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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
8-88 Diff erential Equations
8.13.9 Laplace’s Equation or Potential Equation
or Two-dimensional Steady-state
Heat Flow Equation
The two-dimensional heat conduction equation is given by
()
22
22
22 2
, where is the Laplacian operator
xy
u
au
t
∂∂
∂∂
==+
——
In the case of steady-state heat fl ow
/0ut∂∂=
and equation reduces to
22
2
22
0
uu
u
xy
∂∂
=+=
∂∂
The solution u(x, y ) of the abo
ve equation can be obtained by the
method of separation of variab
les in a rectangular region both in the
Dirichlet problem as well as in Neumann’s problem. A rectangular thin
plate with its two faces insulated is considered so that the heat fl ow is
two-dimensional. The boundary conditions ...
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Publisher Resources

ISBN: 9781299487406Publisher Website