Sample Problems > Usage > Coordinate_Scaling > unscaled

{ UNSCALED_Z.PDE

This is a reference problem for SCALED_Z.PDE.

It solves for heatflow in a sandwich.

}

title 'Unscaled Z coordinate'

coordinates

cartesian3

variables

definitions

long = 1/2 { thickness of the upper and lower layers }

wide = 1

w=0.01 { half-thickness of the imbedded slab }

K =0.1 { thermal conductivity -- modified later by layer }

Q = 0 { Thermal source - modified later by layer }

T0 = 0

initial values

Tp = 0.

equations { the heat equation }

Tp: dx(k*dx(Tp)) + dy(k*dy(Tp)) + dz(k*dz(Tp)) + Q = 0

extrusion

surface 'bottom' z = -long-w

layer 'under'

surface 'slab_bottom' z = -w

layer 'slab'

surface 'slab_top' z= w

layer 'over'

surface 'top' z= long+w

boundaries

surface 'bottom' load(Tp)=0.1*(T0-Tp)

surface 'top' load(Tp)=0.1*(T0-Tp)

Region 1

layer 2

Q = 100*exp(-x^2-y^2) { a heat source in the slab layer only }

k = 1 { redefine conductivity in layer 2 }

start 'sidewall' (-wide,-wide)

load(Tp) = 0

layer 2 load(Tp) = 0.1*(T0-Tp)

line to (wide,-wide)

to (wide,wide)

to (-wide,wide)

to close

monitors

contour(Tp) on z=0 as "XY Temp"

contour(Tp) on x=0 as "YZ Temp"

contour(Tp) on y=0 as "ZX Temp"

plots

contour(Tp) on z=0 as "XY Temp"

contour(Tp) on x=0 as "YZ Temp"

contour(Tp) on y=0 as "ZX Temp"

elevation(Tp) from (-wide,0,0) to (wide,0,0) as "X-Axis Temp"

elevation(Tp) from (0,-wide,0) to (0,wide,0) as "Y-Axis Temp"

elevation(Tp) from (0,0,-long-w) to (0,0,long+w) as "Z-Axis Temp"

vector(-k*dx(Tp),-k*dz(Tp)) on y=0 as "Flux on Y=0"

vector(-k*dx(Tp),-k*dy(Tp)) on z=0 as "Flux on Z=0"

elevation(k*dx(Tp)) from (-wide,0,0) to (wide,0,0) as "Center X-Flux"

elevation(k*dz(Tp)) from (0,0,-(long+w)) to (0,0,(long+w)) as "Center Z-Flux"

SUMMARY

{ form some integrals for comparison with Scaled_Z: }

report(sintegral(-k*dz(Tp),'slab_top','slab'))

report(sintegral(-k*dz(Tp),'slab_top','over'))

report("--")

report(sintegral(-normal(k*grad(Tp)),'sidewall','slab'))

end

unscaled_z

unscaled_z