This Demonstration shows solutions for the one-dimensional heat diffusion equation
in a semi-infinite region. Starting from a uniform initial temperature,
, and using normalized parameters (
, the dimensionless temperature distribution is animated in time for the three classical boundary conditions at
, namely: constant surface temperature,
; constant surface heat flux,
; and convective exchange with a fluid at
,
. For the convection case, temperature distributions for a relatively high, medium, and low value of the heat transfer coefficient
are displayed. A high
(red curve) gives results close to the constant surface temperature case, while a low
value (blue curve) gives results similar to the constant heat flux case. In all cases the thermal affected zone is of the order of
.
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