat flux, an Euler transformation and extraction of the nearest singularity at infinity yield an approximation in good agreement with existing experiment and numerical solution. The Nusselt number is found to grow asymptotically as the $\frac{2}{15}$-power of the parameter, whereas boundary-layer analyses have suggested a 1/5-power.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 289 - 308
Copyright
© 1990 Cambridge University Press

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