analyses of heat exhangers-2011 - copy

7/29/2019 Analyses of Heat Exhangers-2011 - Copy

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Heat Exchangers

A heat exchanger is used to exchange heat between twofluids of different temperatures, which are separated by a

solid wall.

Applications in heating and air conditioning, powerproduction, waste heat recovery, chemical processing,

food processing, sterilization in bio-processes.

Heat exchangers are classified according to flowarrangement and type of construction.

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HEX Classification According to Flow Arrangement


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double pipe heat exchanger


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Configuration of an induced-draft air-cooled

heat exchanger


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Task

Heat Exchanger Sizing

Given: inlet and outlet temperatures and flow rates of

the two fluids.

Find: Surface area of heat exchanger

Heat Exchanger Rating

Given: flow rates, inlet temperatures and surface area of

heat exchanger.Find: heat transfer rate, fluid outlet temperatures.

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Heat Exchanger Analysis

In a two-fluid heat exchanger, consider the hot and cold fluids separately:

)(

)(

,,,

,,,

icoccpcc

ohihhphh

TTcmq

TTcmq

lmTUAq and

The usual design goal is to determine the required area A for a heating

duty q

Need to determine U and Tlm

(1&2) (3)

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Tubular geometry

For the unfinned and clean tubular HEX, the

overall heat transfer coefficient is given by

1 1ln( / )1 1

2

o o i i

t o i

i i o o

U A U AR r r

h A kL h A


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Fouling

For the HEX whose walls are fouled by deposit

formation on both the inside and outside surfaces,

the total thermal resistance can be expressed as

Rw : wall resistance

Rf : fouling factor / unit fouling resistance

1 1 1 1 1fi fot w

o o i i i i i o o o

R RR R

UA U A U A h A A A h A


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U based on outside surface rea

U is usually based on the outer area. U based on

the outside surface area of the wall for an unfinned,tubular HEX is given by

If fins are present on the wall(s), fin efficiency andfin area should be considered in calculating U.

1

ln( )1 1o

o o o o ifi fo

i i i o

U

r r r r r R Rr h r k h


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Orders of Magnitude for h [w/m2K]

Gases (natural convection) 3-25

Engine oil (natural convection) 30-60

Flowing liquids (nonmetal) 100-10,000

Flowing liquid metals 5000-250,000

Film boiling 300-400

Dropwise condensation 60,000-120,000


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Tlm: 1. Parallel-Flow Heat Exchangers

where

lmTUAq

)/ln( 12

12

TT

TTTlm

ocoh

icih

TTT

TTT

,,2

,,1

T1 T2

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Tlm: 2. Counter-Flow Heat Exchangers

where

lmTUAq

)/ln( 12

12

TT

TTTlm

icoh

ocih

TTT

TTT

,,2

,,1

T1 T2

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Overall Heat Transfer Coefficient

For tubular heat exchangers we must take into account the conductionresistance in the wall and convection resistances of the fluids at the inner

and outer tube surfaces.

kL

DDR

AhR

AhUA

iocond

oo

cond

ii

2

)/ln(

111

where inner tube surface

outer tube surface LDA

LDA

oo

ii

(4)

ooii AUAUUA

111

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Example 1

A counterflow, concentric tube heat exchanger is used to cool the

lubricating oil for a large industrial gas turbine engine. The flow rate ofcooling water through the inner tube (Di=25 mm) is 0.2 kg/s, while the

flow rate of oil through the outer annulus (Do=45 mm) is 0.1 kg/s. The

oil and water enter at temperatures of 100 and 30C respectively. How

long must the tube be made if the outlet temperature of the oil is to be

60C?

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Heat Exchangers 15

Table 1 Nusselt number for fully developed

laminar low in an annulus with one surfaceisothermal and the other adiabatic


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Shell-and-Tube Heat Exchangers

Baffles are used to

establish a cross-flow and

to induce turbulent mixing

of the shell-side fluid, both

of which enhance

convection.

The number of tube and

shell passes may be variedOne Shell Pass and One Tube Pass

One Shell Pass,

Two Tube Passes

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Multipass and Cross-Flow Heat Exchangers

To account for complex flow conditions in multipass, shell and tubeand cross-flow heat exchangers, the log-mean temperature difference

can be modified:

CFlmlm TFT ,

where F=correction factor, to be determined from

the next figure in terms of parameters P & R .

: Logarithmic mean temperature

difference for counter flowCFlm

T,

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Correction Factor F

where t is the tube-

side fluid

temperature

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Heat Exchangers 19

Example

A shell-and-tube heat exchanger must be designed to heat 2.5 kg/s of water

from 15 to 85C. The heating is to be accomplished by passing hot engine

oil, which is available at 160C, through the shell side of the exchanger. The

oil is known to provide an average convection coefficient of ho=400 W/m2.K

on the outside of the tubes. Ten tubes pass the water through the shell.

Each tube is thin walled, of diameter D=25 mm, and makes eight passes

through the shell. If the oil leaves the exchanger at 100C, what is the flow

rate? How long must the tubes be to accomplish the desired heating?

Eff ti N b f T f U it ( NTU)


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Effectiveness-Number of Transfer Units (e-NTU)for HEX Analysis

When exit temperatures are unknown, a trial anderror procedure may be needed. Instead, the

method of number of transfer units (NTU) based

on HEX effectiveness may be used.

The e - NTU method is based on the fact that theinlet or exit temperature differences of a heat

exchanger are a function of UA/Ch and Ch/Cc.

Where, Ch = (mCP)h and Cc =(mCP)c

The HEX heat transfer equations may be written

in dimensionless form resulting in some

dimensionless groups.


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Dimensionless groups

1. Heat capacity rate ratio: , C* 1

2. HEX heat transfer effectiveness:

eis the ratio of the actual heat transfer rate in a HEXto the thermodynamically limited maximum possibleheat transfer rate if an infinite heat transfer areawere available in a counter flow HEX.

min

max

CCC

max

Q

Qe


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The actual heat transfer is obtained either by the

energy given off by the hot fluid or the energyreceived by the cold fluid

If Ch> Cc, then (Th1-Th2) < (Tc2-Tc1)If Ch< Cc, then (Th1-Th2) > (Tc2-Tc1)

The above equations are valid for CF and PF.The fluid that might undergo the maximumtemperature difference is the fluid having theminimum heat capacity rate Cmin.

1 2 2 1( ) ( ) ( ) ( )p h h h p c c cQ mc T T mc T T


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Maximum heat transfer:

or

Therefore, HEX effectiveness can be written as

The above equation is valid for all heat

exchanger flow arrangements. The value of eranges between 0 and 1.

For a given e and Qmax, the actual HT rate is

Q =e(mcp)min(Th1-Tc1)

max 1 1( ) ( ) if p c h c c hQ mc T T C C

max 1 1( ) ( ) if p h h c h cQ mc T T C C

1 2 2 1

min 1 1 min 1 1

( ) ( )( ) ( )

h h h c c c

h c h c

C T T C T T C T T C T T

e


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3. Number of Transfer Units:

The third dimensionless number NTU shows the

nondimensional heat transfer size of the HEX

min min

1NTUA

AU UdAC C


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e-NTU Expressions for different types of HEX arrangements

Type of HEX e(NTU,C*) NTU(e,C*)

Counterflow

Parallel Flow

Cross flow, Cmin

mixed and Cmax

unmixed

Cross flow, Cmax

mixed and Cmin

unmixed

1 to 2 shell-and-

tube HEX

NTU1exp1NTU1exp1

CC

Ce

e

e

1

1ln

1

1NTU C

C

NTU1exp11

1

CC

e

C

C NTUexp1exp1e

NTUexp1exp11

C

C

e

2/121NTUexp1

2/121NTUexp1

2/1211

2

C

C

CC

e

CC

11ln

1

1NTU e

e 1ln1ln1

NTU C

C

C

C

e1ln1

1-lnNTU

2/1

2112

2/12112

ln2/12

1

1NTU

CC

CC

Ce

e


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Example 2.9

A two-pass tube, baffled single-pass shell, shell-and-tubeHEX is used as an oil cooler. Cooling water flows

through the tubes at 20oC at a flow rate of 4.082 kg/s.

Engine oil enters the shell side at a flow rate of 10 kg/s.

The inlet and outlet temperatures of oil are 90oC and60oC, respectively. Determine the surface area of the

HEX using both the LMTD and e-NTU methods, if the

overall heat transfer coefficient based on the outside tube

area is 262 W/m2K. The specific heats of water and oil

are 4179 J/kgK and 2118 J/kgK, respectively.


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Heat Exchanger Sizing

If inlet temperatures, one of the outlettemperatures and mass flow rates are known, we

can use LMTD method for sizing problem:

1. Calculate Q and the unknown temperature

2. Calculate LMTD and obtain F if necessary

3. Calculate U

4. Determine A from A=Q/(UFTlm,cf)


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Heat Exchanger Rating

For an available heat exchanger (size, massflow rates, inlet temperatures and materials areknown) using e-NTU method we can rate theheat exchanger:

1. Calculate C*=Cmin/Cmax and NTU=UA/Cmin2. Determine e from appropriate charts ore-NTU

equations

3. Calculate Q=e Cmin(Th1-Tc1)

4. Calculate outlet temperatures


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Sizing Using e-NTU method1. Calculate e using Cmin, Cmax and temperatures2. Calculate C*=Cmin/Cmax

3. Calculate U

4. Determine NTU from charts or equations5. When NTU is known calculate heat transfer area

from A=(CminNTU)/U

analyses of heat exhangers-2011 - copy

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