Steady-State Temperature Distribution in Conducting Square

​
temperatures (°C)
left
20
top
0
right
0
bottom
0
Laplace's differential equation in two dimensions,
2
∂
T(x,y)
∂
2
x
+
2
∂
T(x,y)
∂
2
y
=0,
with
T(x,y)
representing a stationary temperature field, is solved in a square region. Uniform and controllable boundary conditions along the edges (excepting the corners) are considered, in a temperature range of -300 °C to 300 °C. The resulting isotherms are plotted.

Details

Snapshot 1: borders at 0 ºC
Snapshot 2: left border at 150 ºC and right border at -150 ºC; top and bottom are kept at 0 ºC
Snapshot 3: borders held at 150 ºC

External Links

Heat (ScienceWorld)

Permanent Citation

Hernan Vivas
​
​"Steady-State Temperature Distribution in Conducting Square"​
​http://demonstrations.wolfram.com/SteadyStateTemperatureDistributionInConductingSquare/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011