# Systems for doing mathematics by computer:
convenient tools for fluid mechanics

* Paul Boomkamp & Rob Miesen *

* Koninglijke/Shell-Laboratorium, Amsterdam *

* (Shell Research B.V.) *

* Badhuisweg 3, 1031 CM Amsterdam *

* The Netherlands *

## Abstract

Systems for doing mathematics by computer are convenient tools for
mathematical modelling in general, and in doing fluid mechanical analyses
in particular; they enable us to handle problems that would be too
complicated or too expensive without them. In the present paper, this thesis
is illustrated by the study of a fluid mechanical problem that is related
to the transport of very viscous oil. The essence of the problem is a stability
analysis of the interface of a two-fluid Poisseuille flow in a pipe, i.e.
core-annular flow, with a very viscous fluid (oil) as the core and a less viscous fluid
(water) as the annulus. It is shown that both axisymmetric as well as
non-axisymmetric interfacial wave modes will be present.
* Computer Algebra in Industry *
Edited by A.M. Cohen © 1993 John Wiley & Sons Ltd

Reproduced by permission of John Wiley & Sons Ltd, 1995

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*Computer Algebra in Industry*

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Last Update: June 24, 1997.