BIRLA VISHVAKARMA MAHAVIDYALAYA

VALLABH VIDYANAGARDept.-Production engineering

Subject:-Engineering thermodynamics & heat transfer

Faculty name:-Dr. Manish mehta

Prepared by….140080125021- Brijesh patel140080125022- Dhruv patel140080125023- Hardik patel140080125024- Harshil patel

Group no.14

HEAT EXCHANGERS• Types of heat exchangers:

1. Double pipe heat exchanger2. Shell and tube exchanger3. Plate-type exchanger4. Cross flow exchanger

• The function of a heat exchanger is to increase the temperature of a cooler fluid and decrease that of a hotter fluid.

1. Double pipe heat exchanger• The simplest configuration in fig.• One fluid flow through the inside pipe, and the second fluid

flows through the annular space between the outside and the inside pipe.

• The fluid can be in co-current or countercurrent flow.• Useful for small flow rates and when not more than 100 – 150

ft2 of surface is required.

2. Shell and Tube Exchanger• The most important type of exchanger in use in oil refineries

and larger chemical processes and is suited for higher-pressure applications.

• Useful for larger flow rates as compared to double pipe heat exchanger.

• The simplest configuration: 1-1 counterflow exchanger (one shell pass and one tube pass) – refer to Figure 1.2.

• consists of a shell (a large pressure vessel) with a bundle of tubes inside it.

• One fluid runs through the tubes, and another fluid flows over the tubes (through the shell) to transfer heat between the two fluids.

• The cold fluid enters and flow inside through all the tubes in parallel in one pass

• The hot fluid enters at the other end and flow counterflow across the outside the tubes in the shell side.

• Cross-baffles – increase the shell side heat transfer coefficient

Fig 1.2 Shell and tube heat exchanger (1 shell pass and 1 tube passes (1-1 exchanger))

Fig 1.3 Shell and tube heat exchanger (1 shell pass and 2 tube passes (1-2 exchanger))

• The liquid on the tube side flows in two passes• The shell-side liquid flows in one pass• In the first pass of the tube side, the cold fluid is flowing

counterflow to the hot shell-side fluid• In the second pass of the tube side, the cold fluid flows in parallel

(co-current)

3. Plate heat exchanger• Use metal plates to transfer heat between two fluids• Consist of many corrugated stainless steel sheets separated

by polymer gaskets and clamped in a steel frame.• The corrugation induce turbulence for improve heat transfer• The space between plates is equal to the depth of the

corrugations (2 - 5 mm)• The plates are compressed in a rigid frame to create an

arrangement of parallel flow channels with alternating hot and cold fluids.

• A common device used to heat or cool a gas such as air • One of the fluids, which is a liquid, flows inside through the tubes,

and the exterior gas flows across the tube bundle by forced or sometimes natural convection.

4. Cross-flow exchanger

Fig. 1.4 Cross-flow heat exchangers: (a) one fluid mixed (gas) and one fluid unmixed; (b) both fluids unmixed.

• The fluid inside the tubes is considered to be unmixed, since it is confined and cannot mix with any other stream. • The gas flow outside the tubes is mixed, since it can move about freely between the tubes, and there will be a tendency for the gas temperature to equalize in the direction normal to the flow.• For the unmixed fluid inside the tubes, there will be a temperature gradient both parallel and normal to the direction of flow.

• A second type of cross-flow heat exchanger shown in Fig. 1.4(b) is typically used in air- conditioning and space-heating applications. •In this type the gas flows across a finned-tube bundle and is unmixed, since it is confined in separate flow channels between the fins as it passes over the tubes. The fluid in the tubes is unmixed.

Log Mean Temperature Difference (LMTD)

•For counter-current flow, LMTD for 1-1 exchanger with one shell pass and one tube pass is given by:

Where: ΔTlm = log mean temperature difference

ΔT1 = T1 - t1

ΔT2 = T2 – t2

T1 = inlet shell-side fluid temperature

T2 = outlet shell-side fluid temperature

t1 = outlet tube-side temperature

t2 = inlet tube-side temperature

T1

t1T2

t2

Temperature cross

----------------- Eq. (1)

ΔT1 ΔT2

2

1

21

lnTT

TTTlm

•For co-current flow, LMTD for 1-1 exchanger with one shell pass and one tube pass is given by:

Where: ΔTlm = log mean temperature difference

ΔT1 = T1 - t1

ΔT2 = T2 - t2

T1 = inlet shell-side fluid temperature

T2 = outlet shell-side fluid temperature

t1 = inlet tube-side temperature

t2 = outlet tube-side temperature

T1

t1

T2

t2

Temperature cross

----------------- Eq. (2)

2

1

21

lnTT

TTTlmΔT1 ΔT2

LMTD in Multi pass Exchanger• Multipass exchangers have more tube passes than shell passes.• The LMTD as given in Eq (1 & 2) does not apply in this case and it is customary to define a correction factor, FT.

• The relationship between LMTD and FT is define as below:

Where is define as the correct mean temperature drop.• The general equation for heat transfer across surface of an exchanger is:

lmTm TFT

mT

moomii TAUTAUq

---------------- Eq. (3)

----------------- Eq. (4)

• Figure 4.9-4 (Geankoplis, 4th ed.) shows the correction factor to LMTD for:

a) 1-2 and 1-4 exchangersb) 2-4 exchangers

• Two dimensionless ratios are used as follows:

• Using the nomenclature of Eqs. (5 & 6), the of Eq. (1) can be written as:

cico

hohi

TTTT

Z

cihi

cico

TTTTY

ciho

cohi

cihocohilm

TTTT

TTTTTln

----------------- Eq. (5 & 6)

---------------- Eq. (7)

Figure 4.9-4(a) Correction factor to LMTD for 1-2 and 1-4 exchangers

Figure 4.9-4(b) Correction factor to LMTD for 2-4 exchangers

Heat Exchanger Effectiveness – NTU Method•The LMTD is used in equation if the inlet and outlet temperatures of the two fluids are known and can be determined by a heat balance.•The surface area can be determined if U is known. •However, when the temperature of the fluids leaving the exchanger are not known, the tedious trial-and-error procedure is necessary.•To solve these cases, a method called the heat exchanger effectiveness is used which does not involve any of the outlet temperatures.•The Effectiveness – NTU (Number of Transfer Unit) method is a procedure for evaluating the performance of heat exchangers if heat transfer area, A and construction details are known .

lmTUAq

•Heat balance for the cold (C ) and hot (H ) fluids is:

•Calling

, then CH > CC

•Designate CC as Cmin or minimum heat capacity.•If there is an infinite area available for heat transfer, TCo = THi , the effectiveness ε is

•If the hot fluid is the minimum fluid, THo = TCi , and

)()(

)()(

min

max

CiHi

HoHi

CiHiC

HoHiH

TTCTTC

TTCTTC

)()(

)()(

min

max

CiHi

CiCo

CiHiH

CiCoC

TTCTTC

TTCTTC

)()()()( CoCiCpHoHiHp TTmCTTmCq ----------- Eq. (8)

CCp

HHp

CmC

CmC

)(

)(

----------- Eq. (10)

----------- Eq. (9)

• In both equations the denominators are the same and the numerator gives the actual heat transfer:

• Note that Eq. (11) uses only inlet temperatures.• For the case of a single-pass, counterflow exchanger, combining

Eqs (9 & 10):

• We consider first the case when the cold fluid is the minimum fluid. Using the present nomenclature,

)( min CiHi TTCq

----------- Eq. (13)

----------- Eq. (12)

----------- Eq. (11)

)()(

)()(

minmin CiHi

CiCoC

CiHi

HoHiH

TTCTTC

TTCTTC

CoHi

CiHo

CoHiCiHoCiCoC

TTTT

TTTTUATTCqln

•Combining Eq. (8) with the left side of Eq. (12) and solving for THi.

•Subtracting TCo from both sides,

•From Eq. (8) for Cmin = CC and Cmax = CH ,

•This can be rearranged to give the following:

)(11)(1CiCoCiCoCoCiCoHi TTTTTTTT

)(1CiCoCiHi TTTT

----------- Eq. (14)

----------- Eq. (16)

----------- Eq. (15)

----------- Eq. (17)

)(max

minCiCoHiHo TT

CCTT

)(max

minCiCoCiHiCiHo TT

CCTTTT

•Substituting Eq. (14) into Eq. (17),

•Finally, substituting Eq. (15) and Eq. (18) into Eq. (13), rearranging, taking the antilog of both sides, and solving for ε,

•We define NTU as the number of transfer unit as follows:

•The same results would have been obtained if CH = Cmin

)(1

max

minCiCoCiCoCiHo TT

CCTTTT

----------- Eq. (19)

----------- Eq. (18)

----------- Eq. (20)

max

min

minmax

min

max

min

min

1exp1

1exp1

CC

CUA

CC

CC

CUA

UA NTUminC

•For parallel flow we obtain:

•Figure 4.9-7 shows the heat exchanger effectiveness, ε for a)counterflow exchanger – using Eq. (19)b)parallel flow exchanger – using Eq. (21)

max

min

max

min

min

1

1exp1

CC

CC

CUA

----------- Eq. (21)

Figure 4.9-7 Heat exchanger effectiveness, ε:a)counter flow exchanger; b)parallel flow

exchanger

Fouling Factors and Typical Overall heat transfer coefficient• After a period of operation, the heat transfer surface for a heat

exchanger may become coated with various deposits present in the flow system, dirt, soot or the surface may become corroded as a result of the interaction between the fluids and the material used for construction of the heat exchanger.

• Biological growth such as algae can occur with cooling water in the biological industries.

• These deposits offer additional resistance to the flow of heat and reduce the overall heat transfer coefficient U.

• To avoid or lessen these fouling problems, chemical inhibitors are often added to minimize corrosion, salt deposition and algae growth.

• It is necessary to oversize an exchanger to allow for the reduction in performance during operation.

•The effect of fouling is allowed for in design by including the resistance of the fouling on the inside and outside of the tube in Eq. (22).

Where:hdi = fouling coefficient for inside of the tube (W/m2.K) hdo = fouling coefficient for outside of the tube (W/m2.K)

•Fouling coefficients or fouling factors must be obtained experimentally by determining the value of U for both clean and dirty conditions in the heat exchanger. The fouling factor, Rf is define as:

doo

i

oo

i

AA

iio

dii

i

hAA

hAA

AkArr

hh

U

lm 11

1----------- Eq. (22)

cleandirtyf UU

R 11 ----------- Eq.

(23)

•Typical Fouling Coefficients is shown in Table 1 and the typical values of overall heat transfer coefficients are given in Table 2.

Table 1 Typical Fouling Coefficients

hd

(W/m2.K)hd

(btu/h.ft2.0F)

Distilled and seawaterCity water

Muddy waterGases

Vaporizing liquidsVegetable and gas oils

113505680

1990-2840284028401990

20001000

350-500500500350

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