# Heat Conduction in Some Standard Solids

Requires a Wolfram Notebook System

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

The dimensionless transient temperature and average temperature* * of a plate (), cylinder (), and sphere (), described by the partial differential equation problem , , , , are plotted (transient in orange, average in blue) as a function of dimensionless time . The numerical values for transient and average temperatures can be computed for any dimensionless coordinate and time .

Contributed by: Mikhail Dimitrov Mikhailov (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The analytical solutions of these classical heat conduction problems are given in numerous books, however this Demonstration explores the built-in *Mathematica* function NDSolve.

For details see: M. D. Mikhailov and M. N. Özisik, *Unified Analysis and Solutions of Heat and Mass Diffusion*, New York: Dover, 1994.

## Permanent Citation

"Heat Conduction in Some Standard Solids"

http://demonstrations.wolfram.com/HeatConductionInSomeStandardSolids/

Wolfram Demonstrations Project

Published: March 7 2011