3d_bricks

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3d_bricks

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{  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  

   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