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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1006 HIGHER-ORDER PARTIAL DIFFERENTIAL EQUATIONS
Example 11.1. Consider the problem of a slow (Stokes) inflow of a viscous fluid into a ha lf-
plane thro ugh a slit of width 2a at a constant velocity U that ma kes an angle β with the normal to
the boundary (the angle is measured off from the nor mal direction counterclockwise).
With the stream function w introduced by the relations v
x
=
∂w
∂y
and v
y
=
∂w
∂x
(v
x
and v
y
are
the fluid velocity c omponents), the problem is reduced to the specia l case of the previous problem
with
f(x) =
(
U cos β fo r |x| < a,
0 for |x| > a,
g(x) =
(
U sin β for |x| < a,
0 for |x| > a.
Dean’s solution:
w(x, y) =
U
π
(x a) cos β + y sin
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Publisher Resources

ISBN: 9781466581494