### Abstract

In this paper calculations are made of the two-dimensional flow field of an incompressible viscous fluid in a long parallel-sided channel whose walls pulsate in a prescribed way. The study covers all values of the unsteadiness parameter alpha and the steady-streaming Reynolds number. The wall motion is, in general, assumed to be of small amplitude and sinusoidal. Particular attention is given to the steady component of the flow at second order in the amplitude parameter epsilon . Next the following problem is considered: the calculation of the wall motion which will result, in response to prescribed unsteady pressures imposed at the ends of the channel and outside its walls, if the walls are assumed to respond elastically to variations in transmural pressure. It is found that the system has a natural frequency of oscillation, and that resonance will occur if this frequency is close to a multiple of the frequency of the external pressure fluctuations. Finally the work is applied in a discussion of blood flow in the coronary arteries of large mammals. Refs.

Original language | English (US) |
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Pages (from-to) | 273-288 |

Number of pages | 16 |

Journal | Journal of Fluid Mechanics |

Volume | 88 |

Issue number | pt 2 |

Publication status | Published - Jan 1 1978 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*88*(pt 2), 273-288.