contact_resistance_heating

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contact_resistance_heating

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{  CONTACT_RESISTANCE_HEATING.PDE

 

 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 outward current across an

 interface is given by

   R*I = -Jump(V) [=(Vinner-Vouter)],

 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

 for this problem is represented as

   CONTACT(V) = JUMP(Temp)/R

 In this problem, we have two variables, voltage and temperature.

 There is an electrical contact resistance of 2 units at the interface between

 two halves, causing a jump in the voltage across the interface.

 The current through the contact is a source of heat in the temperature equation,

 of value P = R*I^2 = Jump(V)^2/R

 

 

}

 

title "contact resistance heating"

 

variables

   V

   Temp

 

definitions

   Kt     { thermal conductivity }

   Heat = 0

   Rc = 2   { Electrical contact resistance }

   rho = 1   { bulk resistivity }

   sigma = 1/rho { bulk conductivity, I=sigma*grad(V) }

   temp0=0

   size = 3

   V1 = 1

   totR = size*rho+Rc

   cur = V1/totR

   jdrop = cur*Rc

initial values

    Temp = temp0

 

equations

   V:       div(sigma*grad(V))  = 0

   Temp:    div(Kt*grad(Temp)) + Heat =0

 

boundaries

Region 1

   Kt=5

  start 'box' (0,0)

  natural(V)=0 natural(temp)=0 line to (size,0)

  value(V)=V1 value(temp)=0   line to (size,size)

  natural(V)=0 natural(temp)=0 line to (0,size)

  value(V)=0   value(temp)=0   line to close

 

Region 2

   Kt=1

  start 'interface' (0,0)

  line to (size/2,0)

      contact(V) = (1/rc)*JUMP(V) { resistance jump }

      natural(temp) = JUMP(V)^2/Rc   { heat generation }

  line to(size/2,size)

      natural(V)=0

      natural(Temp)=0

  line to (0,size) to close

 

monitors

  contour(Temp)

 

plots

  grid(x,y)

  contour(V) painted

  contour(Temp) painted

  surface(Temp)

  contour(kt*dx(temp)) painted

  contour(kt*dx(temp)) painted

  elevation(V) from(0,1.5) to (3,1.5)

  elevation(temp) from(0,1.5) to (3,1.5)

  elevation(dx(v)) from(0,1.5) to (3,1.5)

  elevation(kt*dx(temp)) from(0,1.5) to (3,1.5)

summary

  report(sintegral(V,'interface',1)/rc)

  report(sintegral(V,'interface',2)/rc)

  report(sintegral(jump(V)^2/rc,'interface',1)) as "contact source"

  report(sintegral(normal(kt*grad(temp)),'box')) as "outer loss"

  report(size*(jdrop)^2/Rc) as "true heat"

 

end