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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: