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Garnet

## Automatic solution of multilayer stady heat transfer as a function of layers number

Hi,

I'm looking a way of automatic solution of HT problem with multilayer steady heat transfer with numbers of layer dependency.

I'd like to put n variable as number of materials layer then put thicknes and thermal conductivity as a consequences of layer namber and finally get a solution for n=2,3...k layers.

Thank you in advance for any idea

I enclose MP 4.0 file.

wzel

1 ACCEPTED SOLUTION

Accepted Solutions

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

I think the link did that, although yours is complicated by having different equations at the start and end.  But the concept is the same.  Since I can probably use something similar someday, I took a stab at it.  Seems to work - you can add or delete rows to the table. But user beware, etc.

T_start is the temp at the start of a 'plate', and T_end is the temp at the end of a plate.

8 REPLIES 8

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

May by this Mathcad-Websheet is any help for you

http://twt.mpei.ac.ru/MCS/Worksheets/Thermal/T-T-2-Chapter-3-3-3-1.xmcd

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

Thank you both, Valery and DJF.

The problem is that I have to solve the non-linear equation due convecting and radiation therms which are set as outflow boundary condition.
This is a first step to get interlayer and inflow temperatures.

wzel

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

I think the link did that, although yours is complicated by having different equations at the start and end.  But the concept is the same.  Since I can probably use something similar someday, I took a stab at it.  Seems to work - you can add or delete rows to the table. But user beware, etc.

T_start is the temp at the start of a 'plate', and T_end is the temp at the end of a plate.

Sapphire III
(in response to DJF)

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

Note that your solution changes the value of Q.  Might try taking it out of the Find statement

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

I thought that finding Q was the (eventual) point.  If I define the temperatures then Q is a result, not an input.  Otherwise I'd need to change thicknesses or heat transfer.  Original post solved for Q, but never called it that - they just set the equations for Q equal to each other.  But I didn't study it very hard so maybe I'm not understanding their question.

Sapphire III
(in response to DJF)

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

I understand the confusion.

If you have the inside/outside temperatures given, then solving for Q and the layer by layer makes sense and should work.

If you set Q (and wither the inside OR the outside temperature), then you can solve for the whole temperature set.

I didn't realize you were solving the first problem.  Sorry!

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

Hi,

Thank you DJF, your solution work perfectly.

I have overlooked my own mistake in first post. In quadratic part of radiation therms should be plus instead minus.

I have checked solution with my old maple mathapps. The results are the same.

Below comparison of 3 and 4 layer solution done in MathCad and Maple.

Q vaule is also correct. it is no surpise beocuse Q=4000W is starting point for looking solution.

Thank you once again.

wzel

## Re: Automatic solution of multilayer stady heat transfer as a function of layers number

I think this is similar to a problem I posted here (N orifices in series).