*3.1.1 Cooling and dehumidification of the air*

The temperature and relative humidity of the ambient air measured in the laboratory was 31°C and 63% respectively. In order to obtain within thermal comfort range as defined by ASHRAE, it is best to cool and dehumidify the air to 22°C with a relative humidity of 50% as shown in **Figure 6**. The cold side of the thermoelectric module would be at a temperature lower than the dew point temperature and therefore condensation is expected to take place which would decrease the relative humidity of the air [5, 6].

State 1 represents the air properties of the ambient air in the lab while state 2 represents the air properties that we would like to have. The following calculations are used to determine the required cooling capacity for the thermoelectric module.

*Theoretical and Experimental Analysis of a Thermoelectric Air-conditioning System*

¼ *m*\_*<sup>a</sup>* ð Þ� *h*<sup>1</sup> � *h*<sup>2</sup> ð Þ *W*<sup>1</sup> � *W*<sup>2</sup> *hf,* <sup>2</sup>

*m*\_*<sup>a</sup>* = mass flow rate in kJ/kg; W = humidity ratio in kg/kg.

*<sup>h</sup>*<sup>1</sup> <sup>¼</sup> <sup>76</sup>*:*91 kJ*=*kg; *<sup>ϑ</sup>*<sup>1</sup> <sup>¼</sup> <sup>0</sup>*:*887m<sup>3</sup>

At state 1:

**Figure 6.**

At state 2:

**63**

31°C, 63% *relative humidity*

*Psychometric chart: cooling and dehumidifying.*

*DOI: http://dx.doi.org/10.5772/intechopen.88664*

22°C, 50% *relative humidity*

15 CFM = 0.00708 m<sup>3</sup>

A fan of 15 CFM was available at the lab:

*<sup>m</sup>*\_ *<sup>a</sup>* <sup>¼</sup> <sup>0</sup>*:*00708 m<sup>3</sup>

¼ 0*:*00798 kg*=*s

¼ 0*:*264 kW ¼ 264 W

/s

*=s* �

*<sup>Q</sup>*\_ *<sup>T</sup>* <sup>¼</sup> *<sup>m</sup>*\_*<sup>a</sup>* ð Þ� *<sup>h</sup>*<sup>1</sup> � *<sup>h</sup>*<sup>2</sup> ð Þ *<sup>W</sup>*<sup>1</sup> � *<sup>W</sup>*<sup>2</sup> *hf,* <sup>2</sup>

where *Q*\_ *<sup>s</sup>* = sensible heat in kW; *Q*\_ *<sup>l</sup>* = latent heat in kW; h = enthalpy in kJ/kg;

*h*<sup>2</sup> ¼ 43*:*04 kJ*=*kg; *W*<sup>2</sup> ¼ 0*:*0082 kg*=*kg; *h*f*,* <sup>2</sup> ¼ 83*:*94 kJ*=*kg

1 0*:*887m3*=*kg

¼ 0*:*00798 76 ½ � ð *:*91 � 43*:*04Þ � ð Þ 0*:*0179 � 0*:*0082 83*:*94

*<sup>Q</sup>*\_ *<sup>T</sup>* <sup>¼</sup> *<sup>Q</sup>*\_ *<sup>s</sup>* <sup>þ</sup> *<sup>Q</sup>*\_ *<sup>l</sup>* (1)

¼ *m*\_*<sup>a</sup>* ð Þþ *h*<sup>2</sup> � *ha m*\_*<sup>a</sup>* ð Þ *ha* � *h*<sup>1</sup> *hf,*<sup>2</sup> (2)

(3)

*=*kg; *W*<sup>1</sup> ¼ 0*:*0179 kg*=*kg

(4)

**Figure 5.** *Thermoelectric air conditioning system.*

*Theoretical and Experimental Analysis of a Thermoelectric Air-conditioning System DOI: http://dx.doi.org/10.5772/intechopen.88664*

#### **Figure 6.** *Psychometric chart: cooling and dehumidifying.*

State 1 represents the air properties of the ambient air in the lab while state 2 represents the air properties that we would like to have. The following calculations are used to determine the required cooling capacity for the thermoelectric module.

$$
\dot{Q}\_T = \dot{Q}\_s + \dot{Q}\_I \tag{1}
$$

$$=\dot{m}\_a(h\_2 - h\_a) + \dot{m}\_a(h\_a - h\_1)h\_{f,2} \tag{2}$$

$$=\dot{m}\_a \left[ (h\_1 - h\_2) - (\mathcal{W}\_1 - \mathcal{W}\_2) h\_{f,2} \right] \tag{3}$$

where *Q*\_ *<sup>s</sup>* = sensible heat in kW; *Q*\_ *<sup>l</sup>* = latent heat in kW; h = enthalpy in kJ/kg; *m*\_*<sup>a</sup>* = mass flow rate in kJ/kg; W = humidity ratio in kg/kg.
