﻿ Sample Problems > Applications > Heatflow > 3d_bricks

# 3d_bricks

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# 3d_bricks   {  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   } title 'steady-state 3D heat conduction'   select    regrid=off { use fixed grid }   coordinates    cartesian3 variables

Tp

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

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"

end