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The fluid is confined between the planes and . Regardless of the nature
of these bounding surface we must require
at |
(21) |

since these planes are maintained at constant temperature and normal component of
velocity must vanish on these planes. There are other boundary conditions which
depends on the type of surfaces distinguished by *rigid surfaces* on which
no slip occurs and *free surfaces* on which tangential shear stresses
vanish.
First consider a rigid surface where no slip condition holds. Hence in
addition to . This with the equation of continuity implies that

on a rigid surface |
(22) |

The condition on the free surface is that the tangential stress vanish i.e.
which imply

Using equation of continuity we get
on a free surface |
(23) |

For the normal component of vorticity we have

on a free surface |
(24) |

on a rigid surface |
(25) |

In summary we have the following boundary conditions
(rigid boundary) |
(26) |

(free boundary) |
(27) |

** Next:** Normal modes
** Up:** The stability problem
** Previous:** Scaling of the equations
A/C for Homepage of Dr. S Ghorai
2003-01-16