Heat Conduction in Some Standard Solids
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 .
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.