March 1, 2002 1

(1) Heat Exchanger Types

(2) Heat Exchanger Analysis Methods• Overall Heat Transfer Coefficient

»fouling, enhanced surfaces

• LMTD Method

• Effectiveness-NTU Method

(3) Homework #4

Outline

March 1, 2002 2

Introduction• Heat exchangers are devices that provide the flow

of thermal energy between two or more fluids at different temperatures.

• Used in wide range of applications

• Classified according to:• Recuperators/Regenerators

• Transfer processes: direct and indirect contact

• Construction Geometry: tubes, plates, extended surfaces

• Heat Transfer Mechanisms: single and two phase

• Flow arrangements: parallel, counter, cross-flow

March 1, 2002 3

HX Classifications

March 1, 2002 4

HX Classifications

March 1, 2002 5

Concentric tube (double piped)Heat Exchanger Types

March 1, 2002 6

Concentric tube (double piped)• One pipe is placed concentrically within the

diameter of a larger pipe• Parallel flow versus counter flow

Heat Exchanger Types

Fluid A

Fluid B

March 1, 2002 7

Concentric tube (double piped)• used when small heat transfer areas are

required (up to 50 m2)

• used with high P fluids

• easy to clean (fouling)

• bulky and expensive per unit heat transfer area

• Flexible, low installation cost, simple construction.

Heat Exchanger Types

March 1, 2002 8

Shell and TubeHeat Exchanger Types

March 1, 2002 9

Shell and Tube• most versatile (used in process industries,

power stations, steam generators, AC and refrigeration systems)

• large heat transfer area to volume/weight ratio

• easily cleaned

Heat Exchanger Types

March 1, 2002 10

Compact Heat Exchangers• generally used in gas flow applications

• surface density > 700 m2/m3

• the surface area is increased by the use of fins

• plate fin or tube fin geometry

Heat Exchanger Types

March 1, 2002 11

Compact Heat

Exchangers

Heat Exchanger Types

March 1, 2002 12

Cross Flow• finned versus unfinned

• mixed versus unmixed

Heat Exchanger Types

March 1, 2002 13

Heat Exchanger Types

March 1, 2002 14

Heat Exchanger Types

March 1, 2002 15

Heat Exchanger Applications

March 1, 2002 16

Heat Exchanger Analysis

• Overall Heat Transfer Coefficient

• LMTD

• Effectiveness-NTU

March 1, 2002 17

Overall Heat Transfer Coefficient

hoho

hfw

co

cf

co hAA

RR

A

R

hAUA )(

1

)()()(

11 ,,

The overall coefficient is used to analyze heat ex-changers. It contains the effect of hot and cold side convection, conduction as well as fouling and fins.

factor fouling fR

March 1, 2002 18

Fouling Factors

Heat exchanger surfaces are subject to fouling by fluid impurities, rust formation, or reactions between the fluid and the wall.

factor fouling fR

March 1, 2002 19

Enhanced Surfaces

Fins are often added to the heat exchange surfaces to enhance the heat transfer by increasing the surface area. The overall surface efficiency is:

)(

)1(1

TThAQ

A

A

bo

ff

o

March 1, 2002 20

Enhanced Surfaces

March 1, 2002 21

Log-Mean Temperature DifferenceNeed to relate the total heat transfer rate to inlet and outlet fluid temperatures. Apply energy balance:

)()(

)()(

,,,,,

,,,,,

ociccpcocicc

ohihhphohihh

TTcmiimQ

TTcmiimQ

March 1, 2002 22

Log-Mean Temperature DifferenceWe can also relate the total heat transfer rate to the temperature difference between the hot and cold fluids.

LM

ch

TUAQ

TTTlet

The log mean temperature difference depends on the heat exchanger configuration.

March 1, 2002 23

Apply energy balance:Assume:• insulated• no axial conduction• PE, KE negligible

• Cp constant

• U constant

LMTD Parallel-Flow HX

March 1, 2002 24

LMTD Parallel-Flow HX

)12

12

,

,

/ln(

:get toIntegrate

TT

TTUAQ

TTTTdAUdQ

dTCdTcmdQ

dTCdTcmdQ

ch

ccccpc

hhhhph

March 1, 2002 25

LMTD Parallel-Flow HX

ocohch

icihch

LMLM

TTTTT

TTTTT

TT

TTTTUAQ

,,2,2,2

,,1,1,1

)12

12

:Flow Parallelfor Where

/ln(

March 1, 2002 26

LMTD Counter-Flow HX

Tlm,CF > Tlm,PF

FOR SAME U:

ACF < APF

March 1, 2002 27

LMTD Counter-Flow HX

icohch

ocihch

LMLM

TTTTT

TTTTT

TT

TTTTUAQ

,,2,2,2

,,1,1,1

)12

12

:FlowCounter for Where

/ln(

Tlm,CF > Tlm,PF FOR SAME U: ACF < APF

March 1, 2002 28

LMTD- Multi-Pass and Cross-Flow

CFLMLMLM TFTTUAQ ,

Apply a correction factor to obtain LMTD

t: Tube Side

March 1, 2002 29

LMTD MethodSIZING PROBLEMS:• Calculate Q and the unknown outlet temperature.

• Calculate DTlm and obtain the correction factor (F) if necessary

• Calculate the overall heat transfer coefficient.• Determine A.

The LMTD method is not as easy to use for performance analysis….

March 1, 2002 30

The Effectiveness-NTU Method• If the inlet temperatures are unknown then

the LMTD method requires iteration.

• Preferable to use the -NTU method under these conditions.

• Define Qmax

for Cc < Ch Qmax = Cc(Th,i - Tc,i)

for Ch < Cc Qmax = Ch(Th,i - Tc,i)

or Qmax = Cmin(Th,i - Tc,i)

March 1, 2002 31

The Effectiveness-NTU Method• Now define the heat exchanger effectiveness, .

• The effectiveness is by definition between 0 & 1

• The actual heat transfer rate is:

Q = Cmin(Th,i - Tc,i)

)(

)(

)(

)(

,,min

,,

,,min

,,

max icih

icocc

icih

ohihh

TTC

TTC

TTC

TTC

q

q

March 1, 2002 32

The Effectiveness-NTU Method• For any heat exchanger:

f(NTU,Cmin/Cmax)

• NTU (number of transfer units) designates the nondimensional heat transfer size of the heat exchanger:

minC

UANTU

March 1, 2002 33

The Effectiveness-NTU Method

March 1, 2002 34

The Effectiveness-NTU MethodPERFORMANCE ANALYSIS

• Calculate the capacity ratio Cr = Cmin/Cmax and NTU = UA/Cmin from input data

• Determine the effectiveness from the appropriate charts or -NTU equations for the given heat exchanger and specified flow arrangement.

• When is known, calculate the total heat transfer rate

• Calculate the outlet temperature.

March 1, 2002 35

The Effectiveness-NTU MethodSIZING ANALYSIS

• When the outlet and inlet temperatures are known, calculate

• Calculate the capacity ratio Cr = Cmin/Cmax

• Calculate the overall heat transfer coefficient, U

• When and C and the flow arrangement are known, determine NTU from the -NTU equations.

• When NTU is known, calculate the total heat transfer surface area.

March 1, 2002 36

Homework Number 4COMPLETE PARTs 1&2 BEFORE CLASS ON THURSDAY. WE WILL USE CLASS/LAB TIME ON Tuesday TO WORK ON PARTS 3 and 4.Part 1:Review Chapter 11 of Incropera and Dewitt. Work through Example Problems 11.3, 11.4, 11.5.Part 2:To ventilate a factory building, 5 kg/s of factory air at a temperature of 27 oC is exhausted and an identical flow rate of outdoor air at a temperature of -12 oC is introduced to take its place. To recover some of the heat of the exhaust air, heat exchangers are placed in the exhaust and ventilation air ducts and 2 kg/s of ethylene glycol is pumped between the two heat exchangers. The UA value of both of these crossflow heat exchangers is 6.33 kW/K. What is the temperature of the air entering the factory?

March 1, 2002 37

Homework Number 4Part 3:Calculate the UA value for the cross flow heat exchanger specified above. The heat exchanger is 1m high by 1 m wide by 1 m long (in flow direction) and contains a tube bank heat transfer surface. The ethylene glycol flows through the tubes and the air flow around them (i.e. figure 11.2B in Incropera and Dewitt). The tubes are made of 1" diameter thin walled copper and are mounted in an aligned pattern (3 inches apart center to center – Review tube bank heat transfer data in Chapter 7 of Incropera and Dewitt). Use the data for internal tube heat transfer coefficient given in the Project 4 technical specifications.

Part 4:Calculate the pressure drop for the ethylene glycol and the air. Use the data for ethylene glycol friction factor given in the Project 4 technical specifications.