3d_contact

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3d_contact

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{ 3D_CONTACT.PDE  

 

 This problem shows the use of a contact resistance boundary between layers in 3D.

 The resistance model is applied to the entire boundary surface.

 

 See 3D_CONTACT_REGION.PDE for restriction of the resistance model to a single region.

 (This is a modification of problem 3D_BRICKS.PDE).

 

}

 

title 'steady-state 3D heat conduction with Contact Resistance'

 

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 }

   e = 0.01                   {'epsilon' offset to avoid plotting on discontinuities }

 

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 2 contact(tp)=jump(tp)/10   { THE CONTACT RESISTANCE }

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

 

  Region 1           { define full domain boundary in base plane }

      layer 1 k=1             { 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=e as "XY Temp - Upper"

  contour(Tp) on z=-e as "XY Temp - Lower"

  contour(Tp) on x=e as "YZ Temp"

  contour(Tp) on y=e as "ZX Temp"

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

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

  elevation(Tp) from (e,e,-long) to (e,e,long) as "Z-Axis Temp"

 

plots

  contour(Tp) on z=e as "XY Temp - Upper"

  contour(Tp) on z=-e as "XY Temp - Lower"

  contour(Tp) on x=e as "YZ Temp"

  contour(Tp) on y=e as "ZX Temp"

  surface(Tp) on y=e as "ZX Temp"

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

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

  elevation(Tp) from (e,e,-long) to (e,e,long) as "Z-Axis Temp"

 

end