{ 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
Page url: index.html?usage_tintegral.html