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

.