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{ 1D_FLOAT_ZONE.PDE  

 

 This is a version of the standard example "Float_Zone.pde" in 1D cartesian geometry.

 

}  

 

title  

"Float Zone in 1D Cartesian geometry"  

 

coordinates  

 cartesian1  

 

variables  

 temp(threshold=100)  

 

definitions  

 k =10                 { 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(-((x-1*t)/.5)^2)*(200/(t+199))  

 

initial value  

 temp = Ta  

 

equations  

 Temp: div(k*grad(temp)) + source -H*(temp - Ta) = cp*dt(temp)  

 

boundaries  

region 1  

  start(0) point value(temp) = Ta  

  line to (long) point value(temp) = Ta  

 

time -0.5 to 19 by 0.01  

 

monitors  

for t = -0.5 by 0.5 to (long + 1)  

elevation(temp) from (0) to (long) range=(0,1800) as "Surface Temp"  

 

plots  

for t = -0.5 by 0.5 to (long + 1)  

elevation(temp) from (0) to (long) range=(0,1800) as "Axis Temp"  

elevation(source) from(0) to (long)  

elevation(-k*grad(temp)) from(0) to (long)  

 

histories  

history(temp) at (0) (1) (2) (3) (4) (5) (6) (7) (8)  

                  (9) (10) (11) (12) (13) (14) (15) (16)  

                  (17) (18)  

 

end