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# 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 .

### DETAILS

These animations were generated from the analytical solutions, which can be found in the source code. The following nomenclature is used.
= temperature (K)
= position (m)
= time (s)
= thermal conductivity (W/m K)
= thermal conductivity (W/m )
= surface heat flux (W/m)
= heat transfer coefficient (W/m K)
= external fluid temperature (K)

### PERMANENT CITATION

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