Double-Pipe Heat Exchangers
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The outer surface of the inner tube can be finned and then the tube can
be placed concentrically inside a large pipe (Figures 1.8 and 7.2). In
another type, there are multi tubes, finned or bare, inside a larger pipe
(Figure 7.3).
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Thermal and Hydraulic Design of Inner Tube
Correlations available in the literature are used to calculate heat transfer
coefficients inside the inner tube. Important correlations are given in
Chapter 3. The frictional pressure drop for flow inside circular tube is
calculated using the Fanning Equation (Equation 4.3):
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Thermal and Hydraulic Analysis of Annulus
Heat transfer and pressure calculations for flow inside the annulus shell are
similar to those for the tube-side flow, provided that the hydraulic diameter
of the annulus is used instead of the tube inner diameter. The hydraulic
(equivalent) diameter is given by Equation 3.14.
It should be noted that only a portion of the wetted perimeter is heated or
cooled. Therefore, the hydraulic (equivalent) diameter for the heat transfer
calculations is not the same as that used in pressure-drop calculations,
given by Equation 3.18.
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Hairpin Heat exchanger with Bare inner Tube
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Hairpin Heat exchangers with Multi-tube
Finned inner Tubes
The total wetted perimeter of the annulus with longitudinally finned inner tubes can
be written as (see Figure 7.2)
and the heat transfer perimeter of the annulus can be calculated from
It is assumed that the outside of the annulus is insulated
against heat losses and the heat transfer occurs through
the wall and the fins of the inner tube. The net crosssectional free flow area in the annulus with longitudinal
finned inner tubes is given by
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Hairpin Heat exchangers with Multitube Finned inner
Tubes
From Equations 7.4, 7.5, 7.8, 7.9, and 7.10, the hydraulic diameter for the
Reynolds number and the pressure drop is
and the equivalent diameter based on heat transfer,
For a double-pipe heat exchanger of length L, the unfinned (bare) and
finned areas are, respectively,
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The total outside heat transfer surface area of a hairpin is the sum of the
unfinned and finned surfaces, given by Equations 7.11 and 7.12 (see Figure
7.2):
The overall heat transfer coefficient based on the outside area of the
inner tube is given by Equation 2.17. It should be noticed that Ao is
replaced by At:
where
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which is defined by Equation 2.15. As can be seen from Equation 7.14,
area ratios At /Ai and Af /At must be calculated to find the overall heat
transfer coefficient based on the outside surface area of the inner tube. It
should be noted that Rw is calculated for bare tubes using Equation
2.12b. The fin efficiency is given by Equation 2.18:
where
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