# 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