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WOLFRAM|DEMONSTRATIONS PROJECT

A Cellular Automaton-Based Heat Equation

​
time step
This Demonstration shows unsteady-state conduction of heat in two dimensions by means of a coupled-map lattice, for example a continuous-state cellular automaton. The heat transfer is governed by
t+1
T
i,j
=
4
t
T
i,j+1
+
t
T
i,j-1
+
t
T
i+1,j
+
t
T
i-1,j
+
t
T
i+1,j+1
+
t
T
i+1,j-1
+
t
T
i-1,j+1
+
t
T
i-1,j-1
20
,
where
t
T
i,j
represents the temperature in degrees Celsius of the
i
th
j
cell at the
th
t
time step.
The initial and boundary conditions are
0
T
i,j
=10°C
,
t
T
1,j
=-22°C
,
t
T
30,j
=22°C
,
which are relatively simple, but can be adjusted in accordance with the problem at hand. The result approaches the solution of the classic PDE-based heat equation for unsteady heat conduction.
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