WOLFRAM|DEMONSTRATIONS PROJECT

Nonsteady-State Heat Conduction in a Cylinder

​
time
2500.
thermal diffusivity coefficient in
2
m
/s
0.00009
Nonsteady-state heat conduction in a cylinder obeys the following PDE:
∂T
∂t
=α
2
∂
T
∂
2
r
+
1
r
∂T
∂r
,
where
α
is the thermal diffusivity coefficient expressed in
2
m
/s
,
T
is the temperature in
°C
, and
r
is the radial position in meters.
The initial condition and boundary conditions are
T(r,t=0)=320°C
(initial temperature);
T(r=1,t)=220°C
(the temperature at the cylinder surface is kept constant);
∂T
∂r
(r=0,t)=0
(symmetry condition).
This Demonstration shows the temperature profile inside the cylinder at different instants for values of the thermal diffusivity coefficient specified by the user.