chapter_11 - Hakan Nilsson: Heat Transfer ˚

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Unformatted text preview: Hakan Nilsson: Heat Transfer ˚ http://www.tfd.chalmers.se/gr-kurs/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) Cross-flow heat exchangers can be tube-fin (mixed or unmixed) (see figure below; fig. 11.2) or plat-fin (compact heat exchangers) (see figure below; fig. 11.5) Incropera & DeWitt. Chapter 11 Hakan Nilsson: Heat Transfer ˚ http://www.tfd.chalmers.se/gr-kurs/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 cross-flow heat exchanger is tube-and 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 ˚ http://www.tfd.chalmers.se/gr-kurs/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 ˚ http://www.tfd.chalmers.se/gr-kurs/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 ˚ http://www.tfd.chalmers.se/gr-kurs/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 ˚ http://www.tfd.chalmers.se/gr-kurs/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 ˚ http://www.tfd.chalmers.se/gr-kurs/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 Cross-Flow Heat Exchangers  They are both consider to be cross-flow 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 ˚ http://www.tfd.chalmers.se/gr-kurs/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.

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