Hi there, I'm not sure if this is the right section of the forum, hopefully yes.
Don't know if there is some area in the forum where newbies like me post newbie-like questions, and then some Yoda out there shows the path... that would be the case of this post :P

Starting from the beginning: just to practice a little bit with programming in SMath (I'm NOT an expert at all), I wanted to set up a small calculation file to determine temperature profiles into big pipelines equipped with internal refractory linings and external insulation layers.
It's both a programming exercise for me, and (in case I succeed) a handy tool for office work..
So, I started preparing the attached file.

PROVA CONDUZIONE TERMICA_bkp.sm (63kb) downloaded 38 time(s).

Basic elements of the file are:
* There are four layers of internal refractory (1 to 4)
* Layer 5 is steel
* Layers 6 and 7 are external insulation
* In case a layer is missing, its thickness is set to zero.
* A database o materials is defined, and conductivity is interpolated between known data (supplied by lining fabricators).

The logic behind is:
1) Input general data
2) Select materials and thicknesses
3) Program loops from a trial linear temperature profile, updating conductivities at each loop, since conductivity is a function of temperature itself... that's the reason for looping.
4) Equivalent thermal resistance is calculated
5) Total heat flux is calculated
6) Trial temperature profile is updated backwards...

... or at least, that was my initial goal
:'(

I found out that the "while" iterations will take A LOT of memory, even if in my mind this problem seems not so demanding in terms of resources.
This is the reason why the "while" loop is temporarily controlled by a maximum number of iterations.
I wanted to add a numerical residual check, in order to break the "while" when residuals where small enough, but I had to begin debugging, so at the moment i'm using the variable "counterlimit" to stop the loop.
It came out that, with counterlimit set to 3 (or below, but in that case results are not yet good enough..), Smath runs the calculation in 20 sec... If counter is set to 4 or above, it runs for minutes (and I always stop it manually).

This said..... why such increase in execution time? Does anybody understand where am I missing something and why is this calculation so demanding, only if counterlimit is increased?
What bothers me the most, is that calculation time does not increase proportionally with the "while" counter number, even if the dataset is not increase in dimension while iterations proceed...
If somebody is willing to dig a little bit into this file, I will be glad to learn something from some expert user!

Thank you
Ciao!


ps: I can see that the conductivity calculation, as I implemented it, is kind of messy (a matrix of materials made up of vectors, used to interpolate conductivity for each material at each loop).... but honestly speaking I couldn't find a better way to fit conductivity equations into (remarkable!) Davide Carpi Comboboxlist plugin.
I will try to store equations as a string, recall it from the database and cook it back again as a formula with "num2string"... Never tried this approach, but it's worth a test or two.

Benvenuto.

I also try Jean Giraud's opinion that I was lost in a jungle, although the project does not seem to be a big one. I think you should first make a logic scheme and then structure the project accordingly. Otherwise, all the best.

I didn't really get a chance to go through the math at all, but I did optimize run time of the current implementation. I used the eval() function in the lamda_t function definition. Took evaluation from 20 seconds to 0.25 seconds on my machine.


PROVA CONDUZIONE TERMICA_bkp_alyles.sm (66kb) downloaded 17 time(s).

Work 1rst modular like in the attached.
Most confusing are different but equivalent maths that output different unit system.
What other simple maths will output another/same unit system or "Units don't match".




PROVA CONDUZIONE TERMICA_bkp [0].sm (95kb) downloaded 18 time(s).

Thanks Carlos for doctoring this project.

1. Refreshed a bit
2. Few more things at the end.
3. "L" is confusing as not explained ... considered "unary"
4. Two pests [in green] wrt to units.
5. The last 4 "clear" removed from program [avoid red]

Wait and see for Originator to comment/complement

Jean

PROVA CONDUZIONE TERMICA_bkp_CBG [Jean].sm (345kb) downloaded 20 time(s).

... maybe the last brick in the wall, if so desired:
I'm only slightly pregnant of understanding the discontinuity
@ [770] ... infinitesimal film is not discontinuous.
Easy to fillet, Hermite tool box will do.

Hi everybody, thanks for all the efforts and support.

I will review all the contributions one by one, I just had the chance right now to go through the posts now quickly..

The use of eval() is somehow new to me, I will look at it's implications, since I understand that it has improved a lot the execution time.
Yesterday morning I spent some minutes again testing my file and became suspicious at how I implemented lambda.
It looks like I was accessing to that database matrix a lot of time.
Now I see that a great improvement has come from this eval() function...

Will go through the details and keep you posted.

Thanks again for the support

Ok, I took my time to study all the files you posted and read all the replies again and again.
I'm happy to see that the "while" was messy, not commented properly, etc etc... but it could work (with some help)!
And also the lambda function and the way I defined the database...

First of all, going to your contributions, now I see what Jean meant with one of the first replies:

I needed to right click and set the while to Numerical optimization?


Setting my original file this way, makes the loop work quickly (shame on me, I wasn't even aware of such setting...)

Also Alyses hint has helped me to understand that the symbolic evaluation was the problem, and that some different setting should be implemented.

Iinfact, the following files by other users did not use the eval() function, so I was kind of lost, until I found that right click setting...
So, in the end, if my understanding is correct, eval() and right-click numeric optimization setting are equivalent, isn't it?

Now, going to Carlos contribution, thanks, I see that you found the way to make all the "if" and "while" loops scalable, meaning that I can add / subtract layers of lining.
The length of arrays, the number of loops will now automatically adapt... that was one of my goals, except that I got stuck in the execution time problem, so stayed simple with seven fixed layers of materials. Thank you.
And by the way, I see that your file uses a plugin with a lot of functions I did not know (that cases() function, for sure I will be using it a lot in the future....)


Jean, what command are you using to generate this kind of matrix? What is the sintax, I mean,to define Q(w) or T.ext (°c) and obtain results without Units? Looks like it is a Custom Function again.


Thanks guys, I definitely learnt something (to say the least) from this thread.

Federico



Ps: by the way, totally on the same page here, but I see Jean's point in running unitless with his example he provided too...

Not so simple !
In the just attached Hermite Polyline, open the first collapsed area.
Observe eval(,) in the subspace module, this is a case of local definition.

Jean