# Transient Heat Conduction with No Steady State

Transient Heat Conduction with No Steady State

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 ) and the other surface is thermally insulated (at ). The governing equation is given by =Θ. 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 .

x=0,=-1

∂Θ

∂x

x=1,=0

∂Θ

∂x

∂Θ

∂t

2

∂

∂

2

x

Θ(x,t)≈t+-x+

2

x

2

1

3