BKF2422 HEAT TRANSFERBKF2422 HEAT TRANSFERCHAPTER 5CHAPTER 5

HEAT EXCHANGERHEAT EXCHANGER

Shell and tube exchangerShell inlet

Shell outlet

Tube inlet

Tube outlet

Shell inlet

Tube inlet

Tube outlet

Shell outlet

Cross-flow heat exchanger

2

1

21

lnT

T

TTTlm

flow, (parallel)cocurrent in or

flowrent countercur in true areexchanger heat ain fluids cold andhot When the

wcounterfloor parallelin pass tube1 and pass

shell 1with exchanger 1-1 andexchanger heat pipe-double afor holds This lmT

cihi

cico

TT

TTY

cico

hohi

TT

TTZ

:follows as used are ratios essdimensionl Two

drop. raturemean tempe true

thecalculate toused factor correction theexchanger,heat pass-multipleFor TF

Tlmm FTT

ciho

cohi

cihocohilm

TT

TT

TTTTT

ln

EXAMPLE 4.9-1 Temperature Correction Factor for a Heat Exchanger

A 1-2 heat exchanger containing one shell pass and two tubes passes heats 5.52 kg/s of water from 21.1 to 54.4oC by using hot water under pressure entering at 115.6 and leaving at 48.9oC. The outside surface area of the tubes in the exchanger is Ao = 9.30 m2

a) Calculate the mean temperature difference ΔTm in the exchanger and the overall heat-transfer coefficient Uo

b) For the same temperature but using 1 2-4 exchanger, what would be the ΔTm

1T

2T

hiTC 15.61 o

C 9.48 ohoT

C 1.21 ociT

coTC 4.54 o

hot water

kJ/kg.K 187.4waterpc

ExchangerHeat 21(a)

352.01.216.115

1.214.54

cihi

cico

TT

TTY

00.21.214.54

9.486.115

cico

hohi

TT

TTZ

K 3.42

1.219.484.546.115

ln

1.219.484.546.115

ln2

1

21

TT

TTTlm

K 31.3C 31.3

)74.0(3.42 o

Tlmm FTT

0.74 4a,-4.9 Fig theFrom TF

(b) ExchangerHeat 42

W348200

)1.214.54)(4187(52.2

cicopm TTcmq

.K W/m1196)3.31(30.9

348200 2

mo

o TA

qU

94.0 4b,-4.9 Fig theFrom TF

K 39.8C 39.8

)94.0(3.42 o

Tlmm FTT

max

fluid min

maxferheat trans possiblemax

ferheat trans actual

T

T

q

qactual

maxminminminmax TCTTCTTcmq ichiichip

ichipactual TTcmq min

minmin where pcmC

,

min

having fluid = fluidmin pcm

EXAMPLE 4.9-2 Effectiveness of Heat Exchanger

Water flowing at rate of 0.667 kg/s enters a countercurrent heat exchanger at 308 K and is heated by an oil stream entering at 383 k at a rate of 2.85 kg/s (cp = 1.89 kJ/kg.K). The overall U = 300 W/m2.K and the area A = 15.0 m2. Calculate the heat-transfer rate and the exit water temperature.

1T

2T

hiTK 833

hoT

K 308ciT

coT

kg/s 85.2 oil, m

kg/s 677.0 water, m

2

2

m 15

.K W/m300

kJ/kg.K 187.4

kJ/kg.K 89.1

A

U

c

c

waterp

oilp

W/K5387)1890(85.2

W/K7.2792)4187(667.0

max

min

oil

water

p

CC

CC

cmC

5.05387

7.2792

max

min C

C

6.12792

)15(300 NTU

min

C

UA

0.71 7a-4.9 Fig. Using

W148900

)308383)(2792(71.0 min

ichiactual TTCq

k 3.361

)308)(4187(667.0148900

max

co

co

waterp

T

T

Tcmq

coho TTq , , determine To

NTU &/ Calculate 1. maxmin CC

graph from Obtain 2.

q Calculate 3.

cp

cico

hphiho

cm

qTT

cm

qTT

Calculate 4.

Calculate 1.

, if (i) min cCC

cihic

hohih

TTC

TTC

, if (ii) min hCC

cihih

cicoc

TTC

TTC

maxmin / Calculate 2. CC

U

CA minNTU

.4

:A determine To

NTUObtain 3.

Example

1T

2T

hiTC 09 o

C 40 ohoT

C 19 ociT

coTC 90 o

kg/s 85.2 oil, m

kg/s 677.0 water, m

?

.K W/m502

kJ/kg.K 180.4

kJ/kg.K 1.2

2

A

U

c

c

waterp

oilp

ExchangerHeat 42

min

max

W/K3150)2100(5.1

W/K4180)4180(1

CC

CC

cmC

h

c

p

75.03150

4180

max

min C

C

7.0

)1990(3150

)4090(3150

cihic

hohih

TTC

TTC

2NTU 7-4.9 Fig. Using

2

min

m 2.25

3150

2502

NTU

A

A

C

UA

Surface not clean – additional resistances

fofiiwalloiii RRRRRARA

U

11

odoidiii

io

ooi

i

AhAhAhkL

rr

AhA

U111

2

)/ln(1

1

tube theof inside for thet coefficien fouling where dih

tube theof outside for thet coefficien fouling doh

)( when0 iowall rrR ＜＜ small & wallk ＞＞ large.

Example – Fouling Factors

Stainless steel double-pipe heat exchanger

W/m.K1.15k

? t,coefficienfer heat trans overall Determine

1.K/Wm 0.0001de)side(outsi shellfactor Fouling

1.K/Wm 0.0004e)side(insid efactor tub Fouling

.KW/m1200

.K W/m800

m 1

cm 2.3

cm 9.1

cm 5.1

2

2

2

2

outer tube

oi

do

di

o

i

o

i

& UU

h

h

h

h

L

D

D

D

.K W/m1200 2oh

m 1

cm 1.9

cm 3.2.K W/m800 2ihcm 1.5

22

22

m 0597.0)1)(109.1(

m 0470.0)1)(105.1(

LDA

LDA

oo

ii

053157.0

0597.0

0001.0

0471.0

0004.0

)0471.0(800

1

)1)(1.15(2

)5.1/9.1ln(

)0597.0(1200

1

111

2

)/ln(1

odoidiii

io

oo

fofiiwallo

AhAhAhkL

rr

Ah

RRRRRR

.K W/m4.399

)053157.0(0471.0

1

1

1

2

RA

RRRRRAU

i

fofiiwalloii

.K W/m11.315

)053157.0(0597.0

1

1

2

RAU

oo