optimization and analysis of tube-in-tube heat exchanger with fins-libre

7/27/2019 Optimization and Analysis of Tube-In-tube Heat Exchanger With Fins-libre

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OPTIMIZATION AND ANALYSIS OF

TUBE-IN-TUBE HEAT EXCHANGER WITH FINS

PROJECT REPORT

Submitted in partial fulfillment of the requirements for the award

of the degree of Bachelor of Technology in Mechanical Engineering

to the University of Kerala.

by

ALPHIN C. TOM

ARJUN RAMANATHAN

ARUN KRISHNAN

Department of Mechanical Engineering

College of Engineering, Thiruvananthapuram-16

April 2007


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OPTIMIZATION AND ANALYSIS OF

TUBE-IN-TUBE HEAT EXCHANGER WITH FINS

PROJECT REPORT

Submitted in partial fulfillment of the requirements for the award

of the degree of Bachelor of Technology in Mechanical Engineering

to the University of Kerala.

by

ALPHIN C. TOM

ARJUN RAMANATHAN

ARUN KRISHNAN


College of Engineering, Thiruvananthapuram-16

April 2007


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DEPARTMENT OF MECHANICAL ENGINEERING

COLLEGE OF ENGINEERING, TRIVANDRUM-16.

CERTIFICATE

This to certify that the Project report entitled OPTIMIZATION AND ANALYSIS

OF TUBE-IN-TUBE HEAT EXCHANGER WITH FINS submitted by

ALPHIN C. TOM, ARJUN RAMANATHAN AND ARUN KRISHNANto the University

of Kerala in partial fulfillment of the requirements for the award of the Degree of Bachelor of

Technology in Mechanical Engineering is a bonafide record of work carried out by them

under my/our guidance and supervision. The contents of this work in full or in parts, have not

been submitted to any other institute or University for the award of any degree or diploma.

DILIP D.

Lecturer


(Guide)

Head of Department



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ACKNOWLEDGMENTS

For the past few months we were engaged in a fruitful exercise which we must admit leaves us

richer in knowledge and experience which is mainly due to the invaluable guidance,

encouragement and assistance acquired from many cognizant resources.

We take this opportunity to thank god Almighty for his blessing to help us finish this project. We

express our profound gratitude to our project guide Dilip D., Lecturer, Department of

Mechanical Engineering for his individual encouragement & guidance .We also thank Dr B.

Anil, Professor, Department of Mechanical Engineering and Prof SarathChandra Das M. R.,

HOD , for their guidance & support for completing this venture.

Alphin C. Tom

Arjun Ramanathan

Arun Krishnan


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ABSTRACT

A heat exchanger is a device built for efficient heat transfer from one fluid to another. They are

widely used in refrigeration, air conditioning, space heating, electricity generation, and chemical

processing. Heat exchangers may be classified as parallel-flow, cross-flow and counter-flow heat

exchangers. The counter current design is most efficient, in that it can transfer the most heat.

Hence such heat exchangers are much preferred for heating and cooling of fluids. The counter-

flow heat exchangers can be classified according to their constructional features as Concentric

Tubes, Shell and Tube, Multiple Shell and Tube passes and Compact heat exchangers. In our

analysis we consider Concentric Tubes or Tube in Tube heat exchanger. In this type, two

concentric tubes are used, each carrying one of the fluids. For designing of a heat exchanger the

total heat transfer may be related with its governing parameters. In this Project we undertake the

complete thermal design and analysis of a Longitudinally Fined Double Pipe Heat Exchanger.

Our aim is to optimize the height of the fin so as to obtain maximum possible heat transfer

without any wastage of material at a given length and inlet conditions. For this we have to

perform the thermal analysis for all possible fin heights. This has to be carried out using a

computer program. Number of fins is fixed by the outer diameter specified from the thermal data

tables. The results obtained from the program will be analyzed to fix the optimum fin height.And this fin height will be used in creating a finite element model of the heat exchanger using

ANSYS. With the help of ANSYS the temperature profile of the heat exchanger can be obtained.

Unfinned heat exchanger is also modeled and compared with the Finned one. Thus a

comprehensive performance evaluation of thermal aspect is carried out.


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TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION

1.1 OBJECTIVE 2

1.2 SCOPE 2

1.3 CLASSIFICATION OF HEAT EXCHANGERS 3

1.3.1.CLASSIFICATION ACCORDING TO CONSTRUCTION 3

1.3.2 CLASSIFICATION ACCORDING TO TRANSFER PROCESS 5

1.3.3 CLASSIFICATION ACCORDING TO SURFACE COMPACTNESS 7

1.3.4 CLASSIFICATION ACCORDING TO FLOW ARRANGEMENT 7

1.3.5 CLASSIFICATION ACCORDING TO PASS ARRANGEMENTS 8

1.3.6 CLASSIFICATION ACCORDING TO PHASE OF FLUIDS 8

1.3.7 CLASSIFICATION ACCORDING TO HEAT TRANSFER 9

MECHANISMS

1.4 SELECTION OF HEAT EXCHANGER 9

1.5 REQUIREMENTS OF A HEAT EXCHANGER 17

CHAPTER 2: LITERATURE REVIEW 19

2.1 EXPERIMENTAL HEAT EXCHANGER STUDIES 20

2.2 EXPERIMENTAL HEAT EXCHANGER CORELATIONS 23

2.3 APPLICATION TO THE PRESENT STUDY 31

CHAPTER 3: PROJECT DESCRIPTION 34

3.1 PROBLEM DEFINITION 35

3.2 COMPUTATIONAL SCHEME 36


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CHAPTER 4: PROJECT THEORY 38

4.1 SOME IMPORTANT DEFINITIONS 39

4.2 HEAT EXCHANGER BASIC ANALYSIS METHODS 44

4.3 THE -NTU METHOD 45

4.4 FINS OR EXTENDED SURFACES 47

4.5 HEAT TRANSFER COEFFICIENT 53

4.6 DOUBLE PIPE HEAT EXCHANGER 58

4.7 FOULING IN HEAT EXCHANGERS 59

CHAPTER 5: THERMAL DESIGN PROCEDURE 60

5.1 ANALYSIS OF DOUBLE PIPE HEAT EXCHANGERS 60

5.2 DESIGN OF LONGITUDINALLY FINNED DOUBLE PIPE

HEAT EXCHANGERS 65

5.3 STEPS INVOLVED IN THE THERMAL DESIGN OF -

A LONGITUDINALLY FINNED DOUBLE PIPE HEAT EXCHANGER 70

CHAPTER 6: OPTIMIZATION USING COMPUTER PROGRAM 74

6.1 DATA INPUT 74

6.2 THERMAL DESIGN 77

6.3. RESULTS AND DISCUSSIONS 79

CHAPTER 7:THERMAL ANALYSIS USING ANSYS 82

7.1 FINITE ELEMENT METHOD 82

7.2. ANSYS 83

7.3. BUILDING THE MODEL 88

7.4. MESHING 90

7.5. APPLYING LOADS 91

7.6. SOLUTION 92

7.7. POSTPROCESSING 92


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7.8. PROBLEM DESCRIPTION 93

7.9. DISCUSSION 113

7.10. COMPARISON OF RESULTS AND CONCLUSION 115

CHAPTER 8: CONCLUSION 117

APPENDIX A 118

C++ PROGRAM CODE FOR THE OPTIMIZATION OF FIN HEIGHT 118


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LIST OF FIGURES

FIGURE NO. TITLE PAGE

FIGURE 1.1. DOUBLE PIPE HEAT EXCHANGER SINGLE PASS

WITH COUNTER FLOW

FIGURE 1.2. DOUBLE PIPE HEAT EXCHANGER MULTI PASS

WITH COUNTER FLOW

FIGURE 1.3. HEAT EXCHANGE CLASSIFICATION ACCORDING

TO CONSTRUCTION

FIGURE 1.4. CLASSIFICATION ACCORDING TO TRANSFER PROCESS

FIGURE 1.5. CLASSIFICATION ACCORDING TO SURFACE

COMPACTNESS

FIGURE 1.6. CLASSIFICATION ACCORDING TO FLOW

ARRANGEMENTS

FIGURE 6.1. DATA INPUT MODE SELECTION MENU

FIGURE 6.2. SAMPLE PROBLEM SCREEN 1



FIGURE 6.5. MANUAL DATA INPUT SCREEN 1

FIGURE 6.6. MANUAL DATA INPUT SCREEN 2

FIGURE 6.7. UNFINNED HEEX CALCULATED RESULTS

FIGURE 6.8. CALCULATION RESULTS AT FIN HEIGHT = 15MM

FIGURE 6.9. THE THERMAL DESIGN RESULTS AT

VARIOUS FIN HEIGHTS

FIGURE 6.10. THE FINAL RESULT OF THE PROGRAM


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FIGURE 7.1. SOLID 90 ELEMENT

FIGURE 7.2. CROSS SECTION

FIGURE 7.3. EXTRUDED MODEL

FIGURE 7.4. MESHED MODEL

FIGURE 7.5. CONTOUR PLOT OF NODAL TEMPERATURE- END VIEW

FIGURE 7.6. CONTOUR PLOT OF NODAL TEMPERATURE

FIGURE 7.7. CONTOUR PLOT OF NODAL HEAT FLUX

FIGURE 7.8. VECTOR PLOT OF THERMAL FLUX

FIGURE 7.9. VECTOR PLOT OF THERMAL GRADIENT

FIGURE 7.10. FLUX VS RADIAL DISTANCE

FIGURE 7.11. HEAT FLOW VS RADIAL DISTANCE



FIGURE 7.14. CONTOUR PLOT OF THERMAL FLUX


FIGURE 7.16. TEMPERATURE VS RADIAL DISTANCE

FIGURE 7.17. HEATFLOW VS RADIAL DISTANCE



FIGURE 7.20. CONTOUR PLOT OF THERMAL FLUX



FIGURE 7.23. HEAT FLOW VS RADIAL DISTANCE

FIGURE 7.24. TEMPERATURE VS RADIAL DISTANCE


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LIST OF TABLES

FIGURE NO. TITLE PAGE

TABLE 2.1. WANG (1998C): PARAMETRIC RANGE

TABLE 2.2. MCQUISTON (1979) PLAIN FIN

CORRELATIONS: PARAMETRIC RANGE

TABLE 2.3. WEBB (1986) PLAIN FIN CORRELATIONS:

PARAMETRIC RANGE

TABLE 2.4. WANG (1999) PLAIN FIN CORRELATIONS:

PARAMETRIC RANGE

TABLE 2.5. WEBB (1998) LOUVERED FIN CORRELATIONS:

PARAMETRIC RANGE

TABLE 2.6. WANG (1998B) LOUVERED FIN CORRELATIONS:

PARAMETRIC RANGE

TABLE 4.1. TEMPERATURE DISTRIBUTION AND HEAT TRANSFER

RATE FOR FINS OF UNIFORM CROSS SECTIONAL AREA

TABLE 5.1. THERMAL DESIGN DATA TABLE

TABLE 7.1. SOLID90 ELEMENT OUTPUT DEFINITIONS

TABLE 7.2. COMPARISON VARIOUS MODEL ANALYSIS RESULTS


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ABBREVIATIONS

LMTD Log Mean Temperature Difference

NTU Number of Transfer Units

HVAC - Heating, Ventilating, And Air Conditioning

FEM Finite Element Method

Re Reynolds Number

Pr Prandtl Number

NFA Net Flow Area

PDE Partial Differential Equation

GUI Graphic User Interface


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CHAPTER 1: INTRODUCTION

Heat Exchangers are the class of equipment used to transfer heat in industrial processes.

Most often the transfer of heat takes place between to fluid streams. However, in

certain cases heat may also e transferred to vacuum (as in the case of space radiators).

Truly speaking, the term Heat Exchangers is a misnomer. Heat is never exchanged

but transferred. The difference between these two terms is that exchange means to

transfer in lieu of something, whereas transfer indicates unconditional flow in one

direction. Hence, the equipment transferring heat should have been called Heat

Transmitter or Heat Transferor. However, engineers have decided to stay with the

traditional term Heat Exchanger often abbreviated as HX.

Heat exchangers are a family of equipment, which are often called by other names in

specific applications. For example, automobile radiators, power plant economizers, air

preheaters, super heaters, condensers, feed water heaters, cooling towers, space

radiators, oil coolers, stirred tanks with cooling jackets are all essentially heat

exchangers. The use of Heat exchangers is extensive in power, chemical processes,

nuclear, aerospace, food processing, petrochemical, metallurgical, refrigeration and

cryogenic industry. Even though the underlying principles, of the construction of heat

exchangers are essentially those of conduction, convection, and sometimes radiation,

the application of these principles is not very straightforward. The factors that make the

construction, design and operation of a heat exchanger complex are economic

considerations, space and weight considerations an above all thermal and hydraulic

performance. In some applications, some specific factor may gain a controlling


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importance, for example weight and space requirements are of prime concern in the

aerospace industry which uses compact heat exchangers; regular cleaning is a

requirement of the brewing and dairy industry and hence that use plate heat exchangers

which can be readily disassembled and assembled, and so on.

1.1. OBJECTIVE

In this Project we undertake the complete thermal design and analysis of a

Longitudinally Fined Double Pipe Heat Exchanger. The thermal analysis was carried

out based on the given geometrical parameters. Our aim is to optimize the height of the

fin so as to obtain maximum possible heat transfer without any wastage of material at a

given length and inlet conditions. For this we have to perform the thermal analysis for

all possible fin heights. This has to be carried out using a computer program. Number

of fins is fixed by the outer diameter specified from the thermal data tables. The results

obtained from the program will be analyzed to fix the optimum fin height. And this fin

height will be used in creating a finite element model of the heat exchanger using

ANSYS. With the help of ANSYS the temperature profile of the heat exchanger can be

obtained. Unfinned heat exchanger can also be modeled and compared with the Finned

one.

1.2. SCOPE

From the Analysis carried out in the Project undertaken we will be able to determine

the optimum fin height for a given length, inlet conditions and other geometric

parameters. The presence of fins provides an increase in heat transfer due to the

increased surface area. Thus instead of providing larger diameter pipes, we can make


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use of expensive durable materials for the construction of thinner pipe and provide fins

of a cheaper material to account for the same heat transfer or more. Moreover form the

optimization program we will be able to demonstrate that just increasing the fin height

does not necessarily result in an increase in heat transfer. There is an optimum height

beyond which increasing the fin height results in nothing more than loss of material. By

computing this value we can conserve material and construction costs.

Fluids with lower specific heats need extra surface area for a particular heat transfer

compared to the others. By providing fins into this surface we can provide an

alternative to increasing the diameter of Pipes used.

1.3. CLASSIFICATION OF HEAT EXCHANGERS

Heat Exchangers appear in a variety of sizes and constructions. It is interesting to note

that heat exchangers can be as huge as a power plant condenser transferring hundreds

of megawatts of heat on one hand and on the other; it can be as tiny as an electronic

chip cooler which transfers only few watts of thermal energy. Hence, a wide range of

design of heat exchangers is available for a variety of application. There is no unique

method of classifying the large family of heat exchangers. They can be classified on

different aspects of their construction and operation.

1.3.1. Classification According To Construction

According to constructional details, heat exchangers are classified as:

1. Tubular heat exchangers-double pipe, shell and tube, coiled tube

2. Plate heat exchangers-gasketed, spiral, plate coil, lamella


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3. Extended surface heat exchangers-tube-fin, plate-fin

4. Regenerators-fixed matrix, rotary


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+

Gas-liquid heat exchangers are mostly tube-fin type compact heat exchangers with the

liquid on the tubeside. The radiator is by far the major type of liquid-gas heat

exchanger, typically cooling the engine jacket water by air.

1.3.6.2. Liquid-Liquid

Most of the liquid-liquid heat exchangers are shell and tube type, and plate heat

exchangers to a lesser extent. Both fluids are pumped through the exchanger, so the

principal mode of heat transfer is forced convection.

1.3.6.3. Gas-Gas

This type of exchanger is found in exhaust gas-air preheating recuperators, rotary

regenerators, intercoolers and/or aftercoolers to cool supercharged engine intake air of

some land-based diesel power packs and diesel locomotives, and cryogenic gas

liquefaction systems

1.3.7. Classification According to Heat-Transfer Mechanisms

The basic heat-transfer mechanisms employed for heat transfer from one fluid to the

other are single-phase convection, forced or free, two-phase convection (condensation

or evaporation) by forced or free convection, and combined convection and radiation.

Any of these mechanisms individually or in combination could be active on each side

of the exchanger.

1.4. SELECTION OF HEAT EXCHANGERS

Selection criteria are many, but primary criteria are type of fluids to be handled,

operating pressures and temperatures, heat duty, and cost. Fluids involved in heat


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#

transfer can be characterized by temperature, pressure, phase, physical properties,

toxicity, corrosivity, and fouling tendency. Operating conditions for heat exchangers

vary over a very wide range, and a broad spectrum of demands is imposed for their

design and performance. All of these must be considered when assessing the type of

unit to be used [It%]. When selecting a heat exchanger for a given duty, the following

points must be considered:

1. Materials of construction

2. Operating pressure and temperature, temperature program, and temperature driving

force

3. Flow rates

4. Flow arrangements

5. Performance parameters-thermal effectiveness and pressure drops

6. Fouling tendencies

7. Types and phases of fluids

8. Maintenance, inspection, cleaning, extension, and repair possibilities

9. Overall economy

10. Fabrication techniques

1 1. Intended applications


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1.4.1. Materials of Construction

For reliable and continuous use, the construction materials for pressure vessels and heat

exchangers should have a well-defined corrosion rate in the service environments.

Furthermore, the material should exhibit strength to withstand the operating

temperature and pressure. Shell and tube heat exchangers can be manufactured in

virtually any materials that may be required for corrosion resistance, for example, from

nonmetals like glass, Teflon, and graphite to exotic metals like titanium, zirconium,

tantalum, etc. Compact heat exchangers with extended surfaces are mostly

manufactured from any metal that has drawability, formability, and malleability. Heat

exchanger types like plate heat exchangers normally require a material that can be

pressed or welded.

1.4.2. Operating Pressure and Temperature

Pressure. The design pressure is important to determine the thickness of the pressure

retaining components. The higher the pressure, the greater will be the required

thickness of the pressure retaining membranes and the more advantage there is to

placing the high-pressure fluid on the tubeside. The pressure level of the fluids has a

significant effect on the type of unit selected.

1. At low pressures, the vapor-phase volumetric flow rate is high and the low

allowable pressure drops may require a design that maximizes the area available for

flow, such as crossflow or split flow with multiple nozzles.

2. At high pressures, the vapor-phase volumetric flow rates are lower and allowable

pressure drops are greater. These lead to more compact units.


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3. In general, higher heat-transfer rates are obtained by placing the low-pressure gas on

the outside of tubular surfaces.

4. Operating pressures of the gasketed plate heat exchangers and spiral plate heat

exchangers are limited because of the difficulty in pressing the required plate thickness,

and by the gasket materials in the case of PHEs. The floating nature of floating-head

shell and tube heat exchangers and lamella heat exchangers limits the operating

pressure.

1.4.3. Temperature:

Design Temperature. This parameter is important as it indicates whether a material at

the design temperature can withstand the operating pressure and various loads imposed

on the component. For low-temperature and cryogenic applications toughness is a

prime requirement, and for high temperature applications the material has to exhibit

creep resistance.

Temperature Program. Temperature program in both a single pass and multipass

shell and tube heat exchanger decides the mean metal temperatures of various

components like shell, tube bundle, and tubesheet, and the possibility of temperature

cross. The mean metal temperatures affect the integrity and capability of heat

exchangers and thermal stresses induced in various components.

Temperature Driving Force. The effective temperature driving force is a measure of

the actual potential for heat transfer that exists at the design conditions. With a

counterflow arrangement, the effective temperature difference is defined by the log

mean temperature difference (LMTD). For flow arrangements other than counterflow


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arrangement, the LMTD must be corrected by a correction factor, F. The F factor can

be determined analytically for each flow arrangement but is usually presented

graphically in terms of the thermal effectiveness P and the heat capacity ratio R for

each flow arrangement.

Flow Rate

Flow rate determines the flow area: the higher the flow rate, the higher will be the

crossflow area. Higher flow area is required to limit the flow velocity through the

conduits and flow passages, and the higher velocity is limited by pressure drop,

impingement, erosion, and, in the case of shell and tube exchanger, by shell-side flow-

induced vibration. Sometimes a minimum flow velocity is necessary to improve heat

transfer, to eliminate stagnant areas, and to minimize fouling.

Flow Arrangement

As defined earlier, the choice of a particular flow arrangement is dependent upon the

required exchanger effectiveness, exchanger construction type, upstream and

downstream ducting, packaging envelope, and other design criteria.

1.4.4. Performance Parameters-Thermal Effectiveness and Pressure Drops

Thermal Effectiveness.

For high-performance service requiring high thermal effectiveness, use brazed plate-fin

exchangers (e.g., cryogenic service) and regenerators (e.g., gas turbine applications),

use tube-fin exchangers for slightly less thermal effectiveness in applications, and use

shell and tube units for low thermal effectiveness service.


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Pressure Drop.

Pressure drop is an important parameter in heat exchanger design. Limitations may be

imposed either by pumping cost or by process limitations or both. The heat exchanger

should be designed in such a way that unproductive pressure drop is avoided to the

maximum extent in areas like inlet and outlet bends, nozzles, and manifolds. At the

same time, any pressure drop limitation that are imposed must be utilized as nearly as

possible for an economic design.

Fouling Tendencies

Fouling is defined as the formation on heat exchanger surfaces of undesirable deposits

that impede the heat transfer and increase the resistance to fluid flow, resulting in

higher pressure drop. The growth of these deposits causes the thermohydraulic

performance of heat exchanger to decline with time. Fouling affects the energy

consumption of industrial processes, and it also decides the amount of extra material

required to provide extra heat-transfer surface to compensate for the effects of fouling.

Compact heat exchangers are generally preferred for nonfouling applications. In a shell

and tube unit the fluid with more fouling tendencies should be put on the tube side for

ease of cleaning. On the shellside with cross baffles, it is sometimes difficult to achieve

a good flow distribution if the baffle cut is either too high or too low.

Stagnation in any regions of low velocity behind the baffles is difficult to avoid if the

baffles are cut more than about 20-25%. Plate heat exchangers and spiral plate

exchangers are better chosen for fouling services. The flow pattern in plate heat

exchanger induces turbulence even at comparable low velocities; in the spiral units, the

scrubbing action of the fluids on the curved surfaces minimizes fouling.


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Types and Phases of Fluids

The phase of the fluids within a unit is an important consideration in the selection of

the heat exchanger type. Various combinations of fluid phases dealt in heat exchangers

are liquid-liquid, liquid-gas, and gas-gas. Liquid phase fluids are generally the

simplest to deal with. The high density and the favorable values of many transport

properties allow high heat-transfer coefficients to be obtained at relatively low pressure

drops .

Maintenance, Inspection, Cleaning, Repair, and Extension Aspects

Consider the suitability of various heat exchangers as regards maintenance, inspection,

cleaning, repair, and extension. For example, the pharmaceutical, dairy, and food

industries require quick access to internal components for frequent cleaning. Since

some of the heat exchanger types offer great variations in design, this must be kept in

mind when designing for a certain application. For instance, consider inspection and

manual cleaning. Spiral plate exchangers can be made with both sides open at one edge,

or with one side open and one closed. They can be made with channels between 5 mm

and 25 mm wide, with or without studs. The shell and tube heat exchanger can be made

with fixed tubesheets or with a removable tube bundle, with small- or large-diameter

tubes, or small or wide pitch. A lamella heat exchanger bundle is removable and thus

fairly easy to clean on the shellside. Inside the lamella, however, cannot be drilled to

remove the hard fouling deposits. Gasketed plate heat exchangers (PHEs) are easy to

open, especially when all nozzles are located on the stationary end-plate side. The plate

arrangement can be changed for other duties within the frame and nozzle capacity.

Repair of some of the shell and tube exchanger components is possible, but the repair


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of expansion joint is very difficult. Tubes can be renewed or plugged. Repair of

compact heat exchangers of tube-fin type is very difficult except by plugging of the

tube. Repair of the plate- fin exchanger is generally very difficult. For these two types

of heat exchangers, extension of units for higher thermal duties is generally not

possible. All these drawbacks are easily overcome in a PHE. It can be easily repaired,

and plates and other parts can be easily replaced. Due to modular construction, PHEs

possess the flexibility of enhancing or reducing the heat transfer surface area,

modifying the pass arrangement, and addition of more than one duty according to the

heat-transfer requirements at a future date.

Overall Economy

There are two major costs to consider in designing a heat exchanger: the manufacturing

cost and the operating costs, including maintenance costs. In general, the less the heat-

transfer surface area and less the complexity of the design, the lower is the

manufacturing cost. The operating cost is the pumping cost due to pumping devices

such as fans, blowers, pumps, etc. The maintenance costs include costs of spares that

require frequent renewal due to corrosion, and costs due to corrosion & fouling

prevention and control. Therefore, the heat exchanger design requires a proper balance

between thermal sizing and pressure drop.

Fabrication Techniques

Fabrication techniques are likely to be the determining factor in the selection of a heat-

transfer surface matrix or core. They are the major factors in the initial cost and to a

large extent influence the integrity, service life, and ease of maintenance of the finished

heat exchanger . For example, shell and tube units are mostly fabricated by welding,


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"

plate-fin heat exchangers and automobile aluminum radiators by brazing, copper-brass

radiators by soldering, most of the circular tube-fin exchangers by mechanical

assembling, etc.

1.5. REQUIREMENTS OF HEAT EXCHANGERS

1. High thermal effectiveness

2. Pressure drop as low as possible

3. Reliability and life expectancy

4. High-quality product and safe operation

5. Material compatibility with the process fluids

6. Convenient size, easy for installation, reliable in use

7. Easy for maintenance and servicing

8. Light in weight but strong in construction to withstand the operational pressures

9. Simplicity of manufacture

10. Low cost

11. Possibility of effecting repair to maintenance problems

The heat exchanger must meet normal process requirements specified through problem

specification and service conditions for combinations of the clean and fouled

conditions, and uncorroded and corroded conditions. The exchanger must be

maintainable, which usually means choosing a configuration that permits cleaning as


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*

required and replacement of tubes, gaskets, and any other components that are damaged

by corrosion, erosion, vibration, or aging. This requirement may also place limitations

on space for tube bundle pulling, to carry out maintenance around it, lifting

requirements for heat exchanger components, and adaptability for in-service inspection

and monitoring.


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+

CHAPTER 2: LITERATURE REVIEW

Finned-tube heat exchangers are common devices; however, their performance

characteristics are complicated. As previously mentioned this study focuses on the air

side performance of fin tube heat exchangers. The working fluid was chosen to be

water to reduce the cost and time to change coils. The water side heat transfer and

pressure drop behavior inside the tubes is well established and fairly straight forward.

In contrast, the air side heat transfer and pressure drop behavior is the subject of

countless research studies and is quite complicated. Designers must rely on

experimental measurement of these characteristics. Often, air side performance is

proprietary. Finned-tube heat exchangers have been tested for at least the last 90 years

(Wilson 1915). During that time, advances in technology as well as the efforts of many

research engineers has increased the knowledge and availability of air side performance

data. The endeavors of D.G. Rich (1973, 1975), F.C. McQuiston (1978, 1981), R.L.

Webb (1986, 1998), and C.C. Wang (1998a, 1998b, 1998c, 1999, 2000a, 200b) serve as

milestones in the road of experimental performance measurement and correlation of

the air-side performance. This literature review will address a number of experimental

studies, experimental correlations, and data reduction publications which focused on

the airside performance of fin tube heat exchangers.

There is a wealth of heat transfer coefficient and friction factor data for finned tube heat

exchangers, which is often presented in correlation equation form. However, there are

also an infinite number of configurations for heat exchangers: e.g. transverse tube

spacing, longitudinal tube spacing, tube diameter, number of tube rows, fin spacing, fin

thickness, and fins type (plain, louvered, or other enhancement), to name a just few


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#

defining parameters. To further confuse the matter, experimental techniques and

methods of data reduction vary from one experimenter to the next. For instance, the

equilibrium criteria or the appropriate -NTU relationship for the given geometry are not

standardized. Also, nomenclature is not standardized and definitions for some

parameters are not readily available.

2.1. EXPERIMENTAL HEAT EXCHANGER STUDIES

Wilson (1915) performed an experimental work in which he developed a graphical

method of calculating the water-side heat transfer coefficient as a function of water

velocity. This method was included in McAdams (1954); it was also incorporated in the

study by Rich (1973). A modified form of Wilsons graphical method was used in this

present study.

Rich published two experimental studies. The first (1973) study focused on the effect

of fin spacing on heat transfer and friction performance of four-row finned-tube heat

exchangers, is discussed in section B because it contains heat transfer coefficient and

friction factor correlations. The second (1975) study focused on the effect of the

number of tube rows on heat transfer performance of heat exchangers, was a

continuation of his previous experimental work. In it Rich tested six coils which were

geometrically identical to his previous research with two exceptions: the number of

tube rows was varied from 1 to 6 and all of the coils had a fin pitch of 14.5 fins/in. The

coils were labeled on the basis of the number of tube rows. The tube diameter was

0.525 in. after expansion. Rich also performed a separate test on the four row coil,

measuring the temperature of the inlet and outlet of each row. The circuiting for this


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test was such that the tubes of each row were connected to form a separate circuit. This

allowed Rich to calculate the heat transfer coefficient for each row.

Rich concluded the following:

1. The average heat transfer coefficient for a deep coil can be higher or lower

than that of a shallow coil, depending on Reynolds number. Similarly the

heat transfer coefficients for a down stream row can be higher or lower than

for an upstream row depending on Reynolds number.

2. The addition of downstream rows has a negligible effect on heat transfer

from upstream rows.

3. At high Reynolds number, heat transfer coefficients of downstream rows are

higher than those of upstream rows; similarly average coefficients for deep

coils are higher than for shallow coils, at high Reynolds number.

4. At low Reynolds number, heat transfer coefficients for deep coils are

significantly lower than for shallow coils.

Wang et al. (1998c) performed a comparison study of eight finned-tube heat

exchangers. Table 1 shows the systematic variation of parameters that define the heat

exchangers studied. This study is similar to the variation of parameters in the present

study. The louver height and major louver pitch are not known. Wang et al. concluded

that the effect of fin pitch on heat transfer performance is negligible for four-row coils

having Re > 1,000 and that for Re < 1,000 heat transfer performance is highly Dc Dc

dependent on fin pitch. The upper Reynolds number range result is supported by

experimental data from Rich (1973), and from several studies performed by Wang et al.


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Wang et al. also concluded that the heat transfer performance of two-row configuration

increases with decrease of fin pitch. This publication discusses the choice of minimum

equilibrium criterion used as well as the method of data reduction. The minimum

equilibrium criterion chosen by Wang states that the heat transfer rate as calculated

from the tube-side and from the air side should be within 3%, and that the tube-side

resistance (evaluated as ) was less than 15% of the overall thermal resistance in allcases. The data reduction methods include: the use of the unmixed-unmixed cross-flow

- NTU relationship, the incorporation of the contact resistance (which was stated to be

less than 4%) into the air-side resistance, and the inclusion of entrance and exit pressure

losses in the calculation of friction factor.

! ' ())*+, "$ -

No. Fin

Pattern

Fin Pitch

mm(fins/in)

Nominal

Tube OD

mm (in)

P1 mm

[in]

P2 mm

[in]

Number

of

Rows

1 Plain 1.78(14.26) 7.0(0.273) 21[0.826] 12.7[0.5] 2

2 Plain 1.22(20.8) 7.0(0.273) 21[0.826] 12.7[0.5] 2

3 Plain 1.78(14.26) 7.0(0.273) 21[0.826] 12.7[0.5] 4

4 Plain 1.22(20.8) 7.0(0.273) 21[0.826] 12.7[0.5] 4

5 Louver 1.78(14.26) 7.0(0.273) 21[0.826] 12.7[0.5] 2

6 Louver 1.22(20.8) 7.0(0.273) 21[0.826] 12.7[0.5] 2

7 Louver 1.78(14.26) 7.0(0.273) 21[0.826] 12.7[0.5] 4

8 Louver 1.22(20.8) 7.0(0.273) 21[0.826] 12.7[0.5] 4


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2.2. EXPERIMENTAL HEAT EXCHANGER CORRELATIONS

Rich (1973) performed experimental work to determine the effect of fin spacing on heat

transfer and friction performance of multi-row fin-and-tube heat exchangers. Except for

the fin spacing all of the physical dimensions of the nine coils tested were identical.

Each coil had 4 rows of staggered tubes in the air flow direction. The tube diameter was

0.525 in. after expansion. The fin spacing varied from 0 to 20.6 fins per inch. Rich

developed a correlation for both heat transfer coefficient and friction factor using row

spacing as a basis for the Reynolds number. It should be noted that Richs correlations

are only valid for his geometry: there is only one tube spacing configuration and one

tube diameter.

Rich concluded the following:

1. The heat transfer coefficient is essentially independent of fin spacing between

3-21 fins per inch at a given mass velocity.

2. The pressure drop can be broken into two additive components, one due to the

tubes, form drag, and one due to the fins, skin drag.

3. The friction factor for the fins is independent of fin spacing for 3-14 fins per

inch at a given mass velocity.

4. For fin spacing of less than 14 fins per inch the friction factor for the fins varies

similar to that of developing flow over a plate where the boundary layer is

retriggered at each tube row rather than flow in a channel with fully developed

flow over the length of the coil width.


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Zukauskas and Ulinskas (1998) developed correlations for the pressure drop of a

staggered bank of bare tubes (no fins) in cross flow. These correlations give pressure

drop as a function of geometry over a range of Reynolds numbers. Geometric

parameters included in the analysis are: tube diameter, transverse tube spacing,

longitudinal tube spacing, and number of tube rows. Zukauskas and Ulinskas discuss

several possible variations that influence the pressure drop, including

1. Wall to bulk viscosity.

2. Property variations through the bank of tubes.

3.

Acceleration pressure drop arising from temperature rise.

McQuiston (1979) developed correlations for both Colburn j and Fanning friction

factors based on several sources of data. McQuistons goal was to make correlations

for wet surface mass transport. In order to do this, he first correlated dry surface

sensible heat transfer and friction data, which are the correlations investigated in this

present study. The j factors were correlated within 10% while the f factors were

correlated within 35%. The parametric range of McQuistons correlation is shown in

Table 2. The application of this correlation to compare with the coils in the present

study stretches the limits of the correlation; the tube spacing in the present study is 0.77

in. in the flow direction, compared to the 1 - 1.5 in. parametric range. All other

parameters are within their respective ranges.

! . ()/)+ " , "$ -

Fin Pattern Plain

Number of Rows 1 4


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Diameter OD (ft) [in] 0.031 0052 [0.375 0.625]

Fin Pitch (fins/ft) [fins/in] 96 168 [8 14]

Tube Spacing 0.083 0.125 [1 1.5]

Webb and Gray (1986) developed heat transfer coefficient and fin friction factor

correlations based on their own experimental data as well as other sources. Data from

16 heat exchanger configurations were used to develop the heat transfer coefficient

correlation; the resulting RMS error is 7.3%. Similarly, data from 18 heat exchanger

configurations were used to develop the fin friction factor correlation; the resulting

RMS error is 7.8%. A multiple regression technique was used with inputs being

geometric quantities: transverse tube spacing, longitudinal tube spacing, tube diameter,

number of tube rows, and fin spacing. Entrance and exit pressure drops were not

included in the fin friction factor. The parametric range of Webb and Greys correlation

is shown in Table 3. The application of this correlation to compare with the coils in the

present study stretches the limits of this correlation; the St/D parameter is 2.63 in the

present study compared to the applicable 1.97 2.55 range. All other parameters are

within their respective ranges.

! ' ()*%+ " , "$ -

Fin Pattern Plain

Number of Rows 1 8

St/D 1.97 2.55

S1/D 1.7 2.58

s/D 0.08 0.64


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Wang et al. (1999) performed a correlation for plain fin geometry based on several

sources of experimental data. Data from a total of 74 coil configurations were used to

develop the correlation. The heat transfer correlation can correlate 88.6% of the

database within 15%, and the friction correlation can correlate 85.1% of the database

within 15%. The parametric range of Wangs correlation is shown in Table 4. The

application of this correlation to compare with the coils in the present study is

appropriate; all of the parameters are within their respective ranges.

! ' ()))+ " , "$ -

Fin Pattern Plain

Number of Rows 1 6

Diameter OD mm(in) 0.635 12.7 (0.25 0.5)

Fin Pitch mm(fins/in) 1.19 8.7 (2.9 21.5)

P1mm(in) 17.7 31.75 (0.694 1.25)

P2mm(in) 12.4 27.5 (0.488 1.08)

Webb and Kang (1998) performed experimental work on eight enhanced fin shapes.

Nine different coil configurations were tested and used to develop the heat transfer

coefficient correlation. The heat transfer coefficient correlation can correlate 63% of

this database within 15%. The parametric range of Webb and Kangs correlation is

shown in Table 5. The application of this correlation to compare with the coils in the

present study stretches the limits of this correlation; the four-row coils in this study are

/D parameter is 2.053 which is outside of the 1.59 1.89 outside of the 1 2 row range,


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"

P1/D parameter is 0.127 (for the 21 fpi coils in the present study) which is range, and

the Pf/D outside the 0.134 - 0.252 range.

! # ' ())*+ 01 , "$ -

Fin Pattern Louvered

Number of Rows 1 2

Pt/D 2.32 2.80

P1/D 1.59 1.89

Pf/D 0.134 0.252

Wang et al. (1998b) performed a correlation for louvered fins based on several sources

of experimental data. Data from a total of 49 coil configurations were used to develop

the correlation. The heat transfer correlation can correlate 95.5% of the database within

15%, and the friction correlation can correlate 90.8% of the database within 15%.

The parametric range of Wangs correlation is shown in Table 6. The application of this

correlation to compare with the coils in the present study stretches the parameter is 0.77

in. which is outside the 0.5 0.75 in. limits of this correlation: the P 1 range and the

major louver pitch is 0.064 in. in the present study which is outside the 0.067 0.147

in. range. All other parameters are within their respective ranges.

! % ' ())*+ 01 , "$ -

Fin Pattern Louvered

Number of Rows 1 6

Diameter OD mm(in) 6.93 10.42 (0.27 0.41)


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*

Fin Pitch mm (fins/in) 1.21 2.49 (10.2 21.2)

Ptmm(in) 17.7 25.4 (0.694 1)

P1mm(in) 12.7 22 (0.5 0.75)

Louver height mm(in) 0.9 1.4 (0.03 0.055)

Major Louver Pitch mm(in) 1.7 3.75 (0.067 0.147)

Fin efficiency calculation is of the greatest importance in refrigerant-to-air heat

exchanger engineering, for the evaluation of the finned surface performance or for the

determination of the air-side heat transfer coefficient from experimental data. High

efficiency heat exchangers use enhanced fin geometry (louvered and slit fins) for which

the fin efficiency could be overestimated by usual formulations and more precisely

equivalent circular fin and conventional 1-D sector methods. Because the slits (or

louvers) alter the conduction path through the fin, the assumption of radial heat flow

pattern is no more valid.

Fin-and-tube heat exchangers are widely used in several domains such as heating,

ventilating, refrigeration and air conditioning systems. In practical application of air-to-

refrigerant heat exchangers, the dominant resistance is on the air-side and improving

the accuracy of the analysis of the air-side heat transfer is required by the growing

demand of high performance heat transfer surfaces. The fin performance is commonly

expressed in terms of heat transfer coefficient and fin efficiency, which is defined as

the ratio of the actual fin heat transfer rate to the heat transfer rate that would exist if all

the fin surface was at the base temperature. This case is the one providing the

maximum heat transfer rate because this corresponds to the maximum driving potential


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+

(temperature difference) for the convection heat transfer. Many experimental studies

available in the open literature have been performed in order to characterize the air-

side heat transfer performance of several type of fins used in finned tube heat

exchangers [1] [2] [3], and establish correlations which are used for design, rating and

modeling of heat exchangers. In order to obtain the heat transfer coefficient, it is

necessary to determine the fin efficiency [4]. What is observed in nearly all published

papers is that, whatever the fin type (plain, louvered, slit), the fin efficiency calculation

is always performed by analytical methods derived from circular fin analysis. When the

heat transfer coefficient h is considered separately from its corresponding fin

efficiency calculation (used for h measurement), error could be generated. If h is

always associated to the fin efficiency calculation that served for h measurement, there

is no possible error. The analytical circular fin analysis involves a number of

assumptions which need to be addressed.

These assumptions, known as ideal fin assumptions (attributed to Gardner [5]), are:

1. 1-D radial conduction,

2. steady state conditions,

3. radiative heat transfer negligible,

4. constant fin conductivity,

5. constant heat transfer coefficient over the entire fin,

6. the fin base temperature is assumed to be constant,

7. the thermal contact resistance between the prime surface and the fin is negligible,


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#

8. the surrounding fluid is assumed at constant temperature.

In the present study, the commonly used analytical methods for fin efficiency

calculation in finned tube heat exchangers are reviewed and compared. Among the

ideal fin assumptions, the first one should be carefully considered because the actual fin

geometry used in finned tube heat exchanger differs significantly from the plain

circular fin shape. In particular, for enhanced fin designs with louvers or slits, the fin

shape alters the conduction path within the fin. 2-D numerical models are used in order

to quantify the deviation generated by the 1-D assumption, depending on the fin

geometry and type

Fouling of heat exchangers used in heating, ventilating, and air conditioning (HVAC)

systems is important both because of their widespread use in commercial, residential

and industrial buildings and the energy and indoor air quality impacts that can result

from fouling. Fouling of indoor fin and tube heat exchangers, particularly air

conditioner evaporators, is especially important as space cooling in buildings is an

important contributor to overall energy use and peak electric demand. Furthermore, the

location of heat exchangers in HVAC systems means that if bioaerosols containing

bacteria, fungi, and viruses deposit on heat exchangers and remain viable, they can

quickly spread through an indoor space if they are re-entrained in the airflow.

Before discussing the details of particle deposition on air conditioner evaporators, it is

important to clearly describe the system being studied. The HVAC heat exchangers of

interest are designed to exchange energy between a refrigerant and an air stream that is

in turn used to condition an indoor space. Typical heat exchangers consist of horizontal

refrigerant tubes with attached thin vertical fins to increase heat transfer. A typical


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residential heat exchanger has two staggered sets of 0.95 cm (3/8 inch) copper

refrigerant tubes that run horizontally through vertical aluminum fins. Commercial and

industrial systems can have much larger tubes. Fin spacings range from 2.4 to 7.9

fins/cm (6 - 20 Fins/inch or FPI), with typical systems having 4.7 fins/cm (12 FPI). The

fins are approximately 100 m thick and are often corrugated to increase surface area

for heat transfer. Heat exchanger depth can vary, but typical residential and small

industrial and commercial heat exchangers are about 5 cm (2 inch) thick and are often

grouped together for larger capacities. Air velocities range from 1 to 5 m/s (200 - 1000

ft/min) in these systems.

2.3. APPLICATION TO THE PRESENT STUDY

This experimental study will incorporate and discuss methods and evaluate correlations

presented in this literature review. The discussion of the application of the reviewed

literature will progress from heat transfer to friction factor and finally to an overview of

the parametric ranges of the presented correlations. The present study incorporates

several methods and practices from the literature reviewed to help calculate the heat

transfer characteristics of heat exchangers, as the following will detail. A modified

Wilson method was used to determine the water side thermal resistance. This method

was also used by Rich (1973). Wang (1998c) opted for Gnielinskis (1976) correlation

to determine the waterside heat transfer coefficient. The use of Gnielinskis correlation

would eliminate the need for the modified Wilson test and therefore reduce the time to

acquire a full data set for a coil. However, an experimental method was preferred to a

correlation, because it more accurately characterizes the water side heat transfer

behavior. Thermal contact conductance between the fins and the tubes is not


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calculated, and is indirectly included in the air side heat transfer results. According to

Wang (1999) it is very difficult to accurately predict the contact resistance and hence,

most of the published works on the airside performance absorbed contact resistance

into the airside performance. Tubes in this study are mechanically expanded to an

interference fit of 0.004 in. to ensure minimal contact resistance. The present study uses

Schmidts (1949) approximation method to calculate the fin efficiency. This is

consistent with Wangs experimental methods.

Wang et al. (2000b) discuss the proper choice of -NTU correlation for a given

geometry. In the present study since the circuiting was serpentine each row was

analyzed independently and furthermore when NTU is less than 1.5 the effect of the

number of rows is insignificant and therefore all available -NTU correlations are

essentially equivalent and the cross-flow unmixed-unmixed -NTU correlation was

used.

The present study incorporates several methods and practices from the literature

reviewed to help calculate the friction characteristics of heat exchangers, as the

following will detail. The work of Rich (1973) was used as a guide to separate the

pressure drop into two additive superimposed components, one component due to the

tubes and one component due to the fins. All literature reviewed followed this

convention when calculating the fanning friction factor for the fins. Rich performed a

tube bundle pressure drop test. Wang opted to use a correlation from Kays and London

(1984) to approximate the pressure drop due to the bare tubes. Correlations from a

more recent study, Zukauskas and Ulinskas (1998), were used to approximate the

pressure drop due to the bare tubes in the present study. Webb also used Zukauskas

correlations to calculate the pressure drop due to the bare tubes. Kays and London


45/145

(1984) states that when the core pressure drop is calculated this takes into account the

tube row contraction and expansion (entrance, Kc, and exit, Ke) loss coefficients, thus

Kc and Ke will be zero. The flow acceleration due to the contraction ratio, , and the

density change is included in the fin friction factor formula.


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CHAPTER 3: PROJECT DESCRIPTION

A heat exchanger can be defined as any device that transfers heat from one fluid to

another or from or to a fluid and the environment. They may be direct contact type or

indirect contact type. Depending on the construction, heat exchangers can be classified

into Shell and tube Heat exchangers, Tube in tube heat exchangers, plate heat

exchangers etc. Another classification is based on the relative direction of flow of fluids

- Parallel Flow, Counter Flow and Cross Flow heat exchangers. In a heat exchanger,

there are two process streams; a hot stream and a cold stream. The heat transfer takes

place between these streams and is described by the enthalpy balance. The basic

equation on which the heat exchanger design is based is the general heat conduction

equation Q=U.A.(T1-T2) where U is the overall heat transfer coefficient, A is the

surface area for heat transfer and T1and T2are the temperature limits. For designing of

a heat exchanger the total heat transfer may be related with its governing parameters: U

(overall heat transfer coefficient), A (total surface area of heat transfer), and T 1and T2

(inlet and outlet fluid temperatures).

Under steady flow conditions and a constant temperature difference, the only

way of increasing heat transfer rates in a heat-exchanger is to increase the surface area.

One way of achieving this is through the use of extended or finned surfaces. Fins can

be either Longitudinal, Transverse or pin type. Usually in a double pipe heat exchanger,

longitudinal fins are used. This is because longitudinal fins provide passages for fluid

flow and has very little effect on the flow properties. Transverse fins, on the other hand

produce some amount of turbulence and a significant pressure loss thus altering the


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flow . Fins can also be of different cross sections-rectangular, parabolic or triangular.

Pin shaped fins are also used in a variety of applications.

3.1. PROBLEM DEFINITION

The project is done based on a longitudinally finned double pipe heat exchanger. The

flow type is taken as counterflow. The hot fluid flows in the inner tube called the pipe

and the cold fluid flows in counterflow in the shell side or annulus. The pressure drop

in the pipe is neglected. Data required to perform the design and optimization of the

above heat exchanger are

1. Pipe Inner Diameter

2. Pipe Outer Diameter

3. Shell Inner Diameter

4. Thickness of Fin

5. No. of Fins

6. Length of Pipe

7. Inlet Temperatures of both the Fluids

8. Mass flow Rate of Hot and Cold Fluids

9.

Fluid Properties of both the fluids at inlet temperature

10.Properties of the Material of Pipe and Fin

11.Fouling Resistances of both pipe and annulus


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3.2. COMPUTATIONAL SCHEME

Based on the above data provided the design, optimization and analysis of the finned

heat exchanger can be performed in the following ways:

1. The thermal design is performed manually for unfinned construction and at a

particular fin height randomly chosen.

2. A computer program is written using Turbo C++ to perform the thermal design

and performance evaluation at all fin heights possible for the given shell

diameter.

3. From the tabulated results from the program as well as graphs obtained, the

optimum fin height is determined.

4. The results are checked with that obtained in the manual calculations to confirm

the accuracy of the program.

5.

ANSYS is used to model the heat exchanger according to earlier said

specifications and the optimum fin height obtained from the program. An

unfinned model is also created. The FEM analysis is done on both of them and

the results are compared. The temperature profile of the heat exchangers can be

also obtained.

6. A heat exchanger with triangular fins is also modeled and the analysis and post-

processing is done. Then it is compared with the rectangular finned heat

exchanger.


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"

Figure 3.1. Cross Section View of Heate Exchanger in Problem Modelled in Auto-Cad


50/145

*

CHAPTER 4: PROJECT THEORY

In this Project we encounter the Design, Optimization and Analysis of a Double Pipe

Heat Exchanger. A variety of methodologies are available for this purpose. Even

though all these methods are the same, but for the different forms of equations, by

virtue of the fat that they all rise from the energy balance equation for the two fluids,

different charts and tables are convenient from different application points of view.

Some methods are convenient for rating (performance evaluation) of heat exchangers

while some other methods are convenient are more convenient for sizing (design of

heat exchangers). Some methods are suited when the heat capacity rates of each fluid

are known apriori while some others are more suited when they are not known

accurately. Due to the presence of a large number of different types of heat exchangers,

no one method can be rated as the best. Another issue which is not accounted for

properly is Fouling. The complex and unpredictable nature of this phenomenon has

probably attracted less number of investigators in this area, but from an industys point

of view this is a critical issue.

The simulation of Heat Exchangers is a fairly complex. The complex 3-dimensional

simulation is too complex to be carried out for a design purpose. Thus in most cases,

we are happy with the overall performance evaluation of the heat exchangers. For this

purpose, some simplifications are made to reduce the mathematical complexities of

modeling.


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+

The fluid streams are transversely mixed which gives a one-dimensional or

plug flow in all the types of heat exchangers except cross flow where a two

dimensional temperature field is assumed only if a stream is unmixed.

The heat transfer is primarily through the main surface, heat transfer through

baffle, tube sheet etc. is negligible.

Fluid leakage, bypass and flow misdistribution are neglected both in tubes and

shells.

The heat exchanger is assumed to be completely completely insulated from the

surroundings.

The fluid thermophysical properties and the heat transfer coefficient in the heat

exchanger are assumed to be constant over the entire length. However, at the

end of this chapter the effect of variable heat transfer coefficient and variable

(temperature dependent) heat capacity have been discussed.

4.1. SOME IMPORTANT DEFINITIONS

4.1.1. Overall Heat Transfer Coefficient:

In a heat exchanger, heat is transferred from one fluid to the other through the wall.

Hence between the two fluids, the thermal conductance comes from the heat transfer

coefficient of both the sides of the wall and the thermal conductance comes from the

heat transfer coefficient of both the sides of the wall and the thermal conductance of the

solid wall. For each fluid the thermal conductance is given by the product of the heat

transfer coefficient on that side and the corresponding heat transfer area. Thus for one

fluid inside and the the other outside of a tube the total heat transfer resistance can be

given by,


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#

R =

+

+

= + +

where Ai and Ao are the inside and outside areas of the tube, hiand hoare the respective

heat transfer coefficients, t is the wall thickness of the tube and k is the thermal

conductivity of the tube material.

However, practically one more factor is added to the thermal resistance to heat flow

known as fouling. Fouling is the phenomenon of deposition of material on the surfaces

from the fluids in the form of scales, layered sediments or biological agents. This

increases the fluids in the form of scales, layered sediments or biological agents. This

increases the resistance to the heat transfer. Under such cases the overall heat transfer

coefficient can be written,

= = + + + +

In tubular heat exchangers, it is customary to use the overall heat transfer

coefficient based on outside area of tubes Ao. Hence normally by U we mean Uo.

It should be mentioned here that if one or both sides of the heat exchanger are

finned the overall heat transfer coefficient is defined as

=

+

+

+

+

Where is the fin efficiency of the particular side. If a side is unfinned then = 1.


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4.1.2. The Temperature Differences

From Newtons law of cooling a heat transfer engineer is tempted to express the heat

transferred in the form of the product of three quantities :

A term similar to heat transfer coefficient

An area which defines the transfer coefficient

A temperature difference term

Locally the heat transfer rate is given by

dQ = U (Th Tc) dA

= U T dA

Where U is the local overall heat transfer coefficient and Thand Tcare the local bulk

temperatures of the fluids. Integrating this equation over the entire length of the heat

exchanger we get

! "#$" = ! %&

The mean overall heat transfer coefficient is defined as

Um= ! %&

Similarly we can define a mean temperatue difference (MTD) Tmas

#'(=

" ! "#$"


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Where Q is the total heat transferred from one fluid to the other in the heat exchanger.

By eliminating ! "#$" we get,

Q = UmATm

4.1.3. Capacity Ratio

Capacity Ratio is an important parameter in a heat exchanger. It is the ratio of heat

capacity of cold fluid to hot fluid or vice versa. Accordingly

R1= )*+,* )-+,-.

R2=)-+,- )*+,*.

R1 = 1 / R2

Where m is the mass flow rate and Cpis the specific heat rate. Suffixes h and c indicate

hot or cold fluid respectively

4.1.4. Temperature Effectiveness (P)

Temperature effectiveness tells about the performance of a heat exchanger with respect

to temperature alone. It is the ratio of temperature difference that one fluid undergoes to

the maximum temperature prevailing across the heat exchanger. Accordingly,

P1= (Tc,out Tc,in) / (Th,in - T c,in)

P1= (Th,in - T h,out)/ (Th,in - T c,in)


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4.1.5. Effectiveness of Heat Exchanger ()

The maximum amount of heat transfer (Qmax) that can occur between two streams in a

countercurrent heat exchanger is that for which the outlet temperature of the stream

with the lowest mCp reaches the inlet temperature of the other stream. This case is

illustrated schematically in the diagram. If the cold stream has a value of mCpgreater

than the hot stream then the maximum heat transfer occurs when the hot stream is

cooled to the inlet temperature of the cold stream. When mCp of the hot stream is

higher, the cold fluid will be heated to the inlet temperature of the hot stream. This is

because of the fact that heat balance should be maintained under such condition which

can be given by,

Qmax= (mCp) minTmax

where (mCp) min is the lower of the two for the respective streams and Tmax is the

difference between the stream inlet temperature.

Tmax = (Th,in Tc,in)

To achieve maximum heat transfer, an infinite surface area for the heat exchanger will

be required because the temperature difference approaches zero at the end of the heat

exchanger at which the end temperatures become equal.Effectiveness of a heat

exchanger is defined as the raio of actual to maximum heat transfer rates.

= ""/

Because Q= UmATm, we see that is given by


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=0(1#'(

2(34(56 7#'(89

It follows that

=:;2$


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The following are some of the commonly used analysis methods:

The LMTD-F method

The -NTU method

The P-NTU method

The -P method

F- -P-NTU method

P-R Combination method

As only the inlet temperatures of the streams and their specific heats are known ,the

analysis is carried out using Effectiveness NTU method.

4.3. THE -NTU METHOD

The LMTD approach to heat exchanger analysis is useful when the inlet and outlet

temperatures are known or easily deermined. The LMTD is then easily determined and

the heat flow can thus be obtained. When the inlet or exit temperatures are to be

evaluated, the analysis frequently involves an iterative procedure because of the

logarithmic function in LMTD. In these cases , the analysis is performed more easily

by utilizing a method based on the effectiveness of the heat exchanger.The

effectiveness method also offers many advantages for analyss of problems in which a

comparison between various types of heat exchangers is to be made.

The heat exchanger effectiveness is defined as

Effectiveness= = >

?/ ;@ >>


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The maximum possible heat transfer rate could be achieved in a counter flw heat

exchanger of infinita length.In such an exchange , one of the fluids would experience

the maximum possible temperature difference,

A< B C AD< B

If mcCpc


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"

NTUmin=

2:;7

Now , = "E(56= #'(2:;7#'(89= NTUmin #'(#'(89

Usually, NTUmin is defined as NTU.

For a Counter Flow Heat Exchanger, the effectiveness in terms of NTU is obtained as,

=F=94 G=H$I=2JKLMJKNO7PQR

F=2JKLMJKNO7/;G=H$I=2

JKLMJKNO7PQR

The value of this expression becomes maximum when NTU is infinity for the given

values of Cminand Cmax.

4.4. FINS OR EXTENDED SURFACES

In the study of heat transfer, a fin is a surface that extends from an object to increase

the rate of heat transfer to or from the environment by increasing convection. The

amount of conduction, convection, or radiation of an object determines the amount of

heat it transfers. Increasing the temperature difference between the object and the

environment, increasing the convection heat transfer coefficient, or increasing the

surface area of the object increases the heat transfer. Sometimes it is not economical or

it is not feasible to change the first two options. Adding a fin to an object, however,

increases the surface area and can sometimes be an economical solution to heat transfer

problems.


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*

The knowledge of temperature distribution along the fin is necessary for the proper

design of fins. The mathematical analysis for finding out the temperature distribution

and heat flow is discussed below-

4.4.1. Simplified Case

To create a simplified equation for the heat transfer of a fin, many assumptions need to

be made.

Assume:

1.

Steady state

2. Constant material properties (independent of temperature)

3. No heat transfer

4. No internal heat generation

5. One-dimensional conduction

6. Uniform cross-sectional area

7. Uniform convection across the surface area

The fin analysis can be carried out using the basic Fourier conduction equation.

Fouriers law states that

Qx= - kAc$/


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+

where Ac is the cross-sectional area of the differential element. Therefore the

conduction rate at x+dx can be expressed as

Hence, it can also be expressed as

.

Since the equation for heat flux is

then dqconvis equal to

whereAsis the surface area of the differential element.

By substitution it is found that

This is the general equation for convection from extended surfaces. Applying certain

boundary conditions will allow this equation to simplify.


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The a

wher

conve

The s

(x) =

wher

and

The c

four

The b

lengt

bove equati

P is the p

ction from

lution to th

C1emx

+ C2

onstants C1

ases have t

oundary co

of the fin.

n will simp

erimeter of

xtended sur

.

simplified

mx

.

and C2can

e boundar

dition at x

lify because

the cross-s

faces with c

equation is

be found by

condition

= L, howev

#

the area is

ctional are

onstant cros

applying t

(x= 0) =

er, is differ

onstant and

a. Thus, th

s-sectional

e proper bo

b for the te

nt for all o

general e

rea simplifi

undary con

mperature a

them, whe

uation for

es to

itions. All

t the base.

re L is the


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! !$ ! - 2$ &

4.4.2. Fin Performance

Fin performance can be described in different ways.

Fin effectiveness-It is the ratio of the fin heat transfer rate to the heat transfer

rate of the object if it had no fin. =S

S

=TFUIVKWX Y 86Z[PR

IVKWX YU86Z[P

where , m= \]^D_ = \^`_ , (for rectangular fin)

L= Height of fin

2`= Thickness of fin


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P=Fin perimeter

In this case, a non-dimensional number named as Biot Number is defined.

Biot number Bi=aT = b> > >c/> > >

where the thermal conductivity K refers to the conducting body.

The value of Biot number directly affects the fin effectiveness.

1. If Bi=1

Then,=1. So there is no use of putting the fins.

2.

If Bi>1

Then,


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f=S >

S > > > ;>>

If the heat lost from the end surfaces and edges of the fin is neglected , then,

f=86Z[

[ , where L= Height of fin.

Fin Uses

Fins are most commonly used in heat exchanging devices such as radiators in

cars and heat exchangers in power plants. They are also used in newer

technology such as hydrogen fuel cells. Nature has also taken advantage of the

phenomena of fins. The ears of jackrabbits act as fins to release heat from the

blood that flows through them.

4.5. HEAT TRANSFER COEFFICIENT

The heat transfer coefficient is used in calculating the convection heat transfer

between a moving fluid and a solid in thermodynamics. The heat transfer coefficient is

often calculated from the Nusselt numberThere are different heat transfer relations for

different liquids, flow regimes, and thermodynamic conditions. A common example

pertinent to many of the necessary power plant efficiency and thermal hydraulic

calculations is the Dittus-Boelter heat transfer correlation, valid for water in a circular

pipe with Reynolds numbers between 10 000 and 120 000 (in the turbulent pipe flow

range) and Prandtl numbers between 0.7 and 120.


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4.5.1.

The

transf

if jus

transf

direct

wher

Nusselt Nu

usselt num

r from a su

conduction

r when con

ion

L= chara

Area of th

mber

beris a di

rface that o

occurred.

vection tak

teristic len

body (use

ensionless

curs in a 'r

ypically it

s place.

th, which i

ul for more

umber that

al' situation

is used to

i

s simply V

complex sh

measures th

, compared

measure th

n perpend

lume of th

pes)

e enhancem

to the heat

enhancem

icular to

body divi

ent of heat

ransferred

nt of heat

the flow

ed by the


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kf= thermal conductivity of the "fluid"

h= convection heat transfer coefficient

4.5.2. Prandtl Number

The Prandtl number is a dimensionless number approximating the ratio of momentum

diffusivity (viscosity) and thermal diffusivity. It is named after Ludwig Prandtl.

It is defined as:

where:

is the kinematic viscosity, = / .

is the thermal diffusivity, = k / (cp).

Typical values for Prare:

around 0.7 for air and many other gases,

around 7 for water

around 71021

for Earth's mantle

between 100 and 40,000 for engine oil,

between 4 and 5 for R-12 refrigerant

around 0.015 for mercury


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"

For flow in pipes for instance, the characteristic length is the pipe diameter, if the cross

section is circular, or the hydraulic diameter, for a non-circular cross section.

Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and

is characterized by smooth, constant fluid motion, while turbulent flow, on the other

hand, occurs at high Reynolds numbers and is dominated by inertial forces, producing

random eddies, vortices and other flow fluctuations.

The transition between laminar and turbulent flow is often indicated by a critical

Reynolds number (Recrit), which depends on the exact flow configuration and must be

determined experimentally. Within a certain range around this point there is a region of

gradual transition where the flow is neither fully laminar nor fully turbulent, and

predictions of fluid behaviour can be difficult. For example, within circular pipes the

critical Reynolds number is generally accepted to be 2300, where the Reynolds number

is based on the pipe diameter and the mean velocity vs within the pipe, but engineers

will avoid any pipe configuration that falls within the range of Reynolds numbers from

about 2000 to 3000 to ensure that the flow is either laminar or turbulent.

For flow over a flat plate, the characteristic length is the length of the plate and the

characteristic velocity is the free stream velocity. In a boundary layer over a flat plate

the local regime of the flow is determined by the Reynolds number based on the

distance measured from the leading edge of the plate. In this case, the tr

optimization and analysis of tube-in-tube heat exchanger with fins-libre

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