WOLFRAM NOTEBOOK

A Parabolic Partial Differential Equation in Three Different Geometries

t
0.1
x
0.5
t
0.1
r
0.5
t
0.1
r
0.5
t
x
U(x, t)
0.1
0.5
0.72916
t
x
U(x, t)
0.1
0.5
0.60076
t
x
U(x, t)
0.1
0.5
0.46164
This Demonstration simulates the solution of a parabolic partial differential equation in three different geometries: rectangular, cylindrical, and spherical.

Details

Partial differential equations occur in diverse areas of engineering and physical sciences, for example, acoustics, aerodynamics, elasticity, electrodynamics, fluid dynamics, geophysics, heat transfer, meteorology, oceanography, optics, plasma physics, and quantum mechanics.
This Demonstration simulates solutions of the following parabolic equation:
u
t
=
1
a-1
x
x
a-1
x
u
x
,
where
a=1,2,3
applies to a rectangle, cylinder, or sphere, with the boundary conditions
u
x
=0
at
x=0
and
u(1,t)=1
and the initial condition
u(x,0)=1.
The problem has applications in transport phenomena, specifically, heat, mass, and momentum transfer.

External Links

Permanent Citation

Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.