With all the described modifications installed, the full script for the 3D canister problem is as follows:
TITLE 'Heat flow around an Insulating Canister'
COORDINATES
Cartesian3
VARIABLES
Phi { the temperature }
DEFINITIONS
K = 1 { default conductivity }
R = 0.5 { blob radius }
EQUATIONS
Div(-k*grad(phi)) = 0
EXTRUSION
SURFACE 'Bottom' z=-1/2
LAYER 'underneath'
SURFACE 'Can Bottom' z=-1/4
LAYER 'Can'
SURFACE 'Can Top' z=1/4
LAYER 'above'
SURFACE 'Top' z=1/2
BOUNDARIES
REGION 1 'box'
START(-1,-1)
VALUE(Phi)=0 LINE TO (1,-1)
NATURAL(Phi)=0 LINE TO (1,1)
VALUE(Phi)=1 LINE TO (-1,1)
NATURAL(Phi)=0 LINE TO CLOSE
LIMITED REGION 2 'blob' { the embedded blob }
LAYER 2 k = 0.001 { the canister only }
START 'ring' (R,0)
ARC(CENTER=0,0) ANGLE=360 TO CLOSE
PLOTS
GRID(y,z) ON x=0
CONTOUR(Phi) ON x=0
VECTOR(-k*grad(Phi)) ON x=0
ELEVATION(Phi) FROM (0,-1,0) to (0,1,0) { note 3D coordinates }
END
Since we have specified no boundary conditions on the top and bottom extrusion surfaces, they default to zero flux. This is the standard default, for reasons explained in an earlier section.
The first three of the requested PLOTS are:
