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Unformatted text preview: Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 11. Heat Exchangers 107
(April 23, 2003) 11.1 Heat Exchangers
Heat exchangers can be classiﬁed according to ﬂow arrangement and type of construction. The simplest type of construction is the concentric tube, where the ﬂow can be either parallel or counterﬂow (see ﬁgure below; ﬁg. 11.1) Crossﬂow heat exchangers can be tubeﬁn (mixed or unmixed) (see ﬁgure below; ﬁg. 11.2) or platﬁn (compact heat exchangers) (see ﬁgure below; ﬁg.
11.5) Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 108 The deﬁnition of a compact heat exchanger is that the
ratio of the total heat transfer area to the volume the heat
exchanger occupies exceeds 700, i.e.
). §§
¤¨¦ ¥ ¤¢ £¡ A special type of crossﬂow heat exchanger is tubeand
shell heat exchanger (see ﬁgure below; ﬁg. 11.3) which can consist of one or several tube passes.
Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 109 11.2 Overall Heat Transfer Coefﬁcient
In Chapter 3 we learned that the overall heat transfer coefﬁcient can be written (index =cold; index =hot) ¢ ¡ ¦
4 ¡ 2 © 0 £
3
&£
¢ ¦ !1 ¦ ! 0¥£ " ¦ ) " ¢ ¦ ©
!
!
&
(%#' #$£
(%#' &$£ # © © ©¨§¦¥£
¤¤ where
are additional resistances due to fouling (impurities) at the surfaces, and
is the resistance
(see
due to conduction. The temperature effectiveness
Section 3.6) for the ﬁnned surface reads G
G
¦ E H& EF & D9 &
CA@8 B6 976 9
¢¦ ©¦
© &5
&
& where
is the total ﬁn surface area, is the sum of the total ﬁn surface area and the exposed base area (i.e.
), and is the efﬁciency of a single ﬁn. I ¡& Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 110 11.3 Heat Exchanger Analysis
If we neglect heat losses to the surroundings of a heat exchanger, energy conservation states that the heat transfer
between the hot and cold ﬂuids is ¤ ' ¥9 ¦ ' £
¢
¢ ¡ © ¦ ' ¥9 ¤ ' £
¢
¢ ©5 ¡ where indices and denote outlet and inlet, respectively.
If there’s no phase changes, it can be simpliﬁed to
¢ 6 §
¤ ' A9 ¦ ' ' ¨¡
6
6 ¡ ¦ §
© ¦ ' D9 ¤ ' ' ¨¡
6
6 ©5 ¡ The temperature difference between the ﬂuids
is a function of . It is convenient to deﬁne a mean temperature difference
which will be computed differently depending
on if it is a parallel or counterﬂow heat exchanger. Independent of this, the heat transfer can be written
.
© 6
6 © ©5 © Parallel ﬂow
The energy balance for the two ﬂuid (no phase change)
for a element ( ) gives (see ﬁgure below; ﬁg. 11.7)
Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 111 5 © 5
6 ©
6 ¡9 © 6 (1)
(2)
(3) ©
6
'
6 © © 5
§
' ¡ ¡ © 5
¡ ¡ © 5
9 §
¨
The temperature difference between the hot and cold ﬂuid
is deﬁned as 6
96
© 6 ©
¢6
£ A9 6 © 6
© Eqs. 1, 2 & last part of 3 into Eq. 4 gives ¥¦
9 9 5
¤ © 6 ©
If we now use the ﬁrst part of 3 we get ¥ !
¤ 6
© Incropera & DeWitt. Chapter 11 (4) ©
9 ©6
Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 112 Integration from station 1 to 2 (see ﬁgure above) gives ¤
¥6 6
¦ ' 6D9 ¦ ' 6 © £6 © E ¤ ' A9 ¤ ' 6 © ¥6 ©
¢
6
¤
© ©5
¡6 ©
©
¤ 6 ¡ ¢ 6 © ¨§¦ ©
¡6 9 £6
¢
© © where
is the logarithmic mean temperature. Note
that this is the same expression we derived in Section 8.3.3.
© Counterﬂow
For the counterﬂow case we get (see ﬁgure below; ﬁg.
11.8) ¤ ' D9 ¦ ' 6 © ¢ 6
6
© E ¦ ' A9 ¤ ' 6 © ¤ 6
6
© Special case
Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 113 Special cases are when either one heat capacity rate is
much larger than the other so that the temperature of the
former ﬂuid is approximately constant (see the ﬁgure below; ﬁg. 11.9) This is also the case if there is a phase change for one of
the ﬂuids. Then we have to use the enthalpy difference
¢ © Multipass and CrossFlow Heat Exchangers
They are both consider to be crossﬂow heat exchangers.
For the multipass type correction factors are used, depending on number of passes and temperatures. Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer
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http://www.tfd.chalmers.se/grkurs/MTF111 114 11.4 NTU Method If all inlet and outlet temperatures are known, it is simple
to analyze the heat exchanger by computing the logarithmic mean temperature (”the LMTD method”). If the outlet
temperatures are not known, the LMTD method requires
iterating: looong time ago (i.e. before the calculator became every engineer’s friend) this used to be inconvenient,
and this was the reason the NTU Method was invented.
Today, this method has been outdated by calculators (and
Matlab), and iterating does not pose any problem, and this
is the reason why this method is not a part of this course. Incropera & DeWitt. Chapter 11 ...
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This note was uploaded on 12/05/2011 for the course MEEG 385 taught by Professor Pr during the Fall '11 term at The Petroleum Institute.
 Fall '11
 PR
 Heat Transfer

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