This article was produced to highlight the fundamentals of single-phase heat exchanger rating using Kern's method. The content is strictly academic with no reference to industrial best practices.

1. 1
THERMAL RATING OF SHELL & TUBE HEAT EXCHANGER
Single Fluid Flow Phase Heat Transfer
Vikram Sharma
Heat transfer is an essential part of any chemical processes. Without it, many
processes would not be operating. The commonly used device to facilitate heat transfer
is called heat exchanger. The equipment itself is relatively simple. However, the design
aspect of a heat exchanger requires a detail understanding on the fundamentals of heat
transfer and construction. Owing to its wide scope of knowledge, this article shall focus
on the thermal design of single-phase heat transfer shell-and-tube heat exchanger.
The thermal design calculation shall be based on a liquid-liquid heat exchanger using
Kern’s method.
First and foremost, it is important for a designer to determine if the heat exchanger is to
be designed for counter-current or co-current flow. The counter-current flow is described
as fluids flowing in the opposite direction whereas the later involves fluids flowing in
parallel. Designers prefer counter-current over co-current due to the following reasons
(Engineers Edge, n.d.):
 Thermal stresses in the heat exchanger is minimized due to a more uniform
temperature difference between two fluids;
 The cold fluid outlet temperature can approach the inlet temperature of the hot
fluid; and
 A more uniform rate of heat transfer can be achieved due to uniform temperature
difference throughout the heat exchanger.
Owing to this, the counter-current flow is preferred. Therefore, the thermal design shall
be based on the counter-current heat exchanger.
The next step is to determine the fluid allocation in the tube-side and shell-side. Correct
fluid allocation in the heat exchanger is important to ensure reliability and operability of
the equipment. Fluids with the tendency to foul should be placed in the tube side as to
facilitate cleaning. However, the above rule is dependent on the exchanger
configuration. The use of fixed tube sheet requires clean fluids to be placed in the shell
side with the exception if the fouling can be removed easily via chemical cleaning. The
use of U-tubes in exchangers requires fouling fluids in shell side; unless if fouling
reduction steps are available, e.g. installation of helical baffles (Sloley, 2013).
Corrosive fluids shall be placed in the tube side as to minimize the cost of purchasing
expensive alloys and cladding material. With this, only the tubes, tubesheets, heads and
channels will require expensive corrosion resistant alloys (Sloley, 2013). If fluid
temperatures are sufficiently high that warrants the use of special alloys, therefore the
fluid shall be placed in the tube side. Besides cost, the allocation of hotter fluids in the

2. 2
tube side will reduce the shell surface temperatures and improving safety. Similarly,
very high pressure fluids to be placed in the tube side of the exchanger as the
construction cost of high pressure tubes are cheaper than the shell. In the terms of
pressure drop, fluids with the lowest available pressure drop should be allocated to the
tube side. For high viscosity fluids, it is advisable to allocate the fluid to the shell side
provided the flow is turbulent (Re ≈ 200). If turbulent flow cannot be achieved, therefore,
the fluid is allocated to the tube-side (Sinnot, 2005). However, viscous fluids in the tube
side tend to have high pressure drop and low heat transfer coefficient. A viscous fluid
flow also demonstrates high pressure drop on the shell side which results to significant
flow by-passing around baffles, reduced heat transfer and vibration damage (Sloley,
2013). In terms of flowrates, allocating the lowest fluid flowrate to the shell side normally
results to economical heat exchanger design (Sinnot, 2005).
The thermal design calculation begins with the determination of duty of the heat
exchanger. The duty of the exchanger is calculated via the expression provided below.
̇ ̇ ̇ …Eq.1
̇ ̇ ̇ ( )…Eq.2
̇ ̇ ( )…Eq.3
where:
̇ Heat transfer, kW
̇ Mass flowrate, kg/h
Inlet and outlet hot stream temperatures, °C
Inlet and outlet cold stream temperatures, °C
Normally, the inlet (T1) and exit temperatures (T2) of one stream are provided. The duty
calculated from Eq.1 is used to calculate the exit temperature (t2) of the other liquid. In
calculating t2, the specific heat of the other liquid taken at the inlet temperature, t1. Once
t2 is calculated, a mean temperature of t1 and t2 is computed. This mean temperature is
used as a reference to obtain the specific heat capacity of the other liquid. An iterative
procedure is carried out to determine if the specific heat of the other liquid varies
significantly based on the new mean temperature. If the deviation is insignificant, the
specific heat is taken at the mean temperature. The exit temperature (t2) is taken based
on the mean temperature used to determine the specific heat capacity.
The next step is to determine the initial heat exchanger dimension. To do so, the
designer shall select an appropriate and preliminary overall heat coefficient, Uo. This
parameter is dependent on the heat exchanger service. Figure 1 provides a diagram in
the selection of the overall heat transfer coefficient with respect to heat exchanger
service.
Before the heat transfer area, Ao, is calculated, a mean temperature difference (ΔTm)
must be estimated based on the inlet and outlet temperature differences. This mean
temperature difference is then multiplied with temperature correction factor (FT) to

3. 3
obtain logarithmic temperature difference (ΔTlm). For counter-current flow, the LMTD is
calculated by the following equation.
( ) ( )
( )
( )
…Eq.4
…Eq.5
where:
LMTD = Log mean temperature difference, °C
FT = Temperature correction factor (dimensionless)
ΔTm = Corrected log mean temperature difference, °C
For co-current flow, the terminal temperature differences shall be (T1-t2) and (T2-t1). The
applicability of Eq.4 is based on the following points:
 No change in specific heats;
 Overall heat transfer coefficient; and
 No heat losses
The temperature correction difference is dependent on the heat exchanger
configuration. Point to note, the FT shall not be lower than 0.75 (FT > 0.75) based on the
following reasons (Smith, 2005, p. 326):
 Inefficient use of heat transfer area;
 Violation of simplifying assumptions used in the approach have significant effect
on the areas of FT chart where slopes are steep; and
 Uncertainties or inaccuracies in design data have more significant effect when
slopes are steep.
Figure 1. Overall heat transfer coefficients with respect to fluids
(Source: Sinnot, 2005)

4. 4
The next step is to calculate the initial heat transfer area (Ao) which is a function of Q,
Uo and LMTD.
̇ Eq.6
̇
…Eq.7
where:
Ao = Initial heat transfer area, m2
Uo,ass = Assumed overall heat transfer coefficient, W/m2
·°C
The layout and tube size of the heat exchanger is determined based on the service and
fluid characteristics. Carbon steel tubes and shell are commonly used as it cheaper
compared to other alloys. Alloys are used when fluids or severe operating conditions
require a more corrosion resistant material of construction.
As the thermal design is iterative by nature, the selection of an appropriate tube size is
also iterative. Therefore, a designer is required to make an initial tube size selection for
design calculations. Point to note, tube size comes in variety of sizes ranging from ¼”
(6.350 mm) to 2” (50 mm) in outer diameter (ENGINEERING page, n.d.). The smaller
tube sizes are preferred for most applications as it results to a more compact and
economical size. The larger tubes are selected for heaving fouling fluids and ease to
clean via mechanical means (Sinnot, 2005). When it comes to length, the preferred
lengths for heat exchangers are 6 ft. (1.83 m), 8 ft. (2.44 m), 12 ft. (3.66 m), 16 ft. (4.88
m), 20 ft. (6.10 m) and 24 ft. (7.32 m). For design calculation purposes, a ¾” (19.05
mm) is a good tube size to start with (Sinnot, 2005).
With the selected tube size, the area of one tube is calculated based on the following
expression.
…Eq.8
The number of tubes in a heat exchanger is computed using the following expression.
…Eq.9
where:
A1,tube = Area of 1 tube, m2
Ntube = Number of tubes
L = Tube length, m
The number of tubes calculated shall be rounded up. Example, if Ntubes is 237, it shall be
rounded up to 240. If the heat exchanger requires 2 tube passes, therefore 120 tubes
per passes (Sinnot, 2005).

5. 5
The next step is to determine if the tube-side velocity is satisfactory. There are available
rules in the tube-side velocity with respect to fluids. Some of the rules are provided
below (Sinnot, 2005).
 Tube-side process liquids: 1-2 m/s with maximum 4 m/s to reduce fouling
 Water: 1.5-2.5 m/s
 Vacuum: 50-70 m/s
 Atmospheric pressure (gas): 10-30 m/s
 High pressure (gas): 5-10 m/s
The tube-side velocity is calculated based on the following expressions.
Tube cross sectional area of 1 tube, …Eq.10
Tube area per pass = …Eq.11
Tube-side velocity, ut =
̇ ⁄
…Eq.12
Where:
AC,1 tube = Cross sectional area of 1 tube, m2
di = Inner diameter of 1 tube, m
Ntubes per pass = Number of tubes per pass
Ut = Tube-side fluid velocity, m/s
ρt = Tube-side fluid density, kg/m3
mtube side = Tube-side mass flowrate, kg/s
If the tube-size velocity is lower than the minimum prescribed velocity, then select a
reduce tube size and repeat the above calculations. Point to note, if the velocity is within
the limits but on the low side, the adequacy is determined from the tube-side pressure
drop calculations (Sinnot, 2005).
The above paragraph provided an approach to determine the tube-side velocity. The
next part is to calculate the bundle diameter (Db) and shell diameter (Ds). The tube
bundle or tube stacks are designed for applications with respect to client’s requirements
which include direct replacement for existing units (Primor, 2012). The shell side is
manufactured based on standards such as British Standards and TEMA. British
Standards, BS 3274, covers the heat exchanger diameters from 6 in (150 mm) to 42 in.
(1067 mm) whereas TEMA covers up to 60 in. (1520 mm) (Sinnot, 2005). Refer to the
equations below
( ) …Eq.13

6. 6
where:
Nt = Number of tubes
Db = Tube bundle diameter, mm
do = Tube outside diameter, mm
With reference Eq.13, it is noticed that Db is a function of tube pitch. There are four
types of tube layouts such as triangular (30°), rotated triangular (60°), square (90°) and
rotated square (45°) (Shoaib, 2013). Figure 2 provides a schematic diagram of four tube
pitch layout.
Figure 2. Tube pitch layout
(Source: Shoaib, 2013)
The application of tube pitch layout is dependent on the service and nature of fluids.
The description of each tube pitch layout is provided below.
Triangular layout
 Accommodate more tubes than other patterns (Shoaib, 2013);
 Produced high turbulence which results to high heat transfer coefficient (Shoaib,
2013);
 Typical pt = 1.25do which restricts mechanical cleaning of tubes due to restricted
access lanes (Shoaib, 2013);
 Preferred when the difference in operating pressure between two fluids are
significant (Shell & Tube Heat Exchanger Design, n.d.);
 Limited to clean shell-side services (Shoaib, 2013); and
 Can be used in dirty shell-side services if a suitable and effective chemical
cleaning is available (Shoaib, 2013).

7. 7
Square layout
 Typically used for dirty shell-side services and when mechanical cleaning is
required (Shoaib, 2013);
 Not used in the fixed head design as cleaning is unfeasible (Shell & Tube Heat
Exchanger Design, n.d.); and
 Used when the shell-side Reynolds number is below 2,000 to induce higher
turbulence (Shoaib, 2013).
The tube pitch is expressed as 1.25 times the outer diameter of tube as it leads to the
smallest shell diameter for a given number of tubes. Point to note, TEMA specified a
minimum 1.25 times the tube OD for triangular and square pitch. TEMA also
recommends an additional minimum 4 in. (6 mm) of cleaning lane between adjacent
tubes. Therefore, the minimum tube pitch for square pattern shall be the larger value of
(Shoaib, 2013):
 pt = 1.25do; and
 do + 6mm
It is noticed that Eq. 13 contains 2 parameters, i.e. K1 and n1. Both parameters are
related to the type of tube pitch and number of passes. Table 1 provides the constants
for K1 and n1 for Eq.13.
Table 1. Constant K1 and n1 for Eq.13 (Sinnot, 2005)
Triangular pitch
No. of passes 1 2 4 6 8
K1
0.319 0.249 0.175 0.0743 0.037
n1
2.142 2.207 2.285 2.499 2.675
Square pitch
No. of passes 1 2 4 6 8
K1
0.215 0.156 0.158 0.0402 0.0331
n1
2.207 2.291 2.263 2.617 2.643
The shell diameter, Ds, is expressed with respect to tube bundle diameter, Db, and shell
bundle clearance. The bundle clearance is dependent on the type of heat exchanger
rear head. The description of each heat exchanger rear end is provided in subsequent
section.
Pull-through floating heads (Type T) (Heat Exchanger Design, Inc., n.d.)
 Advantages
 Removable tube bundle and individual tubes;

8. 8
 Allows differential thermal expansion between shell and tube bundle;
 Mechanical cleaning is possible for both shell and tube sides; and
 Possible of installing double tubesheets.
 Disadvantages
 The heat exchanger seal cannot be seen externally. This could lead to
fluid leakage that might go undetected for a period of time;
 Costlier than other types of rear head heat exchanger.
Figure 3. Pull-through floating head
(Source: Mukherjee, 1998)
Split-Ring floating head (Type S) (Heat Exchanger Design, Inc., n.d.)
 Advantages
 Suited for high pressure applications;
 Floating head allows the differential thermal expansion between shell and
tube bundle;
 Mechanical cleaning is possible for both shell and tube sides; and
 Tube bundles can be removed.
 Disadvantages
 The failure heat exchanger gasket cannot be seen externally. This could
lead to fluid leakage that might go undetected for a period of time;
 Tube bundle cannot be removed from the front and rear end; and
 Heat exchanger maintenance shall require front end, rear end and backing
device to be removed (ENGINEERING page, n.d.)
Figure 4. Floating head with backing device (split ring)
(Source: ENGINEERING page, n.d.)

9. 9
Outside packed floating heads (Type P) (Heat Exchanger Design, Inc., n.d.)
 Advantages
 Allocation of high pressure fluid on the tube side is possible;
 Removable tube bundle and individual tubes;
 Differential thermal expansion between shell and tube bundle is possible
due to the packing;
 Failure of the packing is externally visible while the equipment is in
operation;
 Mechanical cleaning is possible for both shell and tube sides; and
 Possible of installing double tubesheets.
 Disadvantages
 The heat exchanger seal cannot be seen externally. This could lead to
fluid leakage that might go undetected for a period of time;
 Costlier than other types of rear head heat exchanger.
Figure 5. Outside packed floating head
(Source: Mukherjee, 1998)
Fixed tube sheet (Type L, M and N) (Heat Exchanger Design, Inc., n.d.)
 Advantages
 Low cost of construction due to its simplicity (Mukherjee, 1998);
 Mechanical cleaning is possible after the removal of channel cover or
bonnet (Mukherjee, 1998);
 Shell-side leakage is minimized due to no flange joints (Mukherjee, 1998);
and
 Installation of double tubesheet is possible (Heat Exchanger Design, Inc.,
n.d.)
 Disadvantages
 The heat exchanger seal cannot be seen externally. This could lead to
fluid leakage that might go undetected for a period of time;
 Costlier than other types of rear head heat exchanger.

10. 10
Figure 6. Fixed tube sheet rear head
(Source: Mukherjee, 1998)
U-tube (Type U) (Heat Exchanger Design, Inc., n.d.)
 Advantages
 Tube bundle can be removed;
 Shell side can be cleaned via mechanical cleaning;
 No requirement for differential expansion joint due to the attachment of
tubes to single tubesheet; and
 Installation of double tubesheets is possible for additional protection from
leakage.
 Disadvantages
 Mechanical cleaning is not possible on the outside row of tubes;
 Limited to clean services on the shell side;
 Tube bundle cannot be removed as it is fixed to the shell (Mukherjee,
1998); and
 Costlier than other types of rear head heat exchanger (Mukherjee, 1998).
Figure 7. U-tube heat exchanger
(Source: Mukherjee, 1998)
Externally sealed tubesheets (Type W) (Heat Exchanger Design, Inc., n.d.)
 Advantages
 Removable tube bundle;
 Tubes can experience differential expansion due to the floating head
design;
 No expansion joint; and

11. 11
 Mechanical cleaning is possible for both shell and tube sides
 Disadvantages
 Only two tube side passes is possible;
 Leakage on both shell and tube side is possible; and
 The use of Type W rear head is limited to a maximum temperature and
pressure of 190.6°C and 20.7 bar
Point to note, Type W is the lowest cost of the floating head designs (Heat Exchanger
Design, Inc., n.d.)
Figure 8. Externally sealed tubesheet (Type W)
(Source: Mukherjee, 1998)
The shell-bundle clearance is determined based on the selected rear head. Reader is
referred to Figure 9. It is noticed that the determination of shell-bundle clearance is a
factor of bundle diameter, Db, and type of rear end. The shell-bundle clearance is
expressed in mm.

12. 12
Figure 9. Shell-bundle clearance
Assuming a split-ring floating head is selected and the Db was calculated to be 0.6 m.
The shell-bundle clearance is approximately 61 mm. Refer to the Figure 9 with red-
coloured arrow as an example.
The shell diameter, Ds, is calculated as the summation of tube bundle diameter, Db, and
shell-bundle clearance. Convert Db and shell-bundle clearance unit from millimeters
(mm) to meter (m).
Shell diameter, Ds = Tube bundle diameter, Db + Shell-bundle clearance…Eq.14
Ds is the inside shell diameter in meters (m).
The next part of the thermal design involves the determination of tube-side heat transfer
coefficient. First and foremost, a designer must determine the fluid flow regime in the
tubes. Therefore, the Reynolds number, Re, is calculated using the following
expression.
𝑅𝑒 = …Eq.15

13. 13
where:
ρt = Tube-side fluid density, kg/m3
Ut = Tube-side fluid velocity, m/s
di = Tube inner diameter, m
µ = Tube-side fluid viscosity, N·s/m2
Laminar flow is characterized when Re < 2,100 whereas the fully turbulent flow occur
when Re > 10,000. Therefore, the tube-side heat transfer coefficient is dependent on
the fluid flow regime.
The tube-side heat transfer coefficient for laminar flow is determined using Sieder-
Tate’s equation as expressed in Eq.15. This equation is applicable when the tube-side
Reynolds number is 100 < Re < 2,100 (Edwards, 2008).
𝑢 = ⁄ [𝑅𝑒 ⁄ ] ( ⁄ ) …Eq.16
where:
hi =Tube inside coefficient, W/m2
·°C
kf = Tube-side fluid thermal conductivity, W/m·°C
L = Tube length, m
µ = Tube-side fluid viscosity at fluid bulk temperature, N·s/m2
µW = Tube-side fluid viscosity at wall temperature, N·s/m2
The calculated Nu from Eq.15 shall be minimum 3.5. If it is calculated to be less than
3.5, Nu shall be 3.5 (Sinnot, 2005)
The Nusselt number, Nu, is defined as the ratio of heat transfer by convection and
conductive heat transfer (Shires, 2011). The Prandlt number, Pr, is defined as the ratio
of momentum diffusivity to thermal diffusivity (Shires, 2011).
…Eq.17
where:
Cp = Fluid specific heat capacity, J/kg·°C
Equations have been formulated to calculate the tube-side heat transfer coefficient, hi,
for fully turbulent flow. Sieder-Tate’s equation is used to calculate hi when the Re >
10,000 with 0.7 < Pr < 700 and L/Ds > 60. Eq.18 is referred to calculate the tube-side
heat transfer coefficient, hi (Edwards, 2008).

14. 14
𝑢 𝑅𝑒 ( ⁄ ) …Eq.18
An expression was formulated to determine hi for fully turbulent flow at 40,000 < Re <
100,000 with 0.7 < Pr < 160 and L/Ds > 60. The expression, known as ESDU method, is
provided in Eq.19 (Edwards, 2008).
𝑢 𝑅𝑒 𝑒[ ( ) ]
…Eq.19
The tube-side heat transfer coefficient, hi, cannot be determined accurately when the
fluid flow regime is transitional. Therefore, this region should be avoided for design. If
this flow region cannot be avoided, Sinnot (2005) recommends taking the least value
calculated from Eq.16 and Eq.18.
The next step is to determine the shell-side heat transfer coefficient, hs. The calculation
of hs is initiated with the determination of Db and Ds as provided in Eq.13 and Eq.14.
Once this done, designer shall calculate the baffle spacing (LB) in the heat exchanger.
Baffles are integral part of a heat exchanger and consist of plate and rod types. The
plate versions are in the form of single-segmental, double-segmental or triple
segmental. Irrespective of its construction, they are designed for the following functions
(Mukherjee, 1998):
 For tube support;
 To maintain a suitable shell-side fluid velocity; and
 To prevent tube failure due to flow-induced vibration
Figure 10. Segmental baffles (a) and rod baffle (b)
(Source: Mukherjee, 1998)
The shell inner diameter, Ds, is calculated with reference to Eq.13 and Eq.14. The
minimum requirement for baffle spacing (B) shall be the maximum value of 1/5 of Ds or
2 inches whichever is greater. Point to note, the maximum baffle spacing (B) is
calculated based on Eq. 20 and expressed in inches (Primor, 2012).
B = 74·do
0.75
…Eq.20

15. 15
It is noticed that a baffle cut of 25% is used for this calculation. However, the baffle cut
can vary between 15% and 45%. The 25% baffle cut is used as the Kern’s shell-side
pressure drop correlation is based with respect to 25% cut. It is a standard for liquid on
shell-side (Primor, 2012).
First, the shell-side cross flow area is calculated with reference to Eq.21 (Sinnot, 2005)..
( )
…Eq.21
where:
As = Shell-side cross flow area, m2
pt = tube pitch, m
do = Tube outside diameter, m
Ds = Shell inner diameter, m
LB = Baffle spacing, m
The linear velocity is then computed based on Eq.22(a) and Eq.22(b) (Sinnot,2005)
…Eq.22(a)
𝑢 …Eq.22(b)
where:
Ws = Shell-side fluid flow-rate, kg/s
ρ = Shell-side fluid density, kg/m3
Point to note, the shell-side velocity, us, shall be restricted between 0.3 m/s to 1.0 m/s
(Sinnot, 2005).
The shell-side equivalent diameter is computed based on the tube pitch, i.e. square or
equilateral triangular pitch. For square pitch arrangement (Sinnot, 2005):
( )
( )…Eq.23
For equilateral traingular pitch, the hydraulic diameter is (Sinnot, 2005):
( )
( )…Eq.24
where:
de = Hydraulic diameter, m

16. 16
pt = Tube pitch, m
do = Tube outer diameter, m
The shell-side velocity (us) and hydraulic diameter (de) are used to determined the shell-
side Reynolds number (Sinnot, 2005).
𝑅𝑒 …Eq.25
where:
Us = Shell-side fluid velocity, m/s
ρ = Shell-side fluid density, kg/m3
µ = Shell-side fluid viscosity, N·s/m2
With the above information, a designer can proceed in calculating the shell-side heat
transfer coefficient, hs. Before proceeding to the calculation, the shell-side heat transfer
factor, jh, for segmental baffles shall be obtained from Figure 11. This heat transfer
factor is a function of shell-side Reynolds number, baffle cut and tube pitch type (Sinnot,
2005).
Figure 11. Shell-side heat transfer factor, jh, for segmental baffles
(Source: Sinnot, 2005)
The shell-side heat transfer (hs) is expressed in Eq.26 (Sinnot,2005)
Nu = hi·de/kf = jh·Re·Pr1/3
·(µ/µW)0.14
…Eq.26

17. 17
The overall heat transfer coefficient, Uo, is the reciprocal of the overall resistance to
heat transfer and it is expressed as the sum of several heat transfer resistances. Each
heat transfer resistances depend on the several factors such as (Sinnot,2005):
 Physical properties of fluids;
 Heat transfer process, i.e. conduction, convection, condensation, boiling or
radiation; and
 Physical arrangement of the heat transfer surface.
( )
( ) ( )…Eq.27
where:
Uo = Overall heat transfer coefficient, W/m2
·C
ho = Outside fluid film coefficient, W/m2
·C
hi = Inside fluid film coefficient, W/m2
·C
hod =Outside dirt coefficient (fouling factor), W/m2
·C
hid =Inside dirt coefficient (fouling factor), W/m2
·C
kw = thermal conductivity of the tube wall material, W/m·C
di = tube inner diameter, m
do = tube outside diameter, m
The calculated Uo,calc shall not be taken as the final answer. This value is compared to
Uo,ass in Eq.6. The calculated Uo,calc from Eq.27 should be of 30% of Uo,ass.
0% < (Uo,calc-Uo,ass) x 100/Uo,ass < 30%...Eq.28
If the above criteria is not met, designer shall repeat the thermal design calculation by
assuming the Uo,ass in Eq.6 as Uo,calc obtained from Eq.27. The calculation is repeated
starting from Eq.6 to Eq.27.
The pressure drop calculation is an important part in a thermal rating exercise. Pressure
losses due to contraction at the tube inlets, expansion at the exits and flow reversal in
the headers are significant to the total tube-side pressure drop. The pressure loss terms
are expressed in velocity heads and it is determined by calculating the number of flow
contractions, expansions and reversals (Sinnot,2005).
ΔPT = NP × [8× jf × (L/di) × (µ/µW)-m
+ 2.5]…Eq.29
The index m is a function of the fluid flow regime. For laminar flow, Re < 2,100, m =
0.25. If the flow regime is turbulent, Re > 2,100, m = 0.14 (Sinnot,2005)
The tube-side heat friction factor, jf, is obtained from Figure 12.

18. 18
Figure 12. Tube-side friction factor, jf
(Source: Sinnot,2005)
The calculated tube-side pressure drop, ΔPT, shall be within the process specifications.
If ΔPT exceeds the requirement, select different tube dimensions and layout and repeat
the calculations from Eq.8 to Eq.29. This step is applicable for shell-side pressure drop,
ΔPS.
The shell-side pressure drop (ΔPS) is computed in the similar manner as tube-side
pressure (ΔPT). With reference to Eq.30, the shell-side friction factor, jf, is obtained
based on the calculated shell-side Reynolds number (refer to Eq.25).
ΔPS = 8 x jf x (Ds/de) x (L/lB) x (½· ρ·Us
2
) x (µ/µW)-0.14
…Eq.30

19. 19
Figure 13. Shell-side friction factor, jf
(Source: Sinnot, 2005)
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