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Thread Subject:
help writing a solver to understand what the authors did.

Subject: help writing a solver to understand what the authors did.

From: matlab_learner

Date: 1 Apr, 2011 03:18:47

Message: 1 of 2

hi all...
hope all is well with you.
================
this original research document is actually free on the internet. the
title of the paper is: "Current and Future Miniature Refrigeration
Cooling Technologies for High Power Microelectronics" and the
formulars are on page 6 and the result is on page 7 of the document.
========================

i am trying to improve on a concept, and need to figure out what the
pioneers did, first of all so i can make my own alterations with my
own approach. i'm needing to understand how to write a solver routine
in matlab or use Excel, where I have a goal and then iterate till i
reach that goal...and then save my data point.
the original authors used a solver in Excel to solve what they were
developed, and then generated data from iterations, and from their
generated data plotted graphs in Excel. - simple relational linear
graphs. They were supposed to have had constraints in their equations,
(maybe like Lagrange equations in their Excel solver; I really don't
know what their constraints were). I have been able to reproduce their
equations which I shall display below and what they said they did to
get their graph....
FULL DISCLOSURE: My direction of interest is different from what they
did. however, I am interested in what they did with available basic
information to generate a ton of data to enable them plot their graph,
which is my goal, to use the same parameters to generate a ton of data
for mine and then plot and compare and analyze.
My hope is that by figuring out what they did, I can generate my own
data using my own sets of equations and then plot my graphs as
required...and then make my own variation in analyzing the problem and
i shall be giving credit to all parties involved - not trying to
cheat or anything. i am using the same system they used, and so my
parameters are going to be the same as their's but we have different
equations as I am trying to improve their work. Once I get what they
did I will then work my own equations. Thanks.
Here is their work:
===========================================
Here are the values for the parameters which are used to in their
equations shown below (same parameters I will use given it is the same
system but a dift approach):
W = 125
N=31
&=0.000 2
P=0.000 01
Tc = ?
Z = .002 667
G=0.011 96
k = 1.5
Th=Ta=25
dT = Th - Tc
dT(max) = 67 --- dT(max) is the maximum value that dT can get to...
R1 = 0.571
R2 = 0.049
here are the equations.
X = (& * Tc * G / P) --- so in my understanding, X is generated each
time Tc changes since it is the only free variable given...
they also gave an equation for dT(max)...unsure if the values changes
or not since it is a max value and that was given by the system in
consideration but here is the equation:
dT(max) = 0.5*Z*Tc^2
and

Q = 2NGk [ dT(max) - dT ] -- i believe this is the version they used
while computing...
and Q also has a variant = 2N [ &*X*Tc - (0.5*X^2 *P/G) - k*G*dT ]
they are the same equation...

W = 2NGk*Z*Tc*Th
the other equation i believe they used in computing is:
R1*Q = Tj - Tc;
and
(Q + W) * R2 = Th - Ta

and also $ = Q/W was the last equation.
--------------------------------------
here are their comments b4 displaying the graphs and the physical
explanation of the system:

heat flow Q is input, and the resulting Tj is determined.
Typically, a value for one of the temperatures (where the temperatures
are Tj, Tc, Ta, Th) is guessed, and then the solution is iterated
until Q reaches the desired input value. The calculations were all
performed on an Excel spreadsheet,
=============================
this document is actually free on the internet. the title of the paper
is: "Current and Future Miniature Refrigeration Cooling Technologies
for High Power Microelectronics" and the formulars are on page 6 and
the result is on page 7 of the document.

Please relay any questions you have to me. thanks very much.

Subject: help writing a solver to understand what the authors did.

From: Torsten

Date: 1 Apr, 2011 08:08:45

Message: 2 of 2

On 1 Apr., 05:18, matlab_learner <cib...@gmail.com> wrote:
> hi all...
> hope all is well with you.
> ================
> this original research document is actually free on the internet. the
> title of the paper is: "Current and Future Miniature Refrigeration
> Cooling Technologies for High Power Microelectronics" and the
> formulars are on page 6 and the result is on page 7 of the document.
> ========================
>
> i am trying to improve on a concept, and need to figure out what the
> pioneers did, first of all so i can make my own alterations with my
> own approach. i'm needing to understand how to write a solver routine
> in matlab or use Excel, where I have a goal and then iterate till i
> reach that goal...and then save my data point.
> the original authors used a solver in Excel to solve what they were
> developed, and then generated data from iterations, and from their
> generated data plotted graphs in Excel. - simple relational linear
> graphs. They were supposed to have had constraints in their equations,
> (maybe like Lagrange equations in their Excel solver; I really don't
> know what their constraints were). I have been able to reproduce their
> equations which I shall display below and what they said they did to
> get their graph....
> FULL DISCLOSURE: My direction of interest is different from what they
> did. however, I am interested in what they did with available basic
> information to generate a ton of data to enable them plot their graph,
> which is my goal, to use the same parameters to generate a ton of data
> for mine and then plot and compare and analyze.
> My hope is that by figuring out what they did, I can generate my own
> data using my own sets of equations and then plot my graphs as
> required...and then make my own variation in analyzing the problem and
> i shall be giving credit to all parties involved  - not trying to
> cheat or anything. i am using the same system they used, and so my
> parameters are going to be the same as their's but we have different
> equations as I am trying to improve their work. Once I get what they
> did I will then work my own equations. Thanks.
> Here is their work:
> ===========================================
> Here are the values for the parameters which are used to in their
> equations shown below (same parameters I will use given it is the same
> system but a dift approach):
> W = 125
> N=31
> &=0.000 2
> P=0.000 01
> Tc = ?
> Z = .002 667
> G=0.011 96
> k = 1.5
> Th=Ta=25
> dT = Th - Tc
> dT(max) = 67   --- dT(max) is the maximum value that dT can get to...
> R1 = 0.571
> R2 = 0.049
> here are the equations.
> X = (& * Tc * G / P)  --- so in my understanding, X is generated each
> time Tc changes since it is the only free variable given...
> they also gave an equation for dT(max)...unsure if the values changes
> or not since it is a max value and that was given by the system in
> consideration but here is the equation:
> dT(max) = 0.5*Z*Tc^2
> and
>
> Q = 2NGk [ dT(max) - dT ]  -- i believe this is the version they used
> while computing...
> and Q also has a variant = 2N [ &*X*Tc  - (0.5*X^2 *P/G) - k*G*dT ]
> they are the same equation...
>
> W = 2NGk*Z*Tc*Th
> the other equation i believe they used in computing is:
> R1*Q = Tj - Tc;
> and
> (Q + W) * R2 = Th - Ta
>
> and also $ = Q/W was the last equation.
> --------------------------------------
> here are their comments b4 displaying the graphs and the physical
> explanation of the system:
>
> heat flow Q is input, and the resulting Tj is determined.
> Typically, a value for one of the temperatures (where the temperatures
> are Tj, Tc, Ta, Th) is guessed, and then the solution is iterated
> until Q reaches the desired input value. The calculations were all
> performed on an Excel spreadsheet,
> =============================
> this document is actually free on the internet. the title of the paper
> is: "Current and Future Miniature Refrigeration Cooling Technologies
> for High Power Microelectronics" and the formulars are on page 6 and
> the result is on page 7 of the document.
>
> Please relay any questions you have to me. thanks very much.


(6)-(11) on page 361 are a system of 6 equations in the unknowns
T_h, T_c, T_j, T_a, W and COP.
Use MATLAB's FSOLVE to solve.

Best wishes
Torsten.

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