Temperature field

#1 Pubblicato: 15/07/2023 03:32:54

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I am trying to plot a temperature field in a three layer wall. There is no problem with the outer layers. But there is a problem in the middle layer - there should be a parabola, not a straight line. How to draw this parabola in the simplest way - with one formula. I know the hard way.

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#2 Pubblicato: 15/07/2023 06:51:42

Laurent Fournier

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There are so many splines and Bezier interpolations in this forum!
But I don't understand why the connecting line has to be a parabola, because inside one wall layer the parameters (conductance, permeability) are constant so you should have only straight lines. Unless you found a way to have a gradual mix of material!!!

#3 Pubblicato: 15/07/2023 06:56:42

Valery Ochkov

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There are so many splines and Bezier interpolations in this forum!
But I don't understand why the connecting line has to be a parabola, because inside one wall layer the parameters (conductance, permeability) are constant so you should have only straight lines. Unless you found a way to have a gradual mix of material!!!

In the outer walls, the thermal conductivity does not depend on temperature, but in the middle wall it depends linearly!

#4 Pubblicato: 15/07/2023 07:17:49

Martin Kraska

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Don't know if that is the simplest solution.

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Valery Ochkov 15/07/2023 07:25:00

#5 Pubblicato: 15/07/2023 07:26:46

Valery Ochkov

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Don't know if that is the simplest solution.

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Fine!

And if the dependence of thermal conductivity on temperature is more complex, obtained, for example, through interpolation of discrete data. I would like to see an integral in the solution!

#6 Pubblicato: 15/07/2023 07:32:04

Martin Kraska

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Version with mathcad block to collect the equations

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Valery Ochkov 15/07/2023 07:40:00

#7 Pubblicato: 15/07/2023 09:13:21

Jean Giraud

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I am trying to plot a temperature field in a three layer wall. There is no problem with the outer layers. But there is a problem in the middle layer - there should be a parabola, not a straight line

1. Three layers linear from min(x).
2. NON-linear from experimental
... project done Mathsoft Collaboratory.
Make the first & third segments linear.
The two documents sanity checked Smath Solver 30405.
Cheers ... Jean.

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#8 Pubblicato: 16/07/2023 05:40:21

Valery Ochkov

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Wrote
I am trying to plot a temperature field in a three layer wall. There is no problem with the outer layers. But there is a problem in the middle layer - there should be a parabola, not a straight line. How to draw this parabola in the simplest way - with one formula. I know the hard way.

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One solution from Alan Stevens
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Temperature field - not straight line but one parabola - Messaggi