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Eduardo Ghershman (edug)
New member
Username: edug

Post Number: 1
Registered: 08-2005
Posted on Saturday, August 27, 2005 - 12:27 pm:   

Considered Forum.

I am studying, as one behaves a laminar conductor who comprises of a made resistance, depositing a metal in a substrate.
The figure represents part of the Film Type Resistor, with a very fine line that join two lines thicknesses.
http://www.geocities.com/lioraghershman/film1.GIF

I want to determine the current density J, the generation of heat q=|J|^2.res (res:resistivity)and the resistance between a and b.
This is my program :
TITLE { exa081.pde }
'Conduction in a film'
SELECT
errlim=1e-5 nodelimit=800 spectral_colors
VARIABLES
U q
DEFINITIONS
cond=5.99e7 { Conductivity of Cu }
Ex=-dx(U) Ey=-dy(U) E=-grad(U) Em=magnitude(E)
Jx=cond*Ex Jy=cond*Ey J=cond*E Jm=magnitude(J)

EQUATIONS
div( J)=0 { 2nd order PDE in U }
q: q=Jm^2*(1/cond)
BOUNDARIES
region 'domain'
start(-0.5,1) value(U)=0 line to (-0.4,1)

{fine line}
natural(U)=0 line to (-0.4,1.5)
natural(U)=0 line to (0.5,1.5)
natural(U)=0 line to (0.5,1.51)
natural(U)=0 line to (-0.4,1.51)
{-----------------------------------------------}

natural(U)=0 line to (-0.4,1.8) { Insulated, Ex=Jx=0 }
natural(U)=0 line to (0.5,1.8) { Insulated, Ex=Jx=0 }
natural(U)=0 line to (0.5,1)
value(U)=1.0 line to (0.6,1)
natural(U)=0 line to (0.6,2)
natural(U)=0 line to (-0.5,2)


natural(U)=0 line to finish { Insulated }

PLOTS
contour( U) surface( U) surface(q)
surface( Jm)
END
In the following figure I discover points of great disipacion of heat,
http://www.geocities.com/lioraghershman/film2.GIF

What is your opinion and on program to determine the resistance?
From already very been thankful.
Eduardo Ghershman
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Takeyuki Ojima (tac)
Junior Member
Username: tac

Post Number: 3
Registered: 07-2005
Posted on Sunday, August 28, 2005 - 05:54 pm:   

To my understanding, your problem of constant current (DC) is a magnetostatic problem and E=-grad(V) is just for electrostatic one and not effective in this case, I think.
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Eduardo Ghershman (edug)
New member
Username: edug

Post Number: 2
Registered: 08-2005
Posted on Monday, August 29, 2005 - 12:43 pm:   

Considered Takeyuki Ojima.

I study this subject from the document of Gunnar Bäckström,"Fields of Physics by Finite Element Analysis",chapter 8,Electric Conduction in (x,y) Space.I apply a voltage over a thin film resistor,so that the potential U of a side is zero and the other side is 1.0 V,the votage is applied between differents parts of the metalic resistor.
The currente density J is related to the fiel strengh E by J=cond.E=-cond.grad(V),where cond is the electric conductivity.
In the descriptor PDE,I type as div(J)=0;my doubt is ,if this program shows a physical reality to us and as I can verify it by another method.

Any experience or recommendations would be much appreciated.

Regards,
Eduardo Ghershman
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 439
Registered: 06-2003
Posted on Monday, August 29, 2005 - 04:55 pm:   

Attached is a model of resistive heating that we did several years ago. I don't remember much about it, but perhaps you can infer from the script what was done.

As to validation, there are two common practices:

1) look in textbooks for problems that have been solved analytically (or in some other trustworthy way - beware of sloppy numerical results), and run the problem on FlexPDE for comparison.

2) Assume a reasonable analytic solution and substitute this solution into the PDE. This will generate the necessary source terms to achieve the assumed result. Put these source terms into FlexPDE and compare the result with the assumed analytic result. Be sure you treat the boundary conditions correctly.



application/octet-streamResistor.pde
resistor.pde (2.2 k)
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Takeyuki Ojima (tac)
Member
Username: tac

Post Number: 4
Registered: 07-2005
Posted on Tuesday, August 30, 2005 - 01:11 am:   

As is known, current is always accompanied with magnetic field which interacts the other part of the current, which will determine the distribution of current density in a resister or metal. I feared that these two problem-descriptions ignored the effect of magnetic field. Let me give time to check.
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Eduardo Ghershman (edug)
Junior Member
Username: edug

Post Number: 3
Registered: 08-2005
Posted on Tuesday, August 30, 2005 - 11:57 am:   

Dear Mr. Nelson.

Thank you very much by the information.

Eduardo
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Takeyuki Ojima (tac)
Member
Username: tac

Post Number: 8
Registered: 07-2005
Posted on Saturday, September 03, 2005 - 09:29 pm:   

Sorry! I had a misunderstanding. As long as the problem of DC is confined in a register or metal, E=-grad(v) is valid because curl(E)=0 but the outside has a magnetostatic field only. The effect of magnetic field in such solids is meaningful only in AC cases.

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