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Heat Exchanger Design
Figure 4: Radial flow at shell entrance.
Figure 5: Axial flow area at shell entrance. Figure 6: Adopted coordinate system.
The first term( πD n
h): is the area of flow directs radially from the nozzle axis through the gap( h) between nozzle entrance / exist and tube bundle. Figure 4 demonstrates differential area of this flow as dA = rdθ. dz
Integrating A = ∫ h 0 ∫2πr dθdz, where r = D / 2 will give
0 n the first term, πD n h.
The second term(( π / 4) × D 2): is the crosssectional area of the nozzle projected on the tube
n
bundle. This term is modified by the fraction(( P t
– D t) /( F 2
P t)) which adjusts for the spacing between tubes— that is, how much clearance is available in the tube pattern( F2). Multiplying by
F 1
= 0 effectively“ turns this term off” when an impingement plate is provided and covered the entire nozzle area.
Bundle entrance area( location 3) This is the total area consists of 3 flow paths at the bundle entrance / exist generally expressed by the formula:
A B
=( B s( D s
– OTL) +(( B s K – A P
) ×(( P t
– D t) /
( F 2
P t
)) + A L) ×( ft 2) / 144 in 2)
Breakdown of the formula: The following coordinate system is first adopted to demonstrate the flow paths: The first term B s
( D s
– OTL): is one of the two flow areas in Y-Direction between Ds and OTL, shaded green in Figure 7. The second terms(( B s
K – A P) ×(( P t – D t) /( F 2 P t)): is the other flow area in Y-direction between tubes at the first row of the bundle in the inlet / outlet baffle chamber Bs, shaded yellow. K is the chord of the first row of tubes, and the modifying factor(( P t
– D t) /( F 2
P t
)) also appears to discount obstructed area. The third terms( A L
): This is the flow area in horizontal X-Direction. The flow direction is parallel to the tubes AND gets freely to the next baffle. Therefore, it is named as free flow, however, should be better named as by-pass flow.
Free flow area for partial tube layout design The free flow must occur at the first row of the bundle entry area. To determine this area, we create two projection lines: one from the first row bundle chord to the Shell ID, and another from the baffle cut to the Shell ID. The space between these two projection lines represents the free flow area, which is highlighted in red in Figure 8.
Figure 7: Cross sectional of shell & tubes at first row of tubes( tubes are shown in first baffle only for simplicity).
Figure 8: Partial tube layout free flow area.
www. heat-exchanger-world. com Heat Exchanger World October 2026
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