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Nonlinear system of equations in heat flow

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Nonlinear system of equations in heat flow

Hi,
I am a student working on a problem to design a hand dryer (heater). I believe all of my equations are correct and complete, but I am having a difficult time solving a nonlinear system of 8 equations and 8 unknowns (bottom of sheet). If somebody could please provide some help or advice as to how to fix this, I would surely appreciate it as I've been trying for hours on both Mathcad and MATLAB and have been unsuccesful thusfar.

Thanks in advance,
Bob
5 REPLIES 5
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Nonlinear system of equations in heat flow

According to the Mathcad error message, your immediate problem is that di is not defined. Poor as they are, the Mathcad error messages are vital and cannot be ignored.
__________________
� � � � Tom Gutman
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Nonlinear system of equations in heat flow

You were careless with several subscripts and also had a poor initial guess for one parameter. See attached.

stv
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Nonlinear system of equations in heat flow

This kind of work deserves a diagram, especially as it is a heat exchanger project and the matter is always traceability. You use "logmean", that is really from the blue for a non versed person. Pipe is "rigid circular conduit", "tube" is a thin wall. A2 is out of the blue also, what is 0.1016 ? Mathcad is idiotic enough showing symbolic result .123456789 instead of 0.123456789, that at least when you plug number, plug them right. For traceability, .123456789 DOES NOT pass ! Subscripts are so much confusing that their use should be very limited or at least near the end , then your solver has one of those gross mistake. First thing to do "This variable is not defined above", make all the constants "Courier New" blue, make all variables "Courier new" and click on each definition to see the expansion and often detect the error.

You don't use units, fine. But what are all these numbers (m, km....peanuts ?), how can they be traced. Certain parts may be OK but not usable outside of this meaningless work sheet and up until now it does nothing useful: It is a heat exchanger, normally the controlled variable is the output Temperature, no diagram where is it ? and for controlling something out, there must be something varying IN, is it ? On STV working sheet, assuming T2 is the controlled variable that you want to have, something must vary, but changing T2 for another value, nothing changes.

That the solver his capable of outputing a lot, fine but most of them are simply resulting and need not be included in the solver as this is confusing, at least at the creation stage and makes the traceability even more difficult. So, to resume what do you control from what ? Would it make sense that in the "logmean" T1 has something to do and should be part of the solver .

Another point is the traceability of the formulas in the solver. If they come from some reference material, how the reader knows. The project may have some value, but not as presented and the Process Control & Instrumentation Engineer can't use it for a control scheme. Some of the T's are visibly temperature but Th, Twi are out of common sense , where do they come from if not calculated or otherwise described ?

Don't think my comments are that negative: you have plenty of numbers but knowing nothing about what is what !

jmG
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Nonlinear system of equations in heat flow

I think I got a blank stare when I deflected the original problem worksheet to my College of Engineering. I don't have the analytical power that jmG has. His comments are very penetrating.
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Nonlinear system of equations in heat flow

On 10/3/2008 8:26:04 PM, wenonah55 wrote:
>I think I got a blank stare
>when I deflected the original
>problem worksheet to my
>College of Engineering...
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Heat exchangers is a classical problem in Chemical Engineering. Professors love the complexicity of this kind of exercise, students hate it. TEMA (Tubular Exchanger Manufacturers Association) maybe of some help, but their site wants to install a gadget "Flash... ? but I want nobody else in my box. The project will surely get lot of attention as soon as a diagram is provided c/w the scope.

jmG
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