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# thermal_contact_resistance

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# thermal_contact_resistance   { THERMAL_CONTACT_RESISTANCE.PDE

This sample demonstrates the application of FlexPDE to heatflow

problems with contact resistance between materials.

We define a square region of material with a conductivity of 5.

Imbedded in this square is a diamond-shaped region of material with a

uniform heat source of 1, and a conductivity of 1.

There is a contact resistance of 1/2 unit between the materials.

Contact resistance is modeled using the keywords JUMP and CONTACT.

JUMP represents the "jump" in the value of a variable across an interface

(outer value minus inner value, as seen from each cell),

and is meaningful only in boundary condition statements.

CONTACT is a special form of NATURAL, which requests that the boundary

should support a discontinuous value of the variable.

The model is one of "contact resistance", where the flux across an interface

is given by flux(Temp) = -Jump(Temp)/R,

and R is the contact resistance.

Since CONTACT, like NATURAL, represents the outward normal component

of the argument of the divergence operator,  the contact resistance condition is

represented as

CONTACT(Temp) = -JUMP(Temp)/R

 }   title "Thermal Contact Resistance"   variables    Temp   definitions   { thermal conductivity - values given in regions: }    K                    Heat             { Heat source }    Flux = -K*grad(Temp)    Rc = 1/2         { contact resistance }   initial values    Temp = 0   equations    Temp: div(Flux) = Heat   boundaries   Region 1           { the outer boundary }        K=5        Heat=0       start "Outer" (0,0)       value(Temp)=0           { cold boundary }       line to (3,0) to (3,3) to (0,3) to close Region 2         { an imbedded diamond }

K=1

Heat=1       { heat source in the inner diamond }

start "Inner" (1.5,0.5)

contact(Temp) = -JUMP(Temp)/Rc { the contact flux }

line to (2.5,1.5) to (1.5,2.5) to (0.5,1.5) to close

monitors

contour(Temp)

plots

grid(x,y)

contour(Temp) as "Temperature"

contour(Temp) zoom(2,1,1,1) as "Temperature Zoom"

elevation(Temp) from (0,0) to (3,3)

surface(Temp)

surface(Temp) zoom(2,1,1,1)

vector(-dx(Temp),-dy(Temp)) as "Heat Flow"

elevation(normal(flux)) on "Outer"

elevation(normal(flux)) on "Inner"

end