Heat Diffusion in a Semi-Infinite Region
Heat Diffusion in a Semi-Infinite Region
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 .
(T=αT)
∂
t
∂
x,x
T
0
k=α=1)
x=0
T=
T
s
-k=
∂T
∂x
q
s
T
∞
-k=h(-T)
∂T
∂x
T
∞
h
h
h
4
αt