Heat Conduction Equation—Disk

Author

Eric W. Weisstein
May 3, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/HeatConductionEquationDisk.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HeatConductionEquationDisk.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<NumericalMath`BesselZeros`

Solution

DSolve[Θ''[θ]/Θ[θ]==-n(n+1),Θ[θ],θ]

DSolve[1/(κ T[t])T'[t]+1/λ^2==0,T[t],t]

T(r,0)

Particular Case with initial conditions T(r,0) and boundary conditions T(1,t)=1

BesselJZeros[3,10]