Float_Zone

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{ FLOAT_ZONE.PDE
*********************************************
This example illustrates time-dependent axi-symmetric heat flow with a
moving source.

A rod of conductive material of unit radius and "long" units length
is clamped to a heat sink at either end. An RF coil passes the
length of the rod, creating a moving heat source of gaussian profile.
This produces a moving melt zone which carries impurities with it as it moves.
A cam adjusts the source amplitude by 200/(t+199) to produce an approximately
constant maximum temperature.

************************************************** }

title
"Float Zone"

coordinates
xcylinder('Z','R')

select
cubic { Use Cubic Basis }

variables
temp(threshold=100)

definitions
k = 0.85 {thermal conductivity}
cp = 1 { heat capacity }
long = 18
H = 0.4 {free convection boundary coupling}
Ta = 25 {ambient temperature}
A = 4500 {amplitude}

source = A*exp(-((z-1*t)/.5)**2)*(200/(t+199))

initial value
temp = Ta

equations
div(k*grad(temp)) + source = cp*dt(temp)

boundaries
region 1
start(0,0)
natural(temp) = 0 line to (long,0)
value(temp) = Ta line to (long,1)
natural(temp) = -H*(temp - Ta) line to (0,1)
value(temp) = Ta line to close
feature
start(0.01*long,0) line to (0.01*long,1)

time -0.5 to 19 by 0.01

monitors
for t = -0.5 by 0.5 to (long + 1)
elevation(temp) from (0,1) to (long,1) range=(0,1800) as "Surface Temp"
contour(temp)

plots
for t = -0.5 by 0.5 to (long + 1)
elevation(temp) from (0,0) to (long,0) range=(0,1800) as "Axis Temp"
contour(temp)

histories
history(temp) at (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0)
(9,0) (10,0) (11,0) (12,0) (13,0) (14,0) (15,0) (16,0)
(17,0) (18,0)

end