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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 4
Second-Order
Parabolic Equations
with Two Space Variables
4.1 Heat Equation
∂w
∂t
= a
2
w
4.1.1 B o u ndary Value Problems i n Cartesian Coordinates
In rectangular Cartesian coordinates, the two-dimensional sourceless heat equation has the
form
∂w
∂t
= a
2
w
∂x
2
+
2
w
∂y
2
.
It governs two-dimensional unsteady heat transfer processes in quiescent media or solid
bodies with constant thermal diffusivity a. A similar equation is used to study analogous
two-dimensional unsteady m ass transfer phenomena with constant diffusivity; in this case
the equation is called a diffusion equation.
Particular solutions:
w(x, y) = Axy + C
1
x + C
2
y + C
3
,
w(x, y, t) = Ax
2
+
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Publisher Resources

ISBN: 9781466581494