- #1
CRich
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Homework Statement
I'm trying to derive the [tex]\epsilon[/tex] - NTU Expression for a double-pipe counter flow heat exchanger. I know what I need to do the only problem I am having is:
I don't know how to algebraically go from
ln( [tex]\frac{\Delta T2}{\Delta T1}[/tex] ) = -UA ( [tex]\frac{1}{Ch}[/tex] + [tex]\frac{1}{Cc}[/tex] )
to
ln( [tex]\frac{Th,o-Tc,i}{Th,i-Tc,o}[/tex] ) = -[tex]\frac{UA}{Cmin}[/tex](1-[tex]\frac{Cmin}{Cmax}[/tex])
2. Homework Equations & attempt at problem
I said (1/Ch + 1/Cc) = ([tex]\frac{Th,i-Th,o}{q}[/tex] + [tex]\frac{Tc,o-Tc,i}{q}[/tex])
Then I used the relationship: [tex]\epsilon = \frac{q}{qmax}[/tex]
where qmax = Cmin(Thi-Tci)
...so q = [tex]\epsilon[/tex] * qmax
substituted these equations in ...
I have a giant mess of Cmin and Cmax
Any help is greatly appreciated!
The only other equations that may be beneficial are:
q = mh*Cph*(Th,i - Th,o)
and
q = mc*Cpc*(Tc,i - Tc,o)
and
[tex]\frac{Cmin}{Cmax}[/tex] = [tex]\frac{mh Cph}{mc Cpc}[/tex] = [tex]\frac{Tc,o - Tc,i}{Th,i - Th,o}[/tex]