College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

CHAPTER9. APPLICATIONS OF HEAT TRANSFER-HEAT EXCHANGERS Heat exchangers are classified according to flow arrangement and type of construction. The simplest type

is the one that the hot and cold fluid flow moves in the opposite and the same direction of the fluid flow.

The cross-fluid flow heat exchanger is the fluid flow moves perpendicular into the fluid. The counter fluid

flow heat exchanger is classified according to the direction of the fluid flow, the fluid flow moves in the

opposite direction, however the parallel (shell tube) fluid flow arrangement is defined as the fluid flow

moves in the same direction, as shown in Fig. 1.3. The compact heat exchanger is a very dense arrays of

finned tubes which is used for liquid and gas.

a. b.

Fig1.3. a) Parallel shell tube heat exchanger, b. Counter shell tube heat exchanger

Fig.1.4. Cross-fluid flow heat exchanger arrangement

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

a.

b.

c. d.

Fig.1.5. a. Counter heat exchanger, b. U-tube heat exchanger, mixed Flow heat exchanger, and d.

compact heat exchanger.

Overall heat transfer Coefficient

The overall heat transfer of the finned heat exchanger can be estimated as:

1

UA=

1

UAc=

1

UhAh=

1

ηohcAc+

1

ηohhAh+ Rw +

Rfc

ηoAc+

Rfh

ηoAh

Where ηois the overall surface efficieny = 1 −Afin

A(1 − ηf)

Rfcand Rfhare the fouing resistance in the cold and hot side, respectively.

The total heat transfer rate is

q = Ahηo(Tb − T∞)

Where the single fin efficiency can be estimated as:

ηfin =tanh(ML)

ML, M = √

2h

kth where th is the thickness

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

Table 1.1. Fouling Resistance

Table 1.2. Values of the overall heat Transfer Coefficient

For unfinned tubular heat exchangers, the overall heat transfer coefficient is

1

UA=

1

UAc=

1

UhAh=

1

hcAc+

1

hhAh+

ln (DoDi

)

2πkL+

Rfc

Ac+

Rfh

Ah

Parallel Flow Heat Exchanger

The two fluids move in the same direction. The temperature distribution associated with the

parallel flow heat exchanger initially large and decays with increasing x.

Fig.1.1. Parallel flow distribution temperature

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

The total heat transfer can be estimated as

qc = mc cpc(Tco − Tci), qh = mh cph(Thi − Tho)

The total heat can be evaluated based on the log mean temperature as:

q = UA∆Tlm where ∆Tlm =∆T2 − ∆T1

ln (∆T2∆T1

)

Counter Flow Heat Exchanger The two fluids move in opposite direction.

Fig.1.2. Counter flow distribution temperature

The hot and cold heat capacity rate can be represented by:

Ch = mcph, and Cc = mc_pc

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

Special heat exchanger conditions:

Fig1.3. Heat capacity rate for different conditions

Effectiveness of Heat Exchanger

The ratio of the actual heat transfer rate to the maximum possible heat transfer rate.

qmax = Cmin(Thi − Tci)

Cmin is either equal to Ch or Cc whichever is smaller.

ε =q

qmax=

Ch(Thi − Tho)

Cmin(Thi − Tci)

The number of transfer unit (NTU) is an important parameter in a heat exchanger design.

ε = f (NTU,Cmin

Cmax)

NTU =UA

Cmin

Table 1.3 shows various formula of NTU which relies on the configurations of the heat

exchanger.

The capacity rate ratio is

Cr =Cmin

Cmax

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

Table 1.3. Heat exchanger effectiveness definitions

Log Mean Temperature Difference Method for Multi-pass and Cross-Flow Heat

Exchanger

The pervious equation can be used to calculate the Multi-pass and Cross flow heat exchanger by

adding the correction factor.

∆Tlm = F∆Tlm,CF

The single tier cross flow heat exchanger correction factor can be evaluated from Fig. 1.1.

The multiple-pass shell and tube heat exchanger correction factor can be evaluated from Fig.1.2.

The single pass unmixed heat exchanger correction factor can be evaluated from Fig.1.3.

The multiple-pass one fluid mixed and the other unmixed heat exchanger correction factor can be

evaluated from Fig.1.3.

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

Fig.1.1. Correction Factor of Tube –Shell heat Exchanger (two tubes)

Fig.1.2. Correction factor of Multiple-pass (Four tubes) shell and tube heat exchanger

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

Fig.1.3. Correction Factor of a single pass of unmixed flow heat exchanger

Fig.1.4. Correction Factor of one fluid mixed and other fluid unmixed

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa

College of Engineering Summer Session- 2015 Heat Transfer - ME 372 Dr. Saeed J. Almalowi, smalowi@taibahu.edu.sa