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

.