**5. Data reduction**

(*Tevap*,1 and *Tevap*,2), one thermocouple in the adiabatic section (*Tadiab*) and three thermocouples in

As is already known, for the correct operation of the heat pipe and thermosyphon, a heating system is needed in the evaporator and a cooling system in the condenser. The evaporator can be power dissipation in any kind of resistor (strip, cartridge) or a heat source, as the TEC hot side. The cooling system can consist of forced convection by air, water, or coolant, in most of the cases. The adiabatic section may have variable dimensions (in some cases, it is absent) and

Thus, in this research, the heating system of the evaporator is conducted by power dissipation from the passage of an electric current in a nickel-chromium alloy power strip resistor *Omega Engineering*™ with 0.1 mm of thickness and 3.5 mm of width. To ensure that the generated heat by Joule effect is transmitted to the evaporator, an aeronautic thermal insulation and a layer of polyethylene are installed in this region. A fiberglass tape is used in adiabatic section as heat insulation between the support and the passive device. The cooling system using air

To ensure the best results and the repeatability of experimental tests, the environment temperature was maintained at 20°C ± 0.5°C. A thermal conditioning system *Carrier™* was used for this purpose. A detailed check of the equipment and the heat pipe or thermosyphon (fixing thermocouples, thermal insulation, resistor connection, among others) must be made before each experimental test. The heat pipe or thermosyphon was carefully fixed to the universal support bracket in the adiabatic region in the desired position. The cooling system was turned on in the condenser region and set at a speed of 5 m/s controlled by a potentiometer with a combined error of ±0.2 m/s. The data acquisition system was turned on, collecting the temperatures measured by the K-type thermocouples. The temperatures should be verified according to the environment temperature, and if these were stable and approximately 20°C, finally, the heating system can be turned on and adjusted to the dissipation power desired. The initial load was 5 W and, after approximately 15 min, the thermocouples showed stationary values. If it happened, the thermal load has been increased by 5 W. The load increment was made until the maximum temperature of the device reached the critical temperature (150°C), where the melting of the materials could happen. Data were acquired every 5 s, recorded on the desktop by the software *Agilent™* 

the condenser (*Tcond*,1, *Tcond*,2, and *Tcond*,3).

**Figure 14.** Thermocouple positions in heat pipes.

364 Bringing Thermoelectricity into Reality

**4.2. Experimental procedure**

*Benchlink Data Logger 3*.

should be insulated from the external environment.

forced convection consisted of a fan in the condenser region.

#### **5.1. Thermal parameters**

The thermal performance of the heat pipes and the thermosyphon was analyzed and compared by the operating temperatures (*Top*), the global thermal resistance (*Rth*), and the effective thermal conductivity (*keff*). The analyzed operating temperature is the temperature of the adiabatic region. The global thermal resistance, *Rth*, of a heat pipe and a thermosyphon can be defined as the difficulty of the passive device to transport the heat power and can be calculated by:

$$R\_{th} = \frac{\Delta T}{q} = \frac{\left(T\_{cray} - T\_{cond}\right)}{q} \tag{1}$$

where, *q* is the heat transfer capability of the device, *Tevap* and *Tcond* are the mean temperature of the evaporator and the condenser, respectively.

The effective thermal conductivity, *keff*, is the property of a certain material to conduct heat. Defined by:

$$k\_{\circ\circ} = \frac{q \, L\_{\circ\circ}}{A\_{\circ} \,\Delta T} = \frac{q \, L\_{\circ\circ}}{A\_{\circ} (T\_{mp} - T\_{cmd})} \tag{2}$$

where, *Leff* is the effective length and *AC* is the heat transfer cross-sectional area. The effective length can be defined by:

$$L\_{gf} = \frac{L\_{sup}}{2} + L\_{addo} + \frac{L\_{cond}}{2} \tag{3}$$

where, *Levap* is the evaporator length, *Ladiab* is the adiabatic section length, and *Lcond* is the condenser length.

The heat transfer cross-sectional area can be defined by:

$$A\_c = \frac{\left(\pi D\_i^2\right)}{4} \tag{4}$$

where *Di* is the inner diameter of the heat transfer passive device.

#### **5.2. Uncertainties analysis**

In general, the experimental uncertainties are associated to the K-type thermocouples, the data logger, and the power supply unit. The experimental measurement uncertainties were analyzed using the uncertainty combination method described in [29] considering the combination of uncertainties of correlated quantities. They are shown in the obtained results. It is known that the accuracy of the thermocouples is ±2.2°C and the uncertainty was evaluated as the rectangle type. Thus, the uncertainty values of the temperature sensors were estimated in:

$$
\mu(T) = \frac{\pm 2,2}{\sqrt{3}} = \pm 1,27^{\circ}C\tag{5}
$$

**6. Evaluation of the thermal performance**

**6.1. Temperature distribution**

**6.2. Operation temperature**

**6.3. Global thermal resistance**

the heat pipe length for different heat loads.

To summarize the analysis of the thermal performance of the heat pipes and the thermosyphon, different types of passive heat transfer devices were experimentally evaluated and compared. The considered devices were a rod, a thermosyphon, a mesh heat pipe, a grooved heat pipe, and a sintered heat pipe. The analyzed operating positions were vertical and horizontal. The experimental tests were repeated three times and the errors were compared taking into account the difference between the mean values less than 0.5°C. The tests were performed

Heat Pipe and Thermosyphon for Thermal Management of Thermoelectric Cooling

http://dx.doi.org/10.5772/intechopen.76289

367

**Figure 15** shows the temperature distributions as a function of time for the heat pipe with axial microgrooves in the vertical position. The heat pipe starts to work at a temperature of 44° C, for a heat load of 5 W. The maximum dissipated power of the grooved heat pipe was 45 W. **Figure 16** presents the temperature distribution in function of the thermocouple position in

The behavior of the operating temperature as a function of the dissipated power for different passive devices is shown in **Figure 17**. It may be noted that as the dissipated power increases,

**Figure 18** presents the global thermal resistance as a function of the power dissipation considering the rod, the thermosyphon, and the heat pipes. The results of two operating positions

the operating temperature also increases for all the devices in both positions.

**Figure 15.** Temperature distribution *versus* time: Grooved heat pipe in vertical.

at increasing heat loads of 5 W, ranging from 5 to 45 W for both positions.

The combined uncertainties of the evaporator, adiabatic section, and condenser temperatures were calculated according to the following equations respectively:

$$u\left(T\_{cnp}\right) = \left|\frac{\partial}{\partial\left}\frac{T\_{cnp}}{T\_{cnp,1}}\right|u\left(T\_{cnp,1}\right) + \left|\frac{\partial\left.T\_{cnp}\right|}{\partial\left.T\_{cnp,2}\right|}\right|u\left(T\_{cnp,2}\right) + \left|\frac{\partial\left.T\_{cnp}}{\partial\left.T\_{cnp,3}}\right|u\left(T\_{cnp,3}\right)\right|\right|\tag{6}$$

$$
u \langle T\_{\
abla} \rangle = \langle \mu(T) = \pm 1, \mathcal{D}T^\* \rangle \tag{7}$$

$$\boldsymbol{u}(T\_{\text{cond}}) = \left| \frac{\partial \boldsymbol{T}\_{\text{cond}}}{\partial \boldsymbol{T}\_{\text{cond,1}}} \right| \boldsymbol{u}(T\_{\text{cond,1}}) + \left| \frac{\partial \boldsymbol{T}\_{\text{cond}}}{\partial \boldsymbol{T}\_{\text{cond,2}}} \right| \boldsymbol{u}(T\_{\text{cond,2}}) + \left| \frac{\partial \boldsymbol{T}\_{\text{cond}}}{\partial \boldsymbol{T}\_{\text{cond,3}}} \right| \boldsymbol{u}(T\_{\text{cond,3}}) + \left| \frac{\partial \boldsymbol{T}\_{\text{cond}}}{\partial \boldsymbol{T}\_{\text{cond,4}}} \right| \boldsymbol{u}(T\_{\text{cond,4}}) \tag{8}$$

The measurement uncertainties associated with the dissipated power in the evaporator were estimated according to the power supply in the electrical resistance of the tests. The uncertainties were evaluated as the rectangle type, considering the voltage accuracy of 0.35% + 20 mV and the current accuracy of 0.35% + 20 mA. The electrical power dissipated by the electric resistance, *P*, is calculated as shown below:

$$P = VI\tag{9}$$

where *V* is the voltage and *I* is the current.

Considering that thermal losses in the evaporator region are negligible and that all energy is transferred to the wall of the heat pipe, the uncertainty of the heat transfer capacity can be estimated as:

$$
\mu(q) = \mu(P) = \left| \frac{\partial q}{\partial V} \right| \mu(V) + \left| \frac{\partial q}{\partial I} \right| \mu(\mathbf{I}) \tag{10}
$$

The global thermal resistance uncertainty can be calculated by the following equation:

$$\mu(R\_{\rm th}) = \left| \frac{\partial R\_{\rm th}}{\partial q} \right| \mu(q) + \left| \frac{\partial R\_{\rm th}}{\partial \Delta T} \right| \mu(\Delta T) \tag{11}$$

where the uncertainty of the temperature difference can be defined as:

$$
\mu(\Delta T) = \left| \frac{\partial \Delta T}{\partial T\_{comp}} \right| \mu(T\_{comp}) + \left| \frac{\partial \Delta T}{\partial T\_{cond}} \right| \mu(T\_{cond}) \tag{12}
$$
