**6.1. Temperature distribution**

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 sen-

<sup>3</sup> <sup>=</sup> ±1, 27° *<sup>C</sup>* (5)

<sup>∂</sup> *Tevap*,3| *<sup>u</sup>*(*Tevap*,3) (6)

<sup>∂</sup> *Tcond*,4| *<sup>u</sup>*(*Tcond*,4) (8)

<sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *cond*

<sup>∂</sup>*I*<sup>|</sup> *<sup>u</sup>*(*I*) (10)

∂Δ*T*<sup>|</sup> *<sup>u</sup>*(Δ*T*) (11)

<sup>∂</sup> *Tcond*<sup>|</sup> *<sup>u</sup>*(*Tcond*) (12)

<sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *evap*

√ \_\_

The combined uncertainties of the evaporator, adiabatic section, and condenser temperatures

<sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *evap*

*u*(*Tadiab*) = *u*(*T*) = ±1, 27° *C* (7)

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

*P* = *V I* (9)

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

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

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

\_\_\_\_\_\_\_\_\_ ∂ Δ*T*

<sup>∂</sup> *Tevap*<sup>|</sup> *<sup>u</sup>*(*Tevap*) <sup>+</sup>

<sup>∂</sup>*<sup>q</sup>* <sup>|</sup> *<sup>u</sup>*(*q*) +|<sup>∂</sup> *<sup>R</sup>*\_\_\_\_*th*

<sup>∂</sup>*V*<sup>|</sup> *<sup>u</sup>*(*V*) +|<sup>∂</sup>*<sup>q</sup>* \_\_\_


<sup>∂</sup> *Tcond*,2| *<sup>u</sup>*(*Tcond*,2) <sup>+</sup>

<sup>∂</sup> *Tevap*,2| *<sup>u</sup>*(*Tevap*,2) <sup>+</sup>

<sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *cond*

<sup>∂</sup> *Tcond*,3| *<sup>u</sup>*(*Tcond*,3) <sup>+</sup>

sors were estimated in:

366 Bringing Thermoelectricity into Reality

*<sup>u</sup>*(*Tevap*) <sup>=</sup> <sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *evap*

*<sup>u</sup>*(*Tcond*) <sup>=</sup> <sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *cond*

estimated as:

*<sup>u</sup>*(*T*) <sup>=</sup> \_\_\_\_ ±2, <sup>2</sup>

<sup>∂</sup> *<sup>T</sup>*cond,1| *<sup>u</sup>*(*Tcond*,1) <sup>+</sup>

resistance, *P*, is calculated as shown below:

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

*<sup>u</sup>*(*q*) <sup>=</sup> *<sup>u</sup>*(*P*) <sup>=</sup> <sup>|</sup>∂*<sup>q</sup>* \_\_\_

*<sup>u</sup>*(*Rth*) <sup>=</sup> <sup>|</sup><sup>∂</sup> *<sup>R</sup>*\_\_\_\_*th*

*<sup>u</sup>*(Δ*T*) <sup>=</sup> <sup>|</sup>

were calculated according to the following equations respectively:

<sup>∂</sup> *Tevap*,1| *<sup>u</sup>*(*Tevap*,1) <sup>+</sup>

<sup>|</sup> <sup>∂</sup> *<sup>T</sup>* \_\_\_\_\_\_ *cond*

**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 heat pipe length for different heat loads.

#### **6.2. Operation temperature**

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

#### **6.3. Global thermal resistance**

**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

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

in the heat pipes, besides gravity, the capillary pumping also has a positive influence on the fluid flow. The heat transfer in the evaporators is governed by boiling, which is facilitated due to the existence of nucleation sites. Thermosyphon nucleation sites happen due to the surface roughness (imperfections). In the heat pipes, the capillary structures (screen meshes, microgrooves, or sintered media) provide the nucleation sites, making the boiling process more efficient. Thus, according to **Figure 18**, the global thermal resistance of the heat pipes is lower than the rod and the thermosyphon. This can be explained by the influence of gravity and the capillary pumping. Also, the boiling process is more efficient due to the existence of more nucleation sites. Finally, note that values of global thermal resistance could be lower if the overall heat transfer coefficient in the condenser of the passive devices were higher, which could be achieved, for example, using fins or

Heat Pipe and Thermosyphon for Thermal Management of Thermoelectric Cooling

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

369

**Figure 18.** Thermal resistance *versus* power dissipation. (a) Vertical and (b) horizontal.

**Figure 19.** Effective thermal conductivity *versus* power dissipation. (a) Vertical and (b) horizontal.

liquid cooling.

**Figure 16.** Temperature distribution *versus* thermocouple position: Grooved heat pipe in vertical.

**Figure 17.** Operating temperature *versus* power dissipation. (a) Vertical and (b) horizontal.

are compared. As the heat dissipation is increased, the thermal resistance decreases for the thermosyphon and the heat pipes in the vertical position. In horizontal, the heat pipes obtain the same behavior; however, the thermosyphon has changed dramatically. It happens due to the necessity of gravity for the fluid return in the thermosyphon. The rod thermal resistance remains almost constant for the entire heat loads in both positions.

As mentioned, the global thermal resistance of the heat pipes and the thermosyphon take into consideration the temperature difference between the evaporator and the condenser and, the dissipated power. However, the processes governing the global thermal resistance are related to the fluid dynamics and the heat transfer. The fluid dynamics is influenced by the gravity and the capillary pumping. In the thermosyphon, the fluid flow from the condenser to the evaporator occurs exclusively by gravity. On the other hand, in the heat pipes, besides gravity, the capillary pumping also has a positive influence on the fluid flow. The heat transfer in the evaporators is governed by boiling, which is facilitated due to the existence of nucleation sites. Thermosyphon nucleation sites happen due to the surface roughness (imperfections). In the heat pipes, the capillary structures (screen meshes, microgrooves, or sintered media) provide the nucleation sites, making the boiling process more efficient. Thus, according to **Figure 18**, the global thermal resistance of the heat pipes is lower than the rod and the thermosyphon. This can be explained by the influence of gravity and the capillary pumping. Also, the boiling process is more efficient due to the existence of more nucleation sites. Finally, note that values of global thermal resistance could be lower if the overall heat transfer coefficient in the condenser of the passive devices were higher, which could be achieved, for example, using fins or liquid cooling.

**Figure 18.** Thermal resistance *versus* power dissipation. (a) Vertical and (b) horizontal.

**Figure 16.** Temperature distribution *versus* thermocouple position: Grooved heat pipe in vertical.

368 Bringing Thermoelectricity into Reality

**Figure 17.** Operating temperature *versus* power dissipation. (a) Vertical and (b) horizontal.

remains almost constant for the entire heat loads in both positions.

are compared. As the heat dissipation is increased, the thermal resistance decreases for the thermosyphon and the heat pipes in the vertical position. In horizontal, the heat pipes obtain the same behavior; however, the thermosyphon has changed dramatically. It happens due to the necessity of gravity for the fluid return in the thermosyphon. The rod thermal resistance

As mentioned, the global thermal resistance of the heat pipes and the thermosyphon take into consideration the temperature difference between the evaporator and the condenser and, the dissipated power. However, the processes governing the global thermal resistance are related to the fluid dynamics and the heat transfer. The fluid dynamics is influenced by the gravity and the capillary pumping. In the thermosyphon, the fluid flow from the condenser to the evaporator occurs exclusively by gravity. On the other hand,

**Figure 19.** Effective thermal conductivity *versus* power dissipation. (a) Vertical and (b) horizontal.

## **6.4. Effective thermal conductivity**

In **Figure 19**, the behavior of the effective thermal conductivity of the passive heat transfer devices is shown as a function of the power dissipated for vertical (a) and horizontal (b) positions. As expected, it can be seen that the passive devices that use phase change (heat pipes and thermosyphon) have a higher effective thermal conductivity and that this parameter increases with increasing power dissipation.

*k* thermal conductivity, [W/mK]

*P* electrical power dissipated, [W]

*Rth* total thermal resistance, [°C/W]

Thiago Antonini Alves\*, Larissa Krambeck and Paulo H. Dias dos Santos

2017; OnLine-First Issue00:300. DOI: 10.2298/TSCI170610300K

[1] Antonini Alves T, Altemani CAC. An invariant descriptor for heaters temperature prediction in conjugate cooling. International Journal of Thermal Sciences. 2012;**58**:92-101.

Heat Pipe and Thermosyphon for Thermal Management of Thermoelectric Cooling

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

371

[2] Nishida FB, Tadano YS, Antonini AT. Conjugate forced convection-conduction heat transfer in channel flow using different cooling fluids. In: Proceedings of the 15th International Heat Transfer Conference (IHTC-15); 10-15 August 2014; Kyoto/JAP. Connecticut/USA:

Begell House; 2014. IHTC15-9594, p. 1957-1970. DOI: 10.1615/IHTC15.eec.009594 [3] Krambeck L, Nishida FB, Aguiar VM, Santos PHD, Antonini Alves T. Thermal performance evaluation of different passive devices for electronics cooling. Thermal Science.

\*Address all correspondence to: thiagoaalves@utfpr.edu.br

Federal University of Technology, Parana, Brazil

DOI: 10.1016/j.ijthermalsci.2012.03.007

*q* heat transfer rate, [W]

*T* temperature, [°C]

*adiab* adiabatic section

*L* length, [m]

*t* time, [s]

*V* voltage, [V]

*Cu* copper

*cond* condenser *eff* effective

*evap* evaporator

**Author details**

**References**

Subscripts
