Temperature field

#1 Posted: 2023/7/15 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 Posted: 2023/7/15 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 Posted: 2023/7/15 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 Posted: 2023/7/15 07:17:49

Martin Kraska

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Don't know if that is the simplest solution.

Stenka-3-eng.sm (58.13 KiB) downloaded 764 time(s).

2023-07-15 12_15_54-SMath Solver - [Stenka-3-eng.sm_].png

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Valery Ochkov 2023/7/15 07:25:00

#5 Posted: 2023/7/15 07:26:46

Valery Ochkov

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Don't know if that is the simplest solution.

Stenka-3-eng.sm (58.13 KiB) downloaded 764 time(s).
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 Posted: 2023/7/15 07:32:04

Martin Kraska

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Version with mathcad block to collect the equations

2023-07-15 12_30_20-SMath Solver - [Stenka-3-eng1.sm].png

Stenka-3-eng1.sm (59.5 KiB) downloaded 819 time(s).

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Valery Ochkov 2023/7/15 07:40:00

#7 Posted: 2023/7/15 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 Posted: 2023/7/16 05:40:21

Valery Ochkov

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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.

Stenka-3-eng.sm (60.64 KiB) downloaded 794 time(s).

One solution from Alan Stevens
Stenka-3-Alan.sm (60.35 KiB) downloaded 741 time(s).

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Temperature field - not straight line but one parabola - Messages