# Heat Diffusion in a Semi-Infinite Region

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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 .

Contributed by: Brian Vick (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## 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

"Heat Diffusion in a Semi-Infinite Region"

http://demonstrations.wolfram.com/HeatDiffusionInASemiInfiniteRegion/

Wolfram Demonstrations Project

Published: March 7 2011