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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
Chapter 3
Second-Order
Parabolic Equations
with One Space Variable
3.1 Constant Coefficient Equations
3.1.1 H eat Equation
∂w
∂t
= a
2
w
∂x
2
This equation is often encountered in the theory of heat and mass transfer. It describes one-
dimensional unsteady thermal processes in quiescent media or solids with constant thermal
diffusivity. A similar equation is used in studying corresponding one-dimensional unsteady
mass-exchange processes w ith constant diffusivity.
Particular solutions (A, B, and µ are arbitrary constants).
w(x) = Ax + B,
w(x, t) = A(x
2
+ 2at) + B,
w(x, t) = A(x
3
+ 6atx) + B,
w(x, t) = A(x
4
+ 12atx
2
+ 12a
2
t
2
) + B,
w(x, t) = A(x
5
+ 20atx
3
+ 60a
2
t
2
x)
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Publisher Resources

ISBN: 9781466581494