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{ TIME_INTEGRAL.PDE

 This example illustrates use of the TIME_INTEGRAL 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))

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(tsource) as "Total Source"

end