﻿ Sample Problems > Applications > Heatflow > radiative_boundary

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at the boundary of a heat transfer system.

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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