Sample Problems > Applications > Heatflow > radiative

{ 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

radiative_boundary