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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
3.3. Equations Containing Power Functions and Arbitrary Parameters 321
3
. The solution of the original equation in the important special case where the drop sur-
face has a time-invariant temperature w
s
and the heat exchange occurs with an infinite
medium having an initial temperature w
0
, namely,
w = w
0
at t = 0 (initial condition ),
w = w
s
at x = 0 (boundary condition ),
w w
0
at x (boundary condition),
is expressed in terms of the error function as follows:
w w
s
w
0
w
s
= erf
2b + 1
2
a
x
t
, erf ξ =
2
π
Z
ξ
0
exp
ζ
2
dζ.
Literature: Yu. P. Gupalo, A. D. Polyanin, and Yu. S. Ryazantsev (1985).
7.
∂w
∂t
= a
2
w
∂x
2
+ (bt
k
x + ct
m
)
∂w
∂x
.
This is a special case of ...
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Publisher Resources

ISBN: 9781466581494