heat exchanger

DKK1493 HEAT TRANSFERDKK1493 HEAT TRANSFER

CHAPTER 4CHAPTER 4

HEAT EXCHANGERHEAT EXCHANGER

Heat exchanger type The Heat Exchanger Analysis: Log Mean

Temperature Difference (LMTD)

CONTENTSCONTENTS

It is expected that students will be able:to classify different types of heat exchangers to calculate the log mean temperature difference (LMTD) and determine correction factor for multi-passes heat exchanger.

TOPIC OUTCOMESTOPIC OUTCOMES

TYPE OF HEAT EXCHANGER

Double-pipe heat exchanger

Shell and Tube Heat Exchanger

1 shell pass I tube pass

(1-1 exchanger)

1 shell pass 2 tube passes

(1-2 exchanger)

Shell and tube exchangerShell inlet

Shell outlet

Tube inlet

Tube outlet

Shell inlet

Tube inlet

Tube outlet

Shell outlet

Cross-Flow Heat exchangers

One fluid mixed,one fluid unmixed

Both fluids unmixed

Gas flowGas flow

LOG MEAN TEMPERATURE DIFFERENCE (LMTD)

1'T

2'T1T

2T

Distance

T1

2T

Countercurrent

1T

1'T

2T

2'T

T2

T1

Distance

Co-current

T1

T’2

T2

T’1

T1

T’2

T2

T’1

Log mean temperature difference

Energy Balances and Heat Transfer Rate

Energy balance on hot fluid:

Energy balance on cool fluid:

Heat transfer rate:

ohhihp TTcmq

cicocp TTcmq

mTUAq

This Tlm holds for a double-pipe heat exchanger and 1-1 exchanger with 1 shell pass and 1 tube pass in parallel or counter-flow.

When the hot and cold fluids in a heat exchanger are in true counter-current flow or in co-current (parallel) flow,

LOG MEAN TEMPERATURE DIFFERENCE (LMTD)

2

1

21

1

2

12

lnlnTT

TT

TT

TTTlm

lmTUAq

Example

An oil which has a cpm = 2.30 kJ/kg.K is being cooled in a heat exchanger from 371.9 K to 349.7 K and flows inside the tube at a rate of 3630 kg/h. A flow of water enters at 288.6 K for cooling out and flows outside the tube at 319.1 K. Calculate the heat-transfer area if the U = 340 W/m2.K for each counter-current and co-current flow. Discuss your result.

(Ans: 2.66 m2; 2.87 m2)

For multiple-pass heat exchanger, the correction factor FT used to calculate the true mean temperature drop. (under assumption of counter-flow conditions)

Two dimensionless ratios are used as follows:

For counter-flow:

Correct mean temperature:

Heat transfer rate:

LOG MEAN TEMPERATURE DIFFERENCE (LMTD) CORRECTION FACTORS

ciho

cohi

cihocohilm

TTTT

TTTTT

ln

)(

Tlmm FTT

cico

hohi

TT

TTZ

cihi

cico

TT

TTY

moomii TAUTAUq

Correction factor FT for shell and tube heat exchanger with one shell pass and any multiple of two tube passes (2, 4, 6, etc, tube passes)

Correction factor FT for shell and tube heat exchanger with two shell pass and any multiple of four tube passes (4, 8, 12, etc, tube passes)

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 2.52 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 a 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

waterkg/s 2.52

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

1T

2T

hiTC 15.61 o

C 9.48 ohoT

C 1.21 ociT

coTC 4.54 o

hot water

waterkg/s 2.52

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

PROBLEM 4.9-2: Cooling Oil by Water in an Exchanger

Oil flowing at the rate of 5.04 kg/s (cpm = 2.09 kJ/kg.K) is cooled in a 1-2 heat exchanger from 366.5 K to 344.3 K by 2.02 kg/s of water entering at 283.2 K. The overall heat transfer coefficient Uo is 340 w/m2.K. Calculate the area required. (Hint: A heat balance must first be made to determine the outlet water temperature)