boundary conditions to represent infinite materal

[ben]

Hi,

I'm really struggling to set boundary conditions. I'm modeling heating within a thin film - where heating is on 1um scale and film width is 5cm (in effect infinite). Heat loss is by conduction only. See picture of situation



Instead of producing a grid 5cm wide. I want to model a volume of 100um - in which the heat flux (heat transfer coefficient) on the lateral boundaries is set to thermal conductivity of the material e.g. aluminum 200 WmK.

However when I run this the temperature of the modelled film is two orders of magnitude higher for a film of 500 um diameter than if the film is 5 cm diameter. Thus the boundary conditions must be wrong. (The amount of heating is correct for a 5cm diameter film - it agrees with empirical calculations).

Can you help - what am I doing wrong?

In the manual it talks about alpha as the heat transfer coefficient -



Should the heat transfer coefficient be alfa rather than the thermal conductivity. How would you calculate it for thermal conductivity in an infinite body?


Many thanks

Ben


Boundary conditions are

Boundary Condition 1
Target Boundaries(1) = 7
Name = "BoundaryCondition 1"
Heat Transfer Coefficient = 200
External Temperature = 0
End

MAterial is

Material 2
Name = "MyAluminium"
Heat Conductivity = 200
Heat Capacity = 897
Density = 2700
End

[mzenker]

Hi,

I would say, you can set

alpha = lambda / d

where lambda is the heat conductivity of your material, and d is the thickness of the layer you want to replace.
Are you sure that your external temperature (i.e. the temperature at the outer side of the layer) is zero?

BTW the images in your post are not visible, at least for me. See here for info on how to upload images so that they are seen.

HTH,

Matthias

[ben]

Hi Matthias,

Thanks that seems to work - except does it force the temperature at the boundary to zero?

I ran a 500um film to compare to the 5 cm film. Temperature adjacent to the boundary at 500 um was approx. 0 when I'd expect it to be higher.

Is there a way of allowing the temperature at the boundary to rise as would be the case in a infinite film?

Thanks again

Ben

ps. I had a look at the post regarding displaying images - to do with admin panel and pixel sizes exceeding 1024 pixels. - I couldn't find the admin panel & I don't know what wrong for pixels in images are less than that

[mzenker]

Hi,

I would try to set the heat transfer coefficient to alpha = lambda_Aluminium/4.5mm and the external temoperature to something realistic (20 deg C?) in your boundary condition. What is your boundary condition in the 5 cm case?

You can't go to the administration panel, and you don't need to. You just need to reduce your pictures so that they have no more than 1024x768 pixels.

HTH,

Matthias

[ben]

Hi,

In the 5 cm case I don't need boundary conditions as it is sufficiently large that the edges of the film don't heat up.

Temperature for a 3 mW input is 1200C in centre, dropping to 300C at 500um away and at 5 cm away it is zero.

The thickness of the film is 20nm. So I set alpha as you suggested to lambda_Aluminium/2e-8m.

For the 500um diameter film the boundary is 0 degrees C, but it should rise to 300C - is there anyway of achieving this?

What I want to know is the relative increase in temperature - the temperature rise above ambient - at 5 cm away from point of heating. Changing the temperature to a fixed value for the boundary at 500um will not achieve this. I don't know what the temperature rise at the boundary will be. But I need the boundary at 500um rather 5cm diameter to reduce the mesh size - so I want the 500um boundary to act as if the film is infinite in lateral directions with the boundary heating up.

Is this possible

Thanks

Ben

[mzenker]

Hi Ben,

this sounds a bit contradictory to me.

In the 5 cm case I don't need boundary conditions as it is sufficiently large that the edges of the film don't heat up.
......
What I want to know is the relative increase in temperature - the temperature rise above ambient - at 5 cm away from point of heating. Changing the temperature to a fixed value for the boundary at 500um will not achieve this. I don't know what the temperature rise at the boundary will be. But I need the boundary at 500um rather 5cm diameter to reduce the mesh size - so I want the 500um boundary to act as if the film is infinite in lateral directions with the boundary heating up.

if you want the temperature at 5 cm (unless this is a typo), the natural way would be to have the mesh go until that distance. And you need a approximately realistic connection to what comes beyond 5 cm.
BTW what is your initial condition? Maybe you could post your sif file here.

Matthias

[ben]

Hi Matthias,

Sorry I wasn't very clear,.

What I want to know is the maximum amount of heating - how much the temperature rises at the point of heating.

The heat is dissipated by conduction through the film. With the temperature rise at the point of heating a balance between heat input and conduction.

This is a steady state situation - except when the diameter of the film is to small so that your heating up the whole body - (when there is no heat loss at the boundary).

Its how to mesh a small area which corresponds to that situation. Without fixing the temperature at the boundary.

I don't set the initial condition. I pasted the file below

Thanks

Ben

Header
CHECK KEYWORDS Warn
Mesh DB "." "."
Include Path ""
Results Directory ""
End

Simulation
Max Output Level = 5
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Simulation Type = Transient
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Timestep intervals = 20
Timestep Sizes = 1
Solver Input File = case.sif
Post File = case.ep
End

Constants
Gravity(4) = 0 -1 0 9.82
Stefan Boltzmann = 5.67e-08
Permittivity of Vacuum = 8.8542e-12
Boltzmann Constant = 1.3807e-23
Unit Charge = 1.602e-19
End

Body 1
Target Bodies(1) = 1
Name = "Body 1"
Equation = 1
Material = 2
Body Force = 2
End

Body 2
Target Bodies(1) = 2
Name = "Body 2"
Equation = 1
Material = 2
End

Solver 1
Equation = Result Output
Output Format = Vtu
Output File Name = case
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Exec Solver = Always
End

Solver 2
Equation = Heat Equation
Variable = Temperature
Procedure = "HeatSolve" "HeatSolver"
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-7
Nonlinear System Max Iterations = 1
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStabl
Linear System Max Iterations = 500
Linear System Convergence Tolerance = 1.0e-10
BiCGstabl polynomial degree = 4
Linear System Preconditioning = ILU9
Linear System ILUT Tolerance = 1.0e-3
Linear System Abort Not Converged = True
Linear System Residual Output = 1
Linear System Precondition Recompute = 1
End

Equation 1
Name = "Equation 1"
Active Solvers(2) = 1 2
End

Material 1
Name = "MyFluorApatiteMod"
Heat Conductivity = 0.2
Heat Capacity = 745
Density = 3200
End

Material 2
Name = "MyAluminium"
Heat Conductivity = 200
Heat Capacity = 897
Density = 2700
End

Body Force 1
Name = "SpecimenHeat_body1"
Heat Source = 0
End

Body Force 2
Name = "coatheat_body13"
Heat Source = 70735530263064.6
End

Boundary Condition 1
Target Boundaries(1) = 7
Name = "BoundaryCondition 1"
Heat Transfer Coefficient = 10000000000
External Temperature = 0
End

Boundary Condition 2
Target Boundaries(1) = 8
Name = "BoundaryCondition 2"
Heat Transfer Coefficient = 10000000000
External Temperature = 0
End

[mzenker]

Hi,

IMO to do this kind of simulation you should either do a steady state simulation (change the simulation type) or do a transient simulation as your sif file is set at the moment, but then with an initial condition.
Since your heat transfer coefficient at the external boundaries is very large, I think you can just as well force the temperature to zero or any other temperature.

HTH,

Matthias

[ben]

Hi,

Thanks, sorry is it possible to set the external temperature on the boundary to equal the temperature just inside the boundary - so as not to force it to zero?

For due to the very thin depth of the film with high heat inputs the film temperature at 500 um can be 300 degrees with the temperature at the centre of heating 1200C?

Thanks

Ben

[mzenker]

Hmmm...

I would suggest that you sit down and think about the physics of your problem once more ...
I think you somehow need to connect your object to the external world, either by forcing the temperature to a certain value at some boundary, or by defining a heat transfer to some external temperature. If you choose total thermal isolation, you will end with an infinite temperature.
And if you want to simulate the evolution of temperature with time, you need an initial condition to start from.

HTH,

Matthias