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- Heat Exchangers

### 1.Types of Heat Exchangers

#### What are they?

Devices for effecting heat transfer from one fluid to another

#### Mechanical Configurations

##### ›Tube within a tube

##### ›Multiple tubes with a shell (vessel)

##### ›Finned tubes

#### Flow Arrangements

##### ›Counter flow

##### ›Parallel flow

##### ›Cross flow

#### Main Design Considerations

##### ›Heat transfer efficiency

##### ›Structural strength

##### ›Pressure drop

##### ›Size and Weight

##### ›Operation and maintenance requirements

##### ›Cost

#### Design Codes

##### ›ASME Codes for Unfired Pressure Vessel

### 2.Log - Mean T Method (LMTD Method)

#### Overall Heat Transfer Coefficient

Consider a parallel flow, tube-within-tube heat exchanger

where: = effective temperature difference

R = thermal resistance

U = overall heat transfer coefficient

A = effective surface area

Thermal conduction analysis showed:

plane wall:

cylinder wall:

Note:

##### ›For cylindrical systems,

##### ›To consider the effects of surface fouling and fins, overall heat transfer coefficient becomes:

#### Parallel Flow

Define:

Noting , we can write:

Newton’s law of cooling gives:

After simplification, it becomes;

where:

#### Counter Flow

Note:1) (when are they equal?)

2)Only for counter flow, could be larger than

#### Complex Heat Exchangers

See Figures 11.10 to 11.13 for F values

Note:1) must be evaluated under counter flow condition

2)F = 1 if or

### 3.NTU - Effectiveness Method

›Alternative to determine the exchanger performance

›Used most conveniently if two or more of the inlet or exit temperatures of both streams are unknown

#### Definition

›Heat exchanger effectiveness

Assuming , the energy balance gives

Realizing the maximum possible heat transfer occurs when the fluid of smaller C undergoes the maximum temperature difference available, we can write

where:Cmin = min(Ch, Cc)

or

›NTU (Number of Transfer Units)

#### Parallel Flow Heat Exchanger

Assume Cmin =Ch

where:Cr = heat capacity ratio

Recall:

In terms of and Cr, it becomes:

After the further transformation, it can be written as:

Note:1)Valid also for Cmin =Cc

2)

#### Other Configurations

›Mathematical relations:Tables 11.3 and 11.4

›Graphical relations:Figures 11.14 to 11.19

Note:1) Cr = 0 for condensers and boilers

### 4.Method Applications

›Design problem: all the inlet and outlet temperatures known, find the type and size of heat exchangers LMTD method

›Performance evaluation problem: the type and size of heat exchanger known, find the heat transfer rate and fluid outlet temperatures for the selected fluid flow rate and inlet temperatures NTU method