Radbdry

{ RADBDRY.PDE }

title "Axi-symmetric Anisotropic Heatflow, Radiative Boundary"

select

errlim=1.0e-4

coordinates

ycylinder("R","Z")            { Define cylindrical coordinates with symmetry

                                       axis along "Y" }

variables

Temp(1)                       { Define Temp as the system variable,

                                 with approximate value range 0 to 1 }

definitions

kr = 1                        { define the R-direction (radial) conductivity }

kz = 4                        { define the Z-direction (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: }

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" print

end