Heat Conduction in Some Standard Solids
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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