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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

 temp : 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"

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