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WOLFRAM|DEMONSTRATIONS PROJECT

Transient Heat Conduction with No Steady State

​
time
27.8
Consider the heat conduction problem with Neumann (constant flux) at both boundaries of a solid slab. A constant radiant heat flux is imposed on one surface (at
x=0,
∂Θ
∂x
=-1
) and the other surface is thermally insulated (at
x=1,
∂Θ
∂x
=0
). The governing equation is given by
∂Θ
∂t
=
2
∂
Θ
∂
2
x
. Initially the solid slab temperature is equal to zero. This Demonstration displays the temperature at various instants. The temperature does not reach a steady-state value and at large times has the form
Θ(x,t)≈t+
2
x
2
-x+
1
3
.
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