Heat Equation with Joule Heating

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maguirre
Posts: 17
Joined: 03 Nov 2022, 17:59
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Location: Buenos Aires, Argentina.

Heat Equation with Joule Heating

Post by maguirre »

Hi everyone!
I'm new to Elmer and I'm trying to simulate a copper bar of 0.77x0.04x0.005 m^3 heated by the Joule Effect with a DC of 1kA between two terminals (0.0509 V if we use the resistivity of copper) and BC on all faces over the heat flux with the Heat Transf. Coef. of air 2.5 and a room temperature of 297 K. I'm using the Heat Equation and Static Current Conduction definitions.

I encountered two problems:
  • I don't understand the use of "Current Source in the Body Force section for the Static Current Cond.
  • The average Joule power simulated between the two terminals is 0.6 W (I think it is in Watts, I've read that the output is in W/m^3, which in that case is worst because...) but if the theoretical value is 15.4 W (conductivity times the square of the electric potential times volume)
Does anyone know what I'm doing wrong?

Edit:
Thanks to Rich_B to point out that more clarification would be better.
Solver Output:

Code: Select all

ELMER SOLVER (v 9.0) STARTED AT: 2022/11/03 14:08:08
ParCommInit:  Initialize #PEs:            1
MAIN: 
MAIN: =============================================================
MAIN: ElmerSolver finite element software, Welcome!
MAIN: This program is free software licensed under (L)GPL
MAIN: Copyright 1st April 1995 - , CSC - IT Center for Science Ltd.
MAIN: Webpage http://www.csc.fi/elmer, Email elmeradm@csc.fi
MAIN: Version: 9.0 (Rev: Release, Compiled: 2022-08-02)
MAIN:  Running one task without MPI parallelization.
MAIN:  Running with just one thread per task.
MAIN:  Lua interpreter linked in.
MAIN: =============================================================

MAIN: 
MAIN: 
MAIN: -------------------------------------
MAIN: Reading Model: case.sif
LoadInputFile: Scanning input file: case.sif
LoadInputFile: Scanning only size info
LoadInputFile: First time visiting
LoadInputFile: Reading base load of sif file
LoadInputFile: Loading input file: case.sif
LoadInputFile: Reading base load of sif file

LoadInputFile: Number of BCs: 3
LoadInputFile: Number of Body Forces: 1
LoadInputFile: Number of Initial Conditions: 0
LoadInputFile: Number of Materials: 1
LoadInputFile: Number of Equations: 1
LoadInputFile: Number of Solvers: 2
LoadInputFile: Number of Bodies: 1
ListTagKeywords: Setting weight for keywords!
ListTagKeywords: No parameters width suffix: normalize by area
ListTagKeywords: Setting weight for keywords!
ListTagKeywords: No parameters width suffix: normalize by volume

ElmerAsciiMesh: Base mesh name: ./.

LoadMesh: Elapsed REAL time:     0.0020 (s)

MAIN: -------------------------------------
AddVtuOutputSolverHack: Adding ResultOutputSolver to write VTU output in file: case

OptimizeBandwidth: ---------------------------------------------------------
OptimizeBandwidth: Computing matrix structure for: static current conduction...done.
OptimizeBandwidth: Half bandwidth without optimization: 440
OptimizeBandwidth: 

OptimizeBandwidth: Bandwidth Optimization ...done.
OptimizeBandwidth: Half bandwidth after optimization: 33
OptimizeBandwidth: ---------------------------------------------------------
OptimizeBandwidth: ---------------------------------------------------------
OptimizeBandwidth: Computing matrix structure for: heat equation...done.
OptimizeBandwidth: Half bandwidth without optimization: 440
OptimizeBandwidth: 
OptimizeBandwidth: Bandwidth Optimization ...done.
OptimizeBandwidth: Half bandwidth after optimization: 33
OptimizeBandwidth: ---------------------------------------------------------
ElmerSolver: Number of timesteps to be saved: 1
MAIN: 
MAIN: -------------------------------------
MAIN:  Steady state iteration:            1
MAIN: -------------------------------------
MAIN: 
StatCurrentSolve: -------------------------------------
StatCurrentSolve: STAT CURRENT SOLVER:
StatCurrentSolve: -------------------------------------
StatCurrentSolve: Static current iteration: 1
StatCurrentSolve:  Assembly (s)          :   1.9999999999999948E-003
      10 0.2080E-01

      20 0.1421E-01
      30 0.3656E-02
      40 0.1953E-02
      50 0.1253E-02
      60 0.1058E-02
      70 0.3134E-03
      80 0.7763E-08
      87 0.1545E-10
ComputeChange: NS (ITER=1) (NRM,RELC): ( 0.37093598E-01  2.0000000     ) :: static current conduction
StatCurrentSolve:  Solve (s)             :   2.0000000000000018E-003

StatCurrentSolve:  Total Heating Power   :   61135.035330349056
StatCurrentSolve:  Effective Resistance  :   4.2378482092965332E-008
StatCurrentSolve: Static current iteration: 2
StatCurrentSolve:  Assembly (s)          :   2.0000000000000018E-003
       1 0.1394E-10
ComputeChange: NS (ITER=2) (NRM,RELC): ( 0.37093598E-01 0.44343631E-11 ) :: static current conduction
StatCurrentSolve:  Solve (s)             :   0.0000000000000000

StatCurrentSolve:  Total Heating Power   :   61135.035330349041
StatCurrentSolve:  Effective Resistance  :   4.2378482092965339E-008
ComputeChange: SS (ITER=1) (NRM,RELC): ( 0.37093598E-01  2.0000000     ) :: static current conduction
HeatSolver: Solving the energy equation for temperature
HeatSolve: 
HeatSolve: 
HeatSolve: -------------------------------------
HeatSolve:  TEMPERATURE ITERATION           1
HeatSolve: -------------------------------------
HeatSolve: 
HeatSolve: Starting Assembly...
HeatSolve: Assembly:

HeatSolve: Assembly done

      10 0.1478E+00

      20 0.4493E-02
      30 0.1606E-03
      40 0.9386E-05

      50 0.7312E-08
      55 0.3394E-10
ComputeChange: NS (ITER=1) (NRM,RELC): (  297.18607      2.0000000     ) :: heat equation
HeatSolve: iter:    1 Assembly: (s)    0.01    0.01
HeatSolve: iter:    1 Solve:    (s)    0.00    0.00
HeatSolve:  Result Norm   :    297.18606681252976
HeatSolve:  Relative Change :    2.0000000000000000
HeatSolve: 
HeatSolve: 
HeatSolve: -------------------------------------
HeatSolve:  TEMPERATURE ITERATION           2
HeatSolve: -------------------------------------
HeatSolve: 
HeatSolve: Starting Assembly...
HeatSolve: Assembly:

HeatSolve: Assembly done

       3 0.7256E-10
ComputeChange: NS (ITER=2) (NRM,RELC): (  297.18607     0.18476890E-11 ) :: heat equation
HeatSolve: iter:    2 Assembly: (s)    0.01    0.03
HeatSolve: iter:    2 Solve:    (s)    0.00    0.00
HeatSolve:  Result Norm   :    297.18606681198065
HeatSolve:  Relative Change :    1.8476889986309466E-012
ComputeChange: SS (ITER=1) (NRM,RELC): (  297.18607      2.0000000     ) :: heat equation
ResultOutputSolver: -------------------------------------
ResultOutputSolver: Saving with prefix: case
ResultOutputSolver: Creating list for saving - if not present
CreateListForSaving: Field Variables for Saving

ResultOutputSolver: Saving in unstructured VTK XML (.vtu) format
VtuOutputSolver: Saving results in VTK XML format with prefix: case
VtuOutputSolver: Saving number of partitions: 1
ResultOutputSolver: -------------------------------------
ElmerSolver: *** Elmer Solver: ALL DONE ***
ElmerSolver: The end
SOLVER TOTAL TIME(CPU,REAL):         0.07        0.07
ELMER SOLVER FINISHED AT: 2022/11/03 14:08:08
Attachments
case.sif
(3.11 KiB) Downloaded 87 times
barra77x4_4ori-BodyCylinder002.step
(35.03 KiB) Downloaded 74 times
Last edited by maguirre on 03 Nov 2022, 21:04, edited 1 time in total.
Lic. Matias A. Aguirre.
Metrología Física, Metrología y Calidad, INTI.
Avenida General Paz 5445 Edificio 3
B1650WAB San Martin, Buenos Aires.
Rich_B
Posts: 422
Joined: 24 Aug 2009, 20:18

Re: Heat Equation with Joule Heating

Post by Rich_B »

Hello,

There are many ways for things to go wrong, and it's hard to tell what to suggest. If you would post a minimal working example, with geometry and the sif file, and maybe even post the solver output, then you are more likely to get some suggestions. The forum allows up to three attachments per post and up to 1 MB per post.

Thanks, Rich.
Rich_B
Posts: 422
Joined: 24 Aug 2009, 20:18

Re: Heat Equation with Joule Heating

Post by Rich_B »

Hello,

Loading the step file into ElmerGUI allows inspecting the boundaries. The attached screen shot seems to show that one boundary, #8, is the bore of a terminal hole, while the other boundary, #3, is the flat face of the bar. Should the other boundary be another bore of a hole, such as #9? Assuming this is the model of a DC millivolt shunt, it should be #9.

Rich.
Attachments
flat-face.png
flat-face.png (96.53 KiB) Viewed 1264 times
maguirre
Posts: 17
Joined: 03 Nov 2022, 17:59
Antispam: Yes
Location: Buenos Aires, Argentina.

Re: Heat Equation with Joule Heating

Post by maguirre »

That's weird. As you mention, the two boundaries are on the bores of two holes you mention, but in my GUI the #3 is a bore of a hole, and the flat faces are #5 and #6.

Hole bores: #2 #3 #8 #9
Big flat faces: #5 #6
Lic. Matias A. Aguirre.
Metrología Física, Metrología y Calidad, INTI.
Avenida General Paz 5445 Edificio 3
B1650WAB San Martin, Buenos Aires.
Rich_B
Posts: 422
Joined: 24 Aug 2009, 20:18

Re: Heat Equation with Joule Heating

Post by Rich_B »

Hello,

Loading the step file into ElmerGUI also allows one to check the bounding box dimensions of the model. Click on 'Model -> Summary', and scroll up to find the bounding box.
BOUNDING BOX
X-coordinate: [ 0 , 770 ]
Y-coordinate: [ 0 , 40 ]
Z-coordinate: [ 0 , 5 ]
For Elmer, SI units are expected, so the model as given is 770 meters long. To scale the model from millimeters to meters, click on 'Model -> Setup' and add 'Coordinate Scaling' equal to 0.001. Adding a single value works okay, it will be applied to all three dimensions.

Rich.
Rich_B
Posts: 422
Joined: 24 Aug 2009, 20:18

Re: Heat Equation with Joule Heating

Post by Rich_B »

Regarding the boundary numbering, if size permits it will help if you upload your elmer mesh files, mesh.*, preferably zipped in an archive.

Rich.
maguirre
Posts: 17
Joined: 03 Nov 2022, 17:59
Antispam: Yes
Location: Buenos Aires, Argentina.

Re: Heat Equation with Joule Heating

Post by maguirre »

Thank you!

Now the Joule Heating is 500000 which I assume is in W/m^3 because if a multiply it by the volume it gives me 50 W, close to what I was expecting. Also, 370 K at the hottest part so I'll be careful with that bar when I'll test this at the lab :lol:
Lic. Matias A. Aguirre.
Metrología Física, Metrología y Calidad, INTI.
Avenida General Paz 5445 Edificio 3
B1650WAB San Martin, Buenos Aires.
Rich_B
Posts: 422
Joined: 24 Aug 2009, 20:18

Re: Heat Equation with Joule Heating

Post by Rich_B »

You are welcome. Feel free to post your working model under User Contributed Cases.

Rich.
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