Temperature field

#1 Publicado: 15/7/2023 3:32:54

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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 Publicado: 15/7/2023 6:51:42

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 Publicado: 15/7/2023 6:56:42

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 Publicado: 15/7/2023 7:17:49

Martin Kraska

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Don't know if that is the simplest solution.

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Valery Ochkov 15/7/2023 7:25:00

#5 Publicado: 15/7/2023 7:26:46

Valery Ochkov

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Don't know if that is the simplest solution.

Stenka-3-eng.sm (58,13 KiB) descargado 1406 vez(es).
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 Publicado: 15/7/2023 7:32:04

Martin Kraska

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Version with mathcad block to collect the equations

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Valery Ochkov 15/7/2023 7:40:00

#7 Publicado: 15/7/2023 9:13:21

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 Publicado: 16/7/2023 5:40:21

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.

Stenka-3-eng.sm (60,64 KiB) descargado 1402 vez(es).

One solution from Alan Stevens
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Foro SMath

Temperature field - not straight line but one parabola - Mensajes