ENCH607-F2012-L07-Heat Transfer and Heat Transfer Equipment

Nashaat Nassar, Ph.D., P.Eng.

ENCH 607-Lecture-07

November 13, 2012

Heat Transfer and Heat

Transfer Equipment

ENCH 607-Dr. Nassar 2

Objectives

By the end of this lecture, students will obtain knowledge and skills on:

heat transfer mechanisms

heat transfer equipment

sizing and evaluating heat transfer equipment performance


Introduction

Heat transfer is required for control of:

fluid temperature and/or its phase

rate of mass transfer between phases

rate of chemical reaction

temperature to prevent failure of equipment

The transfer of heat takes place in most equipment, but we deal here with equipment that is designed specifically for the transfer of

heat. Heat transfer equipment can be divided into three basic types:

fluid-fluid, such as pipe in pipe, shell and tube, plate and frame, etc

air coolers, such as fin fans, and cooling towers fired heaters

Regardless of the type of exchanger, each makes use of the fundamental heat transfer mechanisms.


Heat Transfer Mechanisms

By definition, heat is that energy transferred solely as a result of a temperature difference that is independent of mass transfer.

There are three mechanisms, by which heat can be transferred:

conduction,

convection, and

radiation.

Heat is seldom transferred by a single mechanism, but usually by a combination of mechanisms operating in series or parallel.

The analysis of heat transfer does not require that all parts be solved with equal care. The engineer needs to develop the

experience to recognize the predominant mechanisms and base

calculations on these while neglecting minor effects.


Conduction

Conduction of heat occurs by the excitation of adjacent molecules as opposed to overall mixing of the molecules.

Fouriers law of heat conduction applies:

dx

dTkAQ (Eq 7-1)

Q: heat conduction in x direction (W)

k: thermal conductivity of conduction medium (W/m K)

A: cross sectional area normal to heat flow (m2)

dT/dx: temperature gradient in x direction (K/m)

The integration of Fouriers equation provides the following solutions for specific geometries as given in the next slide1:


Conduction

wdt

dTkAQ (Eq 7-2)

For perpendicular heat flow through a flat wall or very large cylindrical tank wall.

T: T1-T2 (K or oC)

tw: wall thickness (m)

For heat flow in a cylindrical shape where the heat flow is normal to the axis, as in heat flow through a cylindrical vessel or pipe wall.

Cylindrical Shape:

Flat Surface:

)/ln(

2

io DD

TLkQ

(Eq 7-3)

T: Ti -To (K or oC)

Do: outside diameter (m)

Di: inside diameter (m)

L: length of surface (m)


Conduction

Equation 7-3 can be multiplied by (Do-Di) in both numerator and denominator to give:

Cylindrical Shape:

io

oi

io

io

DD

TT

DD

DDLkQ

)/ln(

)(2 (Eq 7-4)

io

oi

io

io

DD

TT

AA

AAkQ

)/ln(

)(2 (Eq 7-5)

D

TkAQ lm

2 (Eq 7-6)

Alm = is the log mean area = )/ln( io

io

AA

AA


Conduction

For radial heat flow through a spherical vessel

Spherical Shape:

)/1/1(

2

oi DD

TkQ

(Eq 7-7)

io

oi

DD

DDTkQ

2 (Eq 7-8)

D

TkAQ gm

2 (Eq 7-9)

Agm: is the geometric mean area = oiAA

The thermal conductivities for refractories and insulations are given in FIG 8-3 of the GPSA Engineering Data Book. Thermal conductivities of metals can be found in

FIG 8-8 and FIG 9-8 in GPSA Engineering Data Book.

A conduction problem is shown as Example 8-1 in the GPSA Engineering Data Book.


Convection is heat transfer that takes place by the physical movement of molecules, usually a fluid passing next to a solid.

Most of the resistance to heat transfer occurs in a thin film at the surface of the solid. This film exists even if the bulk fluid flow is very

turbulent.

Newtons law of cooling applies in this situation:

Convection

ThAQ (Eq 7-10)

h = heat transfer coefficient (W/m2 K)

Convection can happen due to gravity and buoyant forces (natural) or due to imposed circulation (forced).


Natural or free convection occurs where the only force promoting fluid flow is a result of the temperature difference of the fluid.

For natural convection the heat transfer coefficient is governed by the Nusselt equation.

Natural Convection

mGrCNu Pr (Eq 7-11)

where the dimensionless numbers are:

Nusselt number, k

hLNu

Grashof number, 2

23

TgDGr

Prandtl number, k

C p1000Pr

h = heat transfer coefficient (W/m2 K)

L = length of surface (m)

k = thermal conductivity of fluid (W/m K)

D = diameter (m)

= fluid density (kg/m3) g = acceleration of gravity (9.81 m/s2)

= fluid coefficient of thermal expansion (K-1) T = temperature difference (K) = fluid viscosity (Pa.s) Cp = fluid heat capacity (kJ/kg K)

(Eq 7-12)

(Eq 7-13)

(Eq 7-14)


The values of C and m in equation 7-11 depend on geometry and dimensions of the surface. Values for the coefficients for various conditions can be found

in FIG 8-4 of the GPSA Engineering Data Book.

Of most interest to us, are long horizontal cylinders (L>D) and vertical plates or cylinders. Table 7-1 provides the coefficients.

Natural Convection

A natural convection problem is shown as Example 8-2 in the GPSA Engineering Data Book.

Table 7-1 Vertical Plates or Cylinders (Y = Gr. Pr) C m

Y < 104 1.36 0.20

104< Y < 104 0.55 0.25

Y > 109 0.13 0.33

Horizontal Cylinder

D < 0.1 0.53 0.25

0.1 < D < 0.5 0.47 0.25

0.5 < D 0.11 0.33

Table 7-1: Heat transfer constants for vertical plates and horizontal cylinders


Natural Convection


Forced convection occurs when the fluid flow adjacent to the solid is promoted by external forces such as pumping or agitation. This increases

the heat transfer rate.

There are two principle cases, one where viscosity effects are minimal, and the other where viscosity is significant.

Forced Convection

Dittus-Boelter Equation

When viscosity effects are minimal

33.0PrRemCNu (Eq 7-15)

Seider-Tate Equation

When viscosity effects are important

14.0

33.0PrRe

w

bmCNu

(Eq 7-16)

b = viscosity of fluid at bulk conditions (Pa s) w = viscosity of fluid at the wall conditions (Pa s)


The value of C and m in equations 7-15 and 7-16 depends on geometry and dimensions of the surface. Values for the coefficients for various conditions

can be found in FIG 8-5 of the GPSA Engineering Data Book. The data

covers flat plates, flow across a cylinder, flow inside pipes, and flow on the

outside of tubes.

Forced Convection


Additional work has been done to fine tune the predictions of the equations 7-15, and 7-16. Rearranging

the equations, we can write

Forced Convection

nm

D

kCh PrRe

(Eq 7-17)

with the values of C, m and n for various configurations given in Table 7-2.


Forced Convection

Table 7-2


Heat transfer in concentric pipes is often encountered. The heat transfer coefficient of the fluid in the annular space can be predicted from equations

similar to those which apply for circular pipes; however the equivalent

diameter must be used. For the annular space

Convection in Noncircular Conduits

ioeq DDD (Eq 7-18)

Weigand has proposed the following for the turbulent flow heat transfer coefficient on the outer wall of the inner pipe

45.04.08.01000023.0

i

opeq

eq D

D

k

CvD

D

kh

(Eq 7-19)

A forced convection problem is shown as Example 8-3 in the GPSA Engineering Data Book.


Eq 7-17 and Table 7-2 can be used to estimate the heat transfer coefficient for a bank of tubes.

The following equation is applied to gases.

Convection Normal to a Bank of Circular Tubes

n

DGC

k

hD

max (Eq 7-20)

Where Gmax is the product of density times velocity at the minimum cross

section. Gas properties are evaluated at the arithmetic mean of the gas and the

tube wall temperature.

The coefficients for tube banks 10 or more rows deep are given in Table 7-3

C n

Triangular pitch, centre to centre = 2 D 0.482 0.556

Square pitch, centre to centre = 2 D 0.229 0.632

Table 7-3: Coefficients for Grimison Equation


For liquids, Grimisons equation is:

Convection Normal to a Bank of Circular Tubes

33.0

max1000

1.1

k

CDGC

k

hD pn

(Eq 7-21)

For banks of tubes less than 10 rows deep, equation 7-20 can be used and the heat transfer coefficient adjusted using the ratio in Table 7-4.

N 1 2 3 4 5 6 7 8 9 10

Triangular 1.0 1.10 1.22 1.31 1.35 1.40 1.42 1.44 1.46 1.47

Square 1.0 1.25 1.36 1.41 1.44 1.47 1.50 1.53 1.55 1.56

Table 7-4: Ratio of Mean Heat Transfer Coefficients for a Bank of Tubes N rows

Deep to the Coefficient for Tubes in a Single Row


Convection from a sphere can be described by an equation attributed to Froessling.

Convection from Spheres

5.033.01000

6.00.2

Dv

k

C

k

hD p (Eq 7-22)

Convection Between a Fluid and a Packed Bed

Ranz developed a model to determine the heat transfer between a fluid and a packed bed. Although the model assumes spherical particles, and

perfect rhombohedral packing, it provides a good approximation for most

packed beds. The equation for the heat transfer coefficient is

rhombohedral packing

Porosity: 26%

67.05.01000

)1(82.26

k

CDvCvh

psps

(Eq 7-23)


Radiation is the process whereby a body emits heat waves that may be absorbed, reflected, or transmitted through a colder body.

A hot body emits a whole spectrum of wavelengths. Heat is transmitted through the full wave length, infrared, visible, ultraviolet. An estimate of the radiant heat flux between two surfaces

is:

Radiation

111

21

4

2

4

1

TTF

A

Q (Eq 7-24)

= Stefan-Boltzmann constant (5.67 x 10-8 W/m2 K) F = view factor (dimensionless)

T1 = temperature of hot surface (K)

T2 = temperature of cold surface (K)

1 = emissivity of hot surface 2 = emissivity of cold surface

The geometry or shape factor, F, is the fraction of the surface area that is exposed to and absorbs radiant heat. The value of F must be determined by

an analysis of the geometry and should normally be greater than 0.67.

The emissivities of common materials are given in FIG 8-9 of the GPSA Engineering Data Book. The emissivities of gases are more complex, as it

depends on the partial pressure of the gas and the path length. Gas

emissivities are given in FIG 8-12.

A radiation problem is shown as Example 8-6 in the GPSA Engineering Data Book.


Heat is seldom transferred by only one mechanism and often heat is transferred through a series of different materials. When this is true, the heat

transfer from each component must be consistent with the overall heat

transfer.

Overall Heat Transfer

Coefficients

Conduction through a series of materials must satisfy the overall conduction equation as well as the individual conduction equations.

Series Conduction Through a Flat Surface

For conduction through a series of flat materials, such as a boiler wall shown in Figure 7-1, the conduction equations are:

Series Conduction

Figure 7-1 Conduction

Through a Flat Wall



Coefficients

Ak

xQTT

a

a 21 (Eq 7-25)

Ak

xQTT

b

b 32 (Eq 7-26)

Ak

xQTT

c

c 43 (Eq 7-27)

Ak

x

Ak

x

Ak

xQTT

c

c

b

b

a

a41

(Eq 7-28)

Adding these equations gives

and therefore

Ak

x

Ak

x

Ak

x

TTQ

c

c

b

b

a

a

41

(Eq 7-29)

This is equivalent to Ohms law for electricity, and the denominator is the overall resistance to heat transfer. Since Q/A is the same for all layers, the temperature

gradient, T/x, is inversely proportional to the thermal conductivity of the layer.



Coefficients

lmcc

c

lmbb

b

lmaa

a

Ak

D

Ak

D

Ak

D

TTQ

2

1

41

(Eq 7-30)

Series Conduction Through a Cylinder

If conduction takes place through a cylinder, such as an insulated pipe, as

shown in Figure 7-2,

Where:

1

2

121

lnA

A

AAAlm

(Eq 7-31)

LDA ii (Eq 7-32)

Figure 7-2 Conduction Through Cylinders



Coefficients

Series Conduction Through a Sphere

Similarly, for a sphere it can be shown that:

gmcc

c

gmbb

b

gmaa

a

Ak

D

Ak

D

Ak

D

TTQ

2

1

41

(Eq 7-32)

where the area term is now the geometric mean area, 21AAAgm


Finned Tubes

Gas side heat transfer coefficients are usually much less than liquid side coefficients, and fins on the gas side are often used to increase the heat

transfer.

For tubes used in combustion gases, typical fins are 1.25 3.0 mm thick, 12.5 40 mm length, with a linear density of 80 - 240 fins/m.

The total external fin area and the cross flow area per linear meter are then given by:

6

22

102

.

1000

.1

1000

ofoo

ddntndA

(Eq 7-34)

610

).(.

1000

ofoCS

ddtndA

(Eq 7-35)

Ao = outside fin area (m2)

Acs = cross sectional area of flow (m2)

do = outside pipe diameter (mm)

df = outside fin diameter (mm)

n = fin density (fin/m)

t = fin thickness (mm)


Finned Tubes

The surface area of the fin is not as efficient as the external pipe surface, so there is an efficiency adjustment that is determined by using FIG 8-6 in the GPSA

Engineering Data Book. The fin efficiency is then applied to the total heat transfer

area.

In order to calculate the fin efficiency, from FIG 8-6, two parameters must be determined as follows:

o

fo

o

f

d

Hd

d

d 2

(Eq 7-36)

Hf = fin height (mm)

ho = outside heat transfer coefficient (W/m2 oC)

kf = thermal conductivity of fin (W/m oC)

t = fin thickness (mm)

do = pipe diameter (mm)

df = fin diameter = do + 2Hf (mm)

(Eq 7-37)

Fin tip temperature must be considered if the tube is in the hot convection zone of a furnace. The fin tip temperature can be determined from FIG 8-7 in the GPSA .

The maximum recommended fin tip temperature for various materials, and the material thermal conductivities are given in FIG 8-8.

A fin efficiency problem is shown as Example 8-5 in the GPSA Engineering Data Book.

5.0

0405.0

tk

hHX

f

of


Overall Heat Transfer Coefficient

We have seen convective and conductive heat transfer in separate equations. When heat is transferred from a fluid, through a pipe and into another pipe, convective and

conductive heat transfer are taking place in series.

It is customary to show the total heat transferred in terms of an overall heat transfer coefficient, U. The overall heat transfer coefficient must be based on some specific

area, and it is common to use the outside area of the tube and write the heat transfer

equation as:

lmoo TAUQ

hi = inside pipe convective heat transfer coefficient (W/m2 K)

hfi = inside pipe fouling factor (W/m2 K)

tw = pipe wall thickness (m)

kw = pipe thermal conductivity (W/m K)

hfo = outside pipe fouling factor (W/m2 K)

ho = outside pipe convective heat transfer coefficient (W/m2 K)

Ao = outside tube area (m2)

Ai = inside tube area (m2)

(Eq 7-38)

For a tube:

ofolmw

ow

ifi

o

ii

oo

hhAk

At

Ah

A

Ah

AU

11

1

(Eq 7-39)



Note that the areas referred to above are the surface area of the pipe, and not the cross sectional area available for flow.

The fouling resistances are often just provided as ri and ro:

fo

o

ifi

oi

hr

Ah

Ar

1

(Eq 7-40)

Typical range for fouling resistances is from 0.0001-0.0005 m2 oC/W. The values of the inside and outside heat transfer coefficients can be calculated

from the Dittus-Boelter equation or the Seider-Tate equation. Typical values for

individual heat transfer coefficients are:

W/m2 oC

Gases (natural convection) 5-25

Gases (forced convection) 10-250

Liquids 100-10,000

Liquid metals 5000-250,000

Boiling 1000-250,000

Condensation 1000-25,000

Typical values for the overall heat transfer coefficients and fouling resistances are given in FIG 9-9 of the GPSA Engineering Data Book. Values can also be found in

the literature.


Heat transfer theory is put into practice by construction equipment to transfer heat between two streams without

physically mixing the streams themselves.

There are a variety of different heat exchangers to transfer heat from one process fluid to another. The most common

types are pipe-in-pipe, shell and tube, spiral, and plate and

frame.

Special exchanger types include brazed aluminum, printed circuit, and coil wound exchangers.

Before looking at the various exchangers, it is worthwhile to look at Figure 7-3 showing the temperature profiles that can

be expected.

Heat Exchangers


Heat Exchangers

Figure 7-3 Exchanger Temperature Profiles


The lines shown in the previous figure represent fluids that have a constant heat capacity. In actual fluids, the heat capacity is a function of temperature so the

cooling curves tend to be slightly curved.

For each side of the exchanger, the heat transferred into or out of the fluid must be equal.

Heat Exchangers

111 )( outinP TTCmQ (Eq 7-41)

222 )( outinP TTCmQ (Eq 7-42)

22 vapHmQ (Eq 7-43)

If there is sensible heat and heat of vapourization on one side, then the Q calculation will have to include a term to capture each region in the exchanger.

In addition, the exchanger must follow the overall heat transfer equation.

lmoo TFAUQ (Eq 7-44)

1

2

12

lnT

T

TTTlm (Eq 7-45)


The factor F has been added here to account for the geometry of the exchanger. For counter-current flow, F = 1.0.

Most exchangers however use cross flow in the way they are configured and the value of F is less than 1.0. The value of F

can be determined from FIG 9-4 through 9-7 in the GPSA

Engineering Data Book.

Again, if there is a phase change, then the exchanger may have to be segmented and the calculation of Q will involve

multiple terms.

Heat Exchangers


There are a variety of heat exchanger calculations that can be done.

The first calculations are related to the process design. The engineer is interested in the amount of heat transferred and the

temperatures in the incoming and outgoing streams. At this point

the process engineer may also indicate the type of exchanger that

should be used, the allowable pressure drop through the

exchanger, and an estimate of the product UoAo.

The next step is the determination of the mechanical design of the exchanger. This involves the physical layout of the exchanger,

determination of dimensions, number of tubes, required wall

thickness, and other design requirements in order to meet the

process specifications. We will focus on the process aspects, but

address some of the mechanical considerations.

When looking at the process aspects of an exchanger, there are three types of calculations that can be performed.

Heat Exchanger Calculations


In design calculations, the two flow rates, and three temperatures will be known. The objective is to determine the quantity of heat transferred, the unknown

temperature, and the product of UoAo. The solution proceeds as follows:

Q is calculated using one of the flow rates and the inlet and outlet temperatures for that side of the exchanger,

The fourth temperature is calculated using the other fluid flow rate and the third temperature (inlet or outlet for that side of the exchanger),

UA is determined from the overall heat transfer equation and an assumption about the type of exchanger,

Details of U and A are then calculated iteratively along with allowable pressure drops

The number, size, and pitch layout of tubes are assumed Ao is calculated based on the tube data Flow velocities are calculated, and inside and outside heat transfer

coefficients are calculated (hi and ho) from fluid properties, geometry, and

the Dittus-Boelter or Sider-Tate equations.

Uo is calculated from all of the individual heat transfer coefficients, The calculated values of Ao and Uo are used to see if the overall duty, Q

can be met.

Pressure drop calculations are performed to see if the hydraulic constraints are met.

1. Design Calculations


For performance calculations the exchanger is existing, so all of the geometry is known, and Ao is known. The following process data should be available:

Four temperatures and two flow rates (best) Three temperatures and two flow rates (better) Four temperatures and one flow rate (good)

The above data is used to calculate Q. In the first case you can calculate Q with two sets of data, and the results will likely be different. Engineering judgment

should be applied to determine if one calculated value is more reliable than the

other, or if the two Q values should be averaged. For the other two data sets, the

missing piece of data must be calculated and there is no check available for data

quality.

Once Q is determined, Uo can be calculated from the heat transfer equation and the known exchanger geometry. The calculated value of Uo can be compared to

the design value of Uo. Individual components of the overall Uo; hi, ho, the

conduction term and the total fouling resistance are determined. The inside and

outside fouling resistances cannot be separated. The results indicate if the

exchanger is fouled more than its design fouling and if cleaning is required.

2. Performance Calculations


Often, the performance of an existing exchanger under new operating conditions is desired. For this case, two flow rates are available, and two

inlet temperatures are available. The exchanger geometry and area, Ao is

known, but Uo must be determined based on the new flow rates and fluid

physical properties.

Multiple calculations of Uo may be required if the fluid physical properties change appreciably, but often one calculation is sufficiently accurate. The

performance calculation is however a trial and error solution, as Tlm must be determined. The solution proceeds as follows:

Assume one outlet temperature and calculate Q1 Using Q1, determine the other outlet temperature Calculate Uo from hi, ho, tube data, and fouling resistances Calculate Tlm Determine Q2 from the heat transfer equation If Q1 = Q2, then converged, else assume new outlet temperature and

repeat.

3. Performance Prediction


This type of exchanger is good for small heat loads where one stream is a gas or viscous liquid, or for relatively small exchangers operating at high

pressure.

In these exchangers a piece of pipe serves as the shell. The internals may be a single concentric pipe or a group of pipes. The internal pipes

have a U-tube design. The process diagram is shown in Figure 7-4.

Pipe-in-Pipe Exchangers

Shell side

Tube side

Counter current flow

Figure 7-4: Pipe in Pipe Exchanger (Brown Fin Tube)


Note that the configuration allows for true counter-current flow. It is possible to enhance the heat exchanger by adding fins to the outside of

the inner tube, by twisting the inner tubes, or by adding turbulators to the

inside of the inner tube. A cutaway of a multi-tube pipe-in-pipe exchanger

is shown in Figure 7-5.


Figure 7-5 Cutaway View of Pipe in Pipe Exchanger


Double pipe exchangers are intended for small duties, where surface areas of 10-20 m2 are required.

They are usually assembled in 12, 15, or 20 ft sections, as longer lengths result in sagging of the inner tube and poor flow distribution.

Standard sizes are:


Outer Pipe (NPS) Inner Pipe (NPS)

2 1

2 1

3 2

4 3


The design equations are used to calculate duty, pipe diameter, wall thickness, pressure drop, and heat transfer coefficient. Some iteration may be required given

the interaction of the variables.

The exchanger duty is calculated based on the flow, heat capacity, and temperature change of one of the fluids. The other fluid flow rate or temperature

change is then determined.

A trial pipe diameter is selected based on a velocity of 1-3 m/s. Higher flow rates will provide better heat transfer.

Wall thick can then be determined based on the operating pressure and the trial pipe diameter. If the high pressure is in the annulus, a calculation for external

pressure will have to be done.

The heat transfer calculation is performed next. The inside and outside heat transfer coefficients can be calculated using the Seider-Tate or the Dittus-Boelter

equations. For the inside heat transfer coefficient, the diameter to use is the inner

diameter of the inside tube.

For the outside heat transfer coefficient, the equivalent diameter for heat transfer must be used. Similar to the equivalent diameter of pressure drop, the equivalent

diameter is defined as the ratio

Flow area/wetted perimeter

Pipe-in-Pipe Exchangers:

Design Equations


For heat transfer, the wetted perimeter is only the outside of the inner pipe. The equivalent diameter for heat transfer is then


Design Equations

1

2

1

2

2

1

2

1

2

2

4

4

D

DD

D

DDDe

(Eq 7-46)

It is customary to use the outside area of the inner tube for the heat transfer equation, so the overall heat transfer coefficient is given by

o

o

lmw

owi

ii

oo

hr

Ak

Atr

Ah

AU

1

1

(Eq 7-47)

The required surface area is now found using

lmo

oTU

QA (Eq 7-48)


Based on the required area and the inner pipe outer wall diameter, the length of pipe is determined. In some cases,

two or three units can be connected together to provide the

required surface.

Pressure drop calculation can now be performed on the inner pipe and the annular space using the methods in Lecture 5.

If the pressure drop is too high, then a larger diameter pipe is required, and the calculation is repeated.


Design Equations


Shell and tube heat exchangers are the most common heat

exchange device in plants.

The major manufactures have a trade association (Tubular

Exchanger Manufacturers

Association, TEMA), which has a

set of standards.

Exchangers can be designed to Class R, C, or B. Class R is the

most stringent and is generally

used for oil and gas applications.

Shell and Tube Exchangers



TEMA Type

Shell and tube exchangers can be made with different end closures and different shell designs. These are designated in TEMA by a three

letter designation indicating front end, shell type, and rear end. Thus,

each exchanger is given three letter designation

A description of the types and their letter designation can be found in FIG 9-23 in the GPSA Engineering Data Book. A shell and tube

exchanger selection guide is provided in FIG 9-24 to help select the

type of exchanger configuration.

Shell Front end

stationary head

type

Rear end

head type


Courtesy of

TEMA


Tubes

Exchanger tubes must be designed to withstand the differential pressure across the tube, but should be checked to ensure that

they can handle the internal or external pressure if the start-up can

pressure up one side prior to the other.

Tubes come in various outside diameters, OD, and different wall thickness. OD is usually specified in inches, and wall thickness in

Birmingham Wire Gauge, BWG. Tubing characteristics are

provided in FIG 9-25 of the GPSA Engineering Data Book.



Shells

The surface area required in an exchanger must be placed inside a shell. The number of tubes that can fit into a circular

cross section depends on the tube OD, and the tube pitch.

Pitch refers to the distance between tube centres, as well as the geometry of the layout.

Shell diameter can be estimated using FIG 9-26 through 9-28 in the GPSA Data Book.

An example calculation is provided as Example 9-3.



Typically, 1 in tubes on a

1.25 in pitch or 0.75 in

tubes on a 1 in pitch

Triangular layouts give

more tubes in a given shell

Square layouts give

cleaning lanes with close

pitch

Tube layout patterns



Design Tips

The tube length is often taken as 20 feet (about 6 m) as this is a common length of tube that can be purchased. Other lengths are of course

available. The following general guidelines are useful:

Shell side viscous fluid to increase the value of U fluid with the lower flow rate condensing or boiling fluid fluid for which pressure drop is critical if one fluid is a gas

Tube side toxic fluid to minimize leakage corrosive fluid fouling fluid, higher velocity and easier to clean high temperature fluids requiring alloy pipe high pressure fluid to minimize cost cool water



Should outside tube surface cleaning be required, square pitch is preferred to triangular pitch.

The shell of the exchanger is often designed to 10/13th of the design pressure of the tubes. This allows for the rupture of a tube,

and the pressuring up of the shell.

During the hydrotest, the shell would have been pressured up to 130% of its design pressure, so for a tube rupture case it has

already been proven that the shell can withstand this pressure.

Although there are exceptions, most tubes are 15-25 mm (5/8-1.0 in.) diameter, with 19 mm (3/4 in.) being the most common. The

minimum tube pitch is 1.25 times the tube OD.

Triangular pitch gives the best heat transfer coefficient and allows more tubes to be placed in a shell.

Square pitch allows for easier cleaning of the outside of the tubes. The tubes are supported in the shell by baffles. The baffles also serve to force the fluid to flow across the tubes as

it flows down the shell, thus increasing the heat transfer coefficient.



Baffle Design

The most common type of baffle is the single segmented baffle.

Baffles can be placed vertically or horizontally. The baffle cut (Figure 7-6) sets the open area

for flow around the baffle. It is expressed as a

fraction of the inside shell diameter. Typical

baffle cuts are 0.20 0.35, and the opening in the baffle should provide roughly the same

area as the crossflow area between the

baffles.

The distance between the baffles is termed the baffle pitch, and typically ranges from 20-

100% of the shell diameter.

The baffle pitch and cut are the primary factors affecting shell side pressure drop and

heat transfer coefficient.

The bundle in Figure 7-7 shows a very low baffle cut and a very low baffle pitch, not the

typical values.


Figure 7-6 Baffle Cut



Figure 7-7 Shell and Tube Exchanger


Types of Baffles


Effect of small and large baffle cut


Shell and Tube Exchanger Thermal Design

The factor F in the heat transfer (Eq 7-44) equation is 1.0 in pipe-in-pipe exchangers and in counter flow shell and tube exchangers with an

equal number of shell and tube passes.

If the number of shell and tube passes differ, or if the exchanger is a crossflow type (TEMA X or J), then F will be less than 1.0.

As a general rule, one should not pick a configuration where F is less than 0.8. The value of F can be determined by referring to FIG 9-4

through 9-7 in the GPSA Engineering Data Book. The figures provide F

values for various shell and tube configurations based on inlet and

outlet temperatures. The parameters on the charts are calculated using

equations 7-49 and 7-50.

Figure 7-8 shows the temperature variables, and Figure 7-9 shows a typical F factor Plot.




Figure 7-8 Configuration for F Factor Calculation

11

12

tT

ttP

(Eq 7-49)

12

21

tt

TTR

(Eq 7-50)

T1 = shell side fluid inlet temperature

T2 = shell side fluid outlet temperature

t1 = tube side fluid inlet temperature

t2 = tube side fluid outlet temperature

The effectiveness of heat exchanger:

The capacity ratio in a heat exchanger:



Figure 7-9 LMTD Correction Factor Chart



The curves on Figure 7-9 can be calculated using

112

1121

1

1ln1

2

2

2

RRP

RRPR

RP

PR

FT (Eq 7-51)

When all four temperatures are known, as in a design case, the values of P and R are calculated and then a configuration is selected. If the value

of F is less than 0.8, then increase the number of shell passes.


In order to determine the area required for an exchanger, the overall heat transfer coefficient needs

to be determined.

Values of typical overall heat transfer coefficient and typical fouling factors are given in FIG 9-9 in the

GPSA Engineering Data Book.

The TEMA standard contains more data for typical U values. For detailed analysis, the overall heat transfer

coefficient is calculated using the individual film

coefficients.

Overall Heat Transfer Coefficients


Fluid Film Coefficients

Tube side and shell side film coefficients are calculated based on the Dittus-Boelter or Siedler-Tate equations. Once film coefficients are

estimated, the overall heat transfer coefficient is calculated using Eq 7-47.

Calculation of the inside film coefficient is straight forward. Calculation of the shell side coefficient is more complicated. The tube

bundle baffles provide cross flow and turbulence resulting in higher film

coefficients than for undisturbed flow along the tube axis. Flow across the

tubes also results in increased turbulence, and the velocity is not constant

across the bundle.

Triangular pitch provides more turbulence than square pitch, and film coefficients are about 25% for triangular pitch.

Clearly, the same equation cannot be used to calculate the tube side and the shell side film coefficients. The form of the equation however has been

retained, with special definitions used for the mass velocity and the

equivalent diameter.



For values of the Reynolds number from 2000 to 1,000,000, the following equation applies

14.033.055.01000

36.0

w

pseseso

k

CGD

k

Dh

(Eq 7-52)



Calculation of the mass velocity is based on the maximum flow area of the hypothetical tube row at the centre of the shell.

The length of the flow area is taken as the baffle spacing. There is usually no row of tubes at the centre, but rather two equal maximum rows on either side,

having fewer tubes than computed for the centre. This difference is negligible.

The flowing area is then given by

T

ss

P

BCDa

'

(Eq 7-53)

s

sa

WG (Eq 7-54)

Ds = shell inside diameter (m)

C = clearance between tubes (mm) B = baffle spacing (m)

PT = tube pitch (mm)

as = flow area (m2)

W = flow rate kg/s

and the mass velocity is



Reference to Figure 7-10 shows the tube spacing measurements.

Figure 7-10 Exchanger Tube Pitch

Tube pitch and clearance are related to the tube diameter as

oT dPC ' (Eq 7-55)

And the equivalent diameters for use in the Reynolds number are

o

oTes

d

dPD

1000

4 22 for square pitch (Eq 7-56)

o

oTes

d

dPD

1000

25.044.3 22 for triangular pitch (Eq 7-57)


For Shell and tube heat exchangers one needs to calculate the pressure drops on both sides. Again, the tube side

pressure drop is easier to calculate because of the simpler

geometry. For the tube side, the pressure drop consists of

three components:

Pf = pressure drop due to friction in tubes (Pa) PN = pressure drop due to nozzles (Pa) Pe = pressure drop due to tube entrance and exits (Pa)

In the absence of a phase change, the pressure drop in the tubes is given by Darcys equation

Pressure Drop

Dg

LGfP

c

f

f

22 (Eq 7-58)


Chopey and Hicks20 provide a simple relationship for the Fanning friction factor for the tubes

Pressure Drop

Re/16ff (Eq 7-59) Re < 2100

Re 2100 2.0Re/054.0ff (Eq 7-60)

Chopey and Hicks also provide a pressure drop correlation for exit and entry losses for the nozzles on

the heads and the head to tube connections.

Nozzle 2/2nN vKP (Eq 7-61)

Tube entrance and exit

2/2tte vKNP (Eq 7-62)

vn = velocity in the shell nozzle (m/s)

vt = velocity in the tubes (m/s)

= density (kg/m3) Nt = number of tube passes

K = 0, head-nozzle fluid entrance loss

1.25, head-nozzle fluid exit loss

1.80, tube entrance and exit


The shell side pressure drop has a similar form with

Pressure Drop

e

Bsss

D

NDfGP

2

)1(2 (Eq 7-63)

Details of the friction factor, equivalent diameter, and effects of baffle spacing can be found in the TEMA handbook.

Pressure drops in an exchanger depend on the system operating pressure. Typical pressure drops are as follows:

Vacuum 5-10% of absolute system pressure

101-170 kPa 3.5-34.5 kPa

>170 kPa 45 kPa up to 50% of gauge pressure

For high pressure drop systems, tube velocity might limit due to erosion concerns. Liquid velocity greater than 5 m/s may cause erosion.


Re-rating Existing Exchangers

It is often required to predict the performance of an exchanger in a new service, or for a different flow rate.

FIG 9-10 and 9-11 in the GPSA Engineering Data Book can be used for this purpose.

The figures are based on the fact that the performance at the new condition, 2, can be prorated from the previous

condition, 1.

FIG 9-10 shows the relationship amongst the variables. FIG 9-11 provides a base exchanger design that serves as

case 1 for various fluids.

An example calculations for a given exchanger data sheet is given as Example 9-1.


A spiral exchanger is a true counter-current exchanger that separates the two

fluids by a single plate.

Cold fluid enters the outside shell and exits the center of the exchanger. Hot fluid

enters the centre of the exchanger and

circulates to the outside as shown in

Figure 7-11.

The surface area is increased by increasing the width of the exchanger.

A gasketed plate covers and seals the channels and can be removed for

cleaning.

The units are compact, have low pressure drop, and a tight approach temperature.

They are ideal for handling sludge.

Capacities up to about 2000 kW are available.

Spiral Exchangers

Figure 7-11 Spiral Exchanger


Plate and Frame Exchangers

Where applicable, the plate and frame exchanger has become a viable alternative to other sorts of exchangers.

The advantages are the small footprint, light weight, lower cost and good heat transfer performance.

The unit is limited by a maximum pressure of about 1600 - 2000 kPa. A cut away view of a plate and frame exchanger is shown as Figure 7-12. The unit

consists of a number of corrugated plates that are held in a frame by bolts that pass

through the end plate. Each plate is gasketed to prevent leakage. There are four entry

ports on each plate that can be arranged in a number of ways to form different flow

patterns.

The plates normally have chevron type grooves that can have different angles. High theta plates provide better heat transfer at the expense of additional pressure drop. The

plates can be mixed and matched to provide more efficient heat transfer.

Stainless steel is a common plate material, but titanium, Monel, nickel, Incoloy, and other materials can also be used.

Plate thickness ranges from 0.5-3.0 mm with an average gap between plates of 1.5-5.0 mm. Most plates have an area of less than 1.5 m2, but as many as 600 plates can be

installed in one frame.

Temperature is limited by metallurgy and gasket material. Temperatures up to 250 oC have been used, but 150 oC gives much better gasket life.

Plate sets can be purchased where one side is welded, which eliminates one set of gaskets. This is a popular configuration for the rich amine side in a gas processing plant.



Figure 7-12 Plate and Frame Exchanger



The theta factor is also called the NTU (number of transfer units). Theta is stated in terms of the required duty of one or both fluids.

A consistent set of units must be used to make theta dimensionless. Theta is calculated as:

Theta Factor

Plm

oi

Cm

UA

T

tt

(Eq 7-64)

ti = inlet temperature to fluid channel

to = outlet temperature from fluid channel

Tlm = log mean temperature difference

U = overall heat transfer coefficient (W/m2 K)

A = total area of thermal plates (m2)

m = mass flow rate of fluid (kg/s)

CP = specific heat of fluid (kJ/kg K)



4.065.0

10002536.0

k

CGd

d

kh Pe

e

(Eq 7-65)

The film coefficients for plate and frame exchangers may be estimated as:

Heat Transfer Coefficients

Turbulent flow11

Laminar flow12 14.067.062.0

1000742.0

w

PeP

k

CGdWCh

(Eq 7-66)

de = effective diameter (4Wb)/(2W+2b) (m)

W = plate width (m)

b = mean distance between plates (m)

G = mass velocity between plates (kg/m2 s)

= fluid viscosity (kg/m s) CP = specific heat (kJ/kg K)

w = fluid viscosity at the wall (kg/m s) k = thermal conductivity (W/m K)

The overall heat transfer coefficient is then given as

21

21

111rr

hk

t

hU w (Eq 7-67)

t = plate thickness (m)

kw = thermal conductivity of plate (W/m K)



LMTD and F

The LMTD is calculated as for any other exchanger. F is a function of and the plate arrangement.

For low values of and for equal passes of hot and cold fluid, F approaches 1.0. The factor F decreases rapidly as the number of passes of hot and cold

fluid become unequal. The passes may become unequal if there is a large

difference in the flow rates of the hot and cold fluids. If this is the case, a plate

and frame exchanger may not be the best choice.

Table 7-3 provides some typical F factors.

7-3



The pressure drop depends on: plate design, flow rate, and flow pattern.

Pressure drop is usually less than in a comparable shell and tube unit.

High pressure drop increases the shear stress in the exchanger and tends to keep the exchanger cleaner.

Pressure drop calculations are best done by the vendor.

Pressure Drop


Compablock Exchangers

The Compablock exchanger, as shown in Figure 7-13, is a

variation of the plate and frame

units.

In a Compablock, the plates are completely welded together and

there are no gaskets between the

plates.

There are four gaskets on the cover plates.

The unit can be used for liquid-liquid exchange, and as a

reboiler or a condenser.

The units are compact and robust.

Figure 7-13 Compablock Exchanger


Brazed Aluminum Exchangers

Brazed aluminum exchangers have been employed in cryogenic gas processing facilities since the 1950s.

Brazed aluminum exchangers are composed of alternating layers of corrugated fins and flat separator sheets called parting sheets.

The number of layers, type of fins, stacking arrangements, and stream circuiting will vary depending on the exchanger service and duty.

A cut away view (FIG 9-34) and a good description of terms are provided in the GPSA Engineering Data Book.

Brazed aluminum exchangers are compact and light weight and can operate at pressures up to 9500 kPa. The surface area to volume ratio for a brazed aluminum

exchanger is 6-8 times greater than for a shell and tube unit. A brazed aluminum

exchanger has a density of 30-35% of a shell and tube unit. This means that about

25 times more surface per kilogram of exchanger is possible.

Because of the compact design, temperature approaches of 1.5 oC are possible on single-phase fluids, and 2.75 oC on two-phase fluids.

Brazed aluminum exchangers should be used with clean fluids. Upstream filters may be used to keep fine particles out.

Brazed aluminum exchangers must be protected from elemental mercury and caustic, as both are extremely corrosive to aluminum. Hydrogen sulphide and carbon

dioxide are not a concern as long as water does not condense out of the stream.


Printed Circuit Exchangers (PCHE)

Printed circuit exchangers are highly compact, corrosion resistant heat exchangers capable of operating at pressures up to 50,000 kPa and

temperatures from cryogenic to several hundred degrees Celsius.

PCHEs are constructed from flat plates into which flow channels have been chemically milled or etched. The plates are stacked and diffusion bonded

together to form a core. Fluid heads and nozzles are attached to the core to

direct fluids to the appropriate channels. Two or more fluids can be

accommodated in a core, and virtually any arrangement of passes or flow

combinations is possible.

Passages are typically 2 mm semicircles, see Figure 7-14, so the fluids need to be relatively clean or blockage of the passages will take place.

Materials of construction include stainless steels, titanium, nickel, and nickel alloys.

The diffusion bonding process ensures that the surfaces are sealed, and these units are well suited to high pressure gas operations.

Vapourization and condensation of fluids is readily accommodated. The major drawback is that failures have occurred due to thermal cycling. This

type of exchanger should not be used in situations where the feed streams have

large changes in flow rates or temperatures. A complete PCHE is shown in

Figure 7-15.


Printed Circuit Exchangers (PCHE)

Figure 7-15 A Complete PCHE

Figure 7-14 PCHE Internals


Coil Wound Exchangers

Spiral wound exchangers are used in natural gas liquefaction plants as the main cryogenic exchanger (MCE).

Thousands of small diameter aluminum tubes are wrapped around a core and encased in a shell.

These units are the heart of the liquefaction process.

Figure 7-16 shows a spiral wound exchanger.


Coil Wound Exchangers

Figure 7-16 Coil Wound Exchanger


Aerial Coolers

Aerial coolers or air-cooled exchangers are used to cool fluids with ambient air.

Aerial coolers are relatively simple, but in cold climates, the addition of freeze protection measures makes them

somewhat more complex.

The advantage of cooling with air is that it is plentiful and cheap.

The temperature achievable with aerial cooling is however about 15 oC above the ambient temperature and significant

extra cost is incurred to reduce this approach temperature.


Mechanical Arrangements

Aerial coolers typically come as forced draft units or induced draft units. Forced draft units have the tube section on the discharge side of the fan, while induced

draft units have the tubes on the suction side of the fan.

A diagram showing typical layouts is shown in FIG 10-2 of the GPSA Engineering Data Book. More than one tube bundle can be included in a unit, and more than

one fan bay can be included in a unit as shown in FIG 10-3.

Advantages and disadvantages of each layout are described in the GPSA. For process fluids above 175 oC, forced draft units should be used to keep the fan

components from becoming too hot.

Fan sizes range from 0.9 8.5 m, but units of 4.3-4.9 m diameter are the most common.

Drivers are usually electric and a speed reducer is required to match motor speed to fan speed. A fan tip speed of 3650 m/min or less is common. V-belt drives are

used up to about 22 kW and gear drives are used for higher power. Maximum

motor size is limited to 37 kW.

The tube bundle is fabricated with multiple rows (3-8) of finned tubes and may have one pass or two passes. Tube diameters are 16-38 mm, fin heights are 12.7

mm to 25.4 mm, and fin densities range from 276 433 fins/metre. Tubes in gas processing services are usually carbon steel, but stainless steel may

also be used in some services.

For low pressure service, header boxes are built with a cover plate. For higher pressure service the end plate must be thicker, and then the header will have plugs

for access to the tubes. FIG 10-5 illustrates the two types of header boxes.


The outlet temperature of the process stream is controlled, but if the process fluid becomes viscous or freezes when cooled, the air temperature may also have to be controlled. When the

ambient temperature is low, recirculation of warm air is often required to keep the bottom row of

tubes from becoming too cold.

The two control schemes must work together. Refer to FIG 10-7 in the GPSA Engineering Data Book to see the arrangement of air control louvers on a typical cooler.

Temperature control of the process stream is usually accomplished by changing the amount of air that flows past the coil. The top louver can be adjusted to change the back pressure on the fan and

change the air flow rate. In addition, fan drivers often have two speed motors or completely

variable speed motors. In addition, in multi-fan units, one of more of the fans can be shut off. Some

older units had variable pitch fans, but these were generally high maintenance units and have

mostly been replaced by variable speed drives.

The cooler is designed to provide sufficient cooling when the ambient temperature is high. In Alberta, a typical design air temperature is 28 - 30 oC. In the Middle East, the air design temperature

can be as high as 50 oC. The process temperature that can usually be achieved is 12 - 15 oC higher

than the air temperature. As the ambient temperature falls below design, less air is required to

provide the process duty, and the fans will slow down or stop to reduce the air flow. As the ambient

temperature gets colder, the operators will close the manual louvers, to limit the intake of cold air.

At some point, the top louvers will start to close to reduce the air flow even more. If this does not

keep the inlet air warm enough, the recirculation louvers will open to allow warm air to mix with the

incoming air. Since the cooler is designed for an inlet air temperature of 28 30 oC, there is no problem with making the process temperature if the blended air temperature is 10 15 oC. If the inlet air temperature is allowed to get too cold, the bottom row of tubes can freeze.

Process Control


Thermal Design

Thermal design of an aerial cooler is done in much the same manner as for any other exchanger. The basic design equations are:

21 TTmCQ P (Eq 7-68)

12 ttCmQ Paa (Eq 7-69)

LMTDFAUQ (Eq 7-70)

The temperature correction factor, F in the heat transfer equation can be found from FIG 10-8 or 10-9 in the GPSA Engineering Data Book. The factor is based

on values of P and R as follows:

11

12

tT

ttP

(Eq 7-71)

12

21

tt

TTR

(Eq 7-72)


Thermal Design

t1 = inlet air temperature (oC)

t2 = outlet air temperature (oC)

T1 = inlet process temperature (oC)

T2 = outlet process temperature (oC)

U = overall heat transfer coefficient (W/m2 K)

Normally Q is known, U and LMTD are calculated and the equation is solved for the required area, A.

The procedure is complicated by the fact that the air flow is not known, and hence the air outlet temperature is not

known.

The design is thus iterative with regard to air flow, which depends on the type of coil, number of tube rows, fin type

etc.


Preliminary Design Calculations

For preliminary calculations for gases, the overall heat transfer coefficients in Table 7-4, based on bare tube area may be used:

7-4



For preliminary calculations for liquids, the overall heat transfer coefficients in Table 7-5, based on bare tube area may be used:

7-5



For preliminary calculations for condensing fluids, the overall heat transfer coefficients in Table 7-6, based on bare tube area may be used.

7-6



The optimum air temperature rise across the tubes may be estimated using

1

1212

2..00088.0 t

TTUCFtt

(Eq 7-73)

210025.089.0 TTCF (Eq 7-74)

The above equations will allow the calculation of the value of maCpa required for the air flow. The Cpa value for the air must consider the relative

humidity of the air.

Cpa = molar heat capacity of air (kJ/kmol K)

RH = relative humidity (%)

Pvpw = vapour pressure of water at air temperature T1 (kPa)

P = air pressure (kPa)

P

PRH

PPRH

C

vpwvpw

pa

100

1.29100

5.33 (Eq 7-75)



The ambient air pressure is a function of plant elevation in metres, h, and is given by:

128.29exp325.101

t

hP (Eq 7-76)

Once Cpa is determined, the molar flow of air, ma, is found.

The molecular mass of the air is determined, considering the relative humidity.

P

PRH

PPRH

MW

vpwvpw

a

100

29100

18 (Eq 7-77)

With the MW of the air and the ambient air conditions, the density of the inlet air can be determined.

1Rt

PMWa (Eq 7-78)



P

Rtmq aa

1 (Eq 7-79)

With the molar flow rate of air and the ambient conditions, the volumetric flow of air is found.

With the volumetric air flow rate determined, the fan power requirements can be estimated using

aaqPkW

(Eq 7-80)

Pa = air side pressure drop (kPa) qa = actual air flow rate (m

3/s)

= fan efficiency (0.4 - 0.75: 0.70 for planning)

For planning purposes, the pressure drop per tube row is 25 - 35 Pa, and a typical cooler has 3 - 6 tube rows.


Rigorous Design Calculations

Rigorous design calculations are best done with a computer program such as HTRI. This program will

calculate:

heat transfer coefficients, air flow rate, pressure drops and duty based on coil design parameters.

Most EPC firms should have the program available. The GPSA Engineering Data Book provides an example

of a more rigorous hand calculation. The procedure is

basically to assume a design, and then prove that it is

correct.

The procedure is detailed in Example 10-1.


Performance Testing

Performance testing of an aerial cooler is complicated by the fact that the air flow rate must be determined. This is done by

measuring the air velocity in a number of locations just under

the fan.

The ambient air temperature is available, so the air outlet can be determined from the value of Q. Q is determined from the

process side conditions.

One can now calculate the overall heat transfer coefficient, the individual heat transfer coefficients for both the air side and

process side, and then determine the overall fouling factor. If

the overall fouling factor is larger than the design value, the

cooler is fouled and may benefit from cleaning.

Both the inside of the tubes and the fins may need to be cleaned.


1. Bennett, C.O., and J.E. Myers, Momentum, Heat, and Mass Transfer, McGraw Hill, 1974.

2. Seider, E.N. and G.E. Tate, Ind. & Eng. Chem., 28, (1936), p. 1429.

3. Colburn, A.P., Trans. AIChE, 29, (1933), p. 174.

4. Marriott, J., Where and How to Use Plate Heat Exchangers, Chem. Eng., April 5, 1971, p. 127. 5. API Standard 661, Air Cooled heat Exchanges for General Refinery Service. 6. Steinmeyer, D., Understanding P and T in Turbulent Flow Heat Exchangers, Chem. Eng. Prog., (June 1996), p. 49.

7. Poddar, T.K. and G.T. Polley, Optimize Shell and Tube Heat Exchanger Design, CEP (Sept. 2000), p.41.

8. Standard of the Tubular Exchanger Mft. Assoc., 6th Edition, New York, 1978.

9. Chen, C.C., Chem. Eng., (Mar. 1984), p. 155

10. Bell, K.J., Oil and Gas J., (Dec. 4,1978), p.59.

11. Buonopane, R.A. et al., Chem. Eng. Prog., Vol. 59, No. 7, (1963), p. 185.

12. Jackson, B.W., and R.A. Troup, Chem. Eng. Prog., Vol. 60, No. 7, (1964), p. 62.

13. Burn, J., A.M. Johnston, N.M. Johnston, Experience With Printed Circuit Heat Exchangers, European GPA Continental Meeting, Budapest, (1999).

14. Rorschach, R.L., Oil and Gas J., (June 13, 1966), p.90.

15. Brown, R., Chem. Eng.,(Mar. 27,1978), p. 108.

16. Glass, J., Chem. Eng.,(Mar. 27,1978), p. 120.

17. Baker, W.J., Hydr. Proc. (May 1980), p.173.

18. Ganapathy, V., Oil and Gas J., (Dec. 3,1979), p.74.

19. Rubin, F.C., Hydr. Proc. (Dec. 1980), p.147.

20. Chopey, N. P., Hicks, T. G., Handbook of Chemical Engineering Calculations, McGraw-Hill, 1984, pp.7-

86.

References Read Section 9 of the GPSA Engineering Data Book Heat Exchangers Read Section 10 of the GPSA Engineering Data Book Air-Cooled Exchangers

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