**5.1. Condenser and evaporator**

*<sup>ε</sup>* <sup>=</sup> *Cmax*(*Th*,*<sup>i</sup>* <sup>−</sup> *<sup>T</sup>* \_\_\_\_\_\_\_\_\_\_\_*<sup>h</sup>*,*<sup>o</sup>*)

*<sup>R</sup>* <sup>=</sup> *<sup>C</sup>*\_\_\_\_ *min*

*Ntu* = \_\_\_\_ *UA*

Regardless of the type of heat exchanger.

**Heat exchanger type Effectiveness (ε) relations**

Parallel flow *<sup>ε</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup> *exp*[−*Ntu*(1 <sup>+</sup> *<sup>R</sup>*)]

R<1 *<sup>ε</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup> *exp*[−*Ntu*(1 <sup>−</sup> *<sup>R</sup>*)]

R=1 *<sup>ε</sup>* <sup>=</sup> \_\_\_\_\_ *Ntu*

Shell and tube one shell pas (2,4…tube

passes) *<sup>ε</sup>*<sup>1</sup> <sup>=</sup> <sup>2</sup>

n Shell passes (2n, 4n… tube passes) *<sup>ε</sup><sup>n</sup>* <sup>=</sup> [(

**Table 4.** Effectiveness relations for different types of heat exchangers [41].

Cross flow both fluid unmixed *ε* = 1 − *exp*[(

where *Th*,*<sup>i</sup>*

Counter flow

Cross flow Cmin (unmixed) Cmax (mixed)

Cross flow Cmax (unmixed) Cmin (mixed)

and *Th*,*<sup>o</sup>*

52 Sustainable Air Conditioning Systems

*Cmin*(*Th*,*<sup>i</sup>* <sup>−</sup> *Tc*,*<sup>i</sup>*) <sup>=</sup> *Cmin*(*Tc*,*<sup>o</sup>* <sup>−</sup> *<sup>T</sup>* \_\_\_\_\_\_\_\_\_\_\_*<sup>c</sup>*,*<sup>i</sup>*)

*Cmax*

*Cmin*

The dimensionless parameter Ntu (number of transfer units) expresses the size of the heat

Effectiveness correlations for different types of heat exchangers are summarized in **Table 4**. If there is a phase change in a heat exchanger, the heat capacity of the fluid-changing phase

*ε* = 1 − *exp*(−*Ntu*) (10)

 \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1 + *R*

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1 <sup>+</sup> *<sup>R</sup> exp*[−*Ntu*(1 <sup>−</sup> *<sup>R</sup>*)]

\_\_1

*<sup>ε</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup> *exp*{−*R*[<sup>1</sup> <sup>−</sup> *exp*(−*Ntu*) ]} \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

{<sup>1</sup> <sup>+</sup> *<sup>R</sup>* <sup>+</sup> (1 <sup>+</sup> *<sup>R</sup>*2)

<sup>1</sup> <sup>−</sup> *<sup>ε</sup>*<sup>1</sup> *<sup>R</sup>* \_\_\_\_\_ <sup>1</sup> <sup>−</sup> *<sup>ε</sup>*<sup>1</sup> ) *n* − 1] [(

*<sup>R</sup>*) *Ntu*0.22{*exp*[−*R*(−*Ntu*0.78)] <sup>−</sup> <sup>1</sup>}]

]}

\_\_1 2] \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1 <sup>−</sup> *exp*[−*Ntu* (1 <sup>+</sup> *<sup>R</sup>*2)

\_\_1 <sup>2</sup>]}

1 + *exp*[−*Ntu* (*R*2)

*<sup>R</sup>*

*<sup>R</sup>*[<sup>1</sup> <sup>−</sup> *exp*(−*Ntu* <sup>∗</sup> *<sup>R</sup>*)

\_\_1 2

> <sup>1</sup> <sup>−</sup> *<sup>ε</sup>*<sup>1</sup> *<sup>R</sup>* \_\_\_\_\_ <sup>1</sup> <sup>−</sup> *<sup>ε</sup>*<sup>1</sup> ) *n* − *R*] −1

1 + *Ntu*

*<sup>ε</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup> *exp*{−\_\_1

are the inlet and outlet temperatures of the hot fluid and *Tc*,*<sup>i</sup>*

inlet and outlet temperatures of the cold fluid. The ratio of capacities is defined by:

exchanger and is commonly used in heat exchanger analysis and is expressed as [40]:

becomes infinite, and Cr is zero, then effectiveness correlations reduce to:

*Cmin*(*Th*,*<sup>i</sup>* <sup>−</sup> *Tc*,*<sup>i</sup>*) (7)

and *Tc*,*<sup>o</sup>*

are the

(8)

(9)

These devices for air-conditioning applications are designed considering the coil flooded with two-phase refrigerant and also a wall temperature equal to the refrigerant in general [42]. The outer side heat transfer coefficient and the physical properties are assumed constant. Thereby, the heat transfer rate is calculated according to [43]:

$$\dot{Q} = \dot{m} \, \text{Cp} (T\_o - T\_i) = \, \varepsilon \, \dot{m} \, \text{Cp} (T\_s - T\_i) \tag{11}$$

where *m*̇ is the mass flow rate, T<sup>i</sup> , To and Ts , are the inlet, outlet, and surface temperatures, respectively.

$$
\dot{\mathcal{Q}} = \varphi A\_s (T\_s - T\_w) \tag{12}
$$

The equation number 12 is the heat transfer rate, Tm is the mean flow temperature over the heat transfer area, and As and ε are the heat exchanger effectiveness.
