Sample Problems > Applications > Heatflow > 3d

{ 3D_BRICKS.PDE

This problem demonstrates the application

of FlexPDE to steady-state three dimensional

heat conduction. An assembly of four bricks

of differing conductivities has a gaussian

internal heat source, with all faces held

at zero temperature. After a time, the

temperature reaches a stable distribution.

This is the steady-state analog of problem

3D_BRICKS+TIME.PDE

}

title 'steady-state 3D heat conduction'

select

regrid=off { use fixed grid }

coordinates

cartesian3

variables

definitions

long = 1

wide = 1

K { thermal conductivity -- values supplied later }

Q = 10*exp(-x^2-y^2-z^2) { thermal source }

initial values

Tp = 0.

equations

Tp : div(k*grad(Tp)) + Q = 0 { the heat equation }

extrusion z = -long,0,long { divide Z into two layers }

boundaries

Surface 1 value(Tp)=0 { fix bottom surface temp }

Surface 3 value(Tp)=0 { fix top surface temp }

Region 1 { define full domain boundary in base plane }

layer 1 k = 1.0 { bottom right brick }

layer 2 k = 0.1 { top right brick }

start(-wide,-wide)

value(Tp) = 0 { fix all side temps }

line to (wide,-wide) { walk outer boundary in base plane }

to (wide,wide)

to (-wide,wide)

to close

Region 2 { overlay a second region in left half }

layer 1 k = 0.2 { bottom left brick }

layer 2 k = 0.4 { top left brick }

start(-wide,-wide)

line to (0,-wide) { walk left half boundary in base plane }

to (0,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 "XZ 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) to (0,0,long) as "Z-Axis Temp"

plots