radiative_boundary

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radiative_boundary

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{  RADIATIVE_BOUNDARY.PDE  

 

  This example demonstrates the implementation of radiative heat loss  

  at the boundary of a heat transfer system.

 

}  

 

title "Axi-symmetric Anisotropic Heatflow, Radiative Boundary"  

 

select  

 errlim=1.0e-4  

 

coordinates  

{ Define cylindrical coordinates with

   symmetry axis along "Y" }  

 ycylinder("R","Z")    

 

variables  

{ Define Temp as the system variable,

   with approximate variation range of 1 }

 Temp(1)              

 

definitions  

 kr = 1 { radial conductivity }  

 kz = 4 { axial conductivity }  

 

{ define a Gaussian source density: }  

 source = exp(-(r^2+(z-0.5)^2))  

 

{ define the heat flux: }  

 flux = vector(-kr*dr(Temp),-kz*dz(Temp))  

 

initial values  

 Temp = 1  

 

equations   { define the heatflow equation: }  

 Temp : div(flux) = Source  

 

boundaries                     { define the problem domain }  

Region 1                     { ... only one region }  

  start "RAD" (0,0)           { start at bottom on axis and name the boundary }  

  natural(temp)= 0.5*temp^4   { specify a T^4 boundary loss }  

  line to (0.5,0)             { walk the boundary }  

  arc(center=0.5,0.5) angle 180   { a circular outer edge }  

  line to (0,1)  

  natural(temp)=0             { define a symmetry boundary at the axis }  

  line to close  

 

monitors  

elevation(magnitude(2*pi*r*flux)) on "RAD" as "Heat Flow"  

contour(Temp)                 { show contour plots of solution in progress }  

 

plots                           { write these hardcopy files at completion }  

grid(r,z)                     { show final grid }  

contour(Temp)                 { show solution }  

surface(Temp)  

vector(2*pi*r*flux) as "Heat Flow"  

elevation(magnitude(2*pi*r*flux)) on "RAD" as "Heat Flow" export  

 

end