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{ TINTEGRAL.PDE

 This example illustrates use of the TINTEGRAL function in time-dependent problems.

}

title

"Float Zone"

coordinates

 xcylinder('Z','R')

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))

 tsource = time_integral(vol_integral(source))

 t1 = time_integral(1.0)

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

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)

contour(dt(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,dt(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)

history(t1) as "Tintegral(1)"

history(tsource) as "Tintegral(Source)"

end

 


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