# Effects of the Aspect Ratio of a Rectangular Thermosyphon on Its Thermal Performance

^{1}

^{2}

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^{*}

## Abstract

**:**

^{2}). The results show that it is feasible to obtain solar heat gain by installing a rectangular thermosyphon inside the metal curtain wall and that increasing the height of the opaque part of the metal curtain wall can increase the aspect ratio of the rectangular thermosyphon installed inside the wall and thus improve the heat transfer efficiency.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Scenarios and Test Cell Development

#### 2.2. Experimental Test Cell

#### 2.2.1. Rectangular Loop

#### 2.2.2. Heating Section

#### 2.2.3. Cooling Section

#### 2.2.4. Adiabatic Sections

#### 2.3. Experimental Apparatus

#### 2.3.1. Power Supply System

^{2}as the nominal solar heat gain on the wall, then the service areas of each test cell are 0.1 m

^{2}(= 30/300; ${q}_{h}$ = 30 W) and 0.2 m

^{2}(= 60/300; ${q}_{h}$ = 60 W).

#### 2.3.2. Thermoregulated Bath

#### 2.3.3. Liquid Flow Meter

#### 2.3.4. Thermocouples

#### 2.4. Experimental Procedures

- Set the temperature of the thermoregulated bath to the cooling section temperature of 30 °C required for the experiment and keep the inlet and outlet valves of the thermo-regulated bath closed.
- Set the required power output (30, 40, 50, and 60 W) on the power supply.
- When the temperature of the heating section is higher than the set temperature of the cooling section wall, open the inlet and outlet valves of the thermo-regulated bath.
- After the temperature of the thermosyphon loop reaches a steady state, increase the input power and carry out the next steady-state experiment.
- Repeat step 4 until the input power reaches 60 W, when the experiment is completed.

#### 2.5. Parameters

- The input power ${q}_{h}=VI$ (W) was obtained from the voltage V and the current I provided by the power supply. During the experiment, the heating from the power supply was not completely transferred to the fluid in the heating section. A small amount of heat entered the cooling section via axial heat conduction ${q}_{a}$ (W) of the thermosyphon or escape into the environment. Therefore, this axial heat transfer was first subtracted from the input thermal power, that is, the corrected actual input thermal power was ${q}_{in}={q}_{h}-{q}_{a}$ (W). Then, the heat flux ${q}_{h}^{\u2033}$ was calculated as ${q}_{in}$/A (W/m
^{2}), where A is the area of the heating section. - Modified Rayleigh number, Ra*$$R{a}^{*}=\frac{g\beta {q}_{h}^{\u2033}{L}_{y}^{4}}{k\alpha \nu}$$
^{2}/s), and α is the thermal diffusivity $\frac{k}{\rho {C}_{p}}$ (m^{2}/s), $\rho $ is the density (kg/m^{3}), ${C}_{p}$ is the specific heat (J/kg K), and $k$ is the thermal conductivity (W/m). The values of these physical properties are based on the average water temperature of the heating section (35 °C). - Reynolds number, Re$$\mathrm{Re}=\frac{V{D}_{i}}{\nu}$$
- Nusselt number
- (1)
- The average thermal convection coefficient h at the hot end was:$$h=\frac{{q}_{h}^{\u2033}}{{\overline{T}}_{w}-{\overline{T}}_{m}}$$
- (2)
- The Nusselt number Nu was calculated as follows:$$\mathrm{Nu}=\frac{h{D}_{i}}{k}$$

- Thermal resistance of the working fluid flow, ${R}_{flow}$$${R}_{flow}=\frac{1}{\dot{m}{C}_{p}}=\frac{1}{\rho V{A}_{f}{C}_{p}}$$

#### 2.6. Experimental Uncertainty

## 3. Results and Discussion

^{2}, the cooling section temperature Tc is 30 °C, and the cold end length Lc is 30 m.

_{loop}of 0 was set at the lower-left corner of the loop system (Figure 2a). The X

_{loop}range of 0–0.43 corresponds to the heating section, the range of 0.43–0.5 corresponds to the adiabatic section between the outlet of the heating section and the inlet of the cooling section, the range of 0.5–0.61 corresponds to the cooling section, the range of 0.61–1 corresponds to the adiabatic section after the cooling section, and X

_{loop}of 1 indicates the return to the starting point of the loop (i.e., the starting point of the heating section).

_{w}of the thermosyphon shows that after entering the heating section, the wall temperature of the loop began to increase linearly and reached the highest temperature at the end of the flow passage. After entering the adiabatic section, the temperature decreased considerably. After entering the cooling section, the wall temperature quickly decreased to the set cold wall temperature. The results confirm that the cold wall temperature met the set isothermal state and that the temperature increased after exiting the cooling section.

_{w}

_{,max}under the specified hot water intake mode (i.e., the cold end circulating water flow rate of 35 mL/s). The results show that at AR = 3.5, as the heating power increased, the maximum wall temperature increased linearly from 42.1 °C (30 W) to 50.3 °C (60 W). The maximum wall temperature decreased nonlinearly with increasing AR. With AR = 6, the minimum temperatures were 39.6 °C (30 W) and 46.2 °C (60 W).

## 4. Conclusions

- It is feasible to install a rectangular thermosyphon inside a metal curtain wall to obtain solar heated water.
- When the AR increased, the maximum wall temperature decreased nonlinearly. The lowest temperature can be reduced to 39.6 °C and 46.2 °C at 30 W and 60 W, respectively, with AR = 6.
- Within the range of parameter values in this study, Nu was between 4.3 and 8.4. The higher the AR was, the higher Nu was, indicating that the AR can affect the heat transfer efficiency of the rectangular thermosyphon.
- When the rectangular thermosyphon is used inside the metal curtain wall to obtain a solar heat gain, the opaque part of the metal curtain wall can be raised to give the thermosyphon a higher AR to enhance the heat transfer efficiency.
- The larger Ra* was, the lower the thermal resistance of the working fluid flow was, that is, a greater heating power or larger AR resulted in greater thermal buoyancy, thereby causing the flow to increase and the thermal resistance of the working fluid flow to decrease.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Steady-state temperature distribution of the wall of the loop with different heating powers.

**Figure 6.**Relationship between the average Nusselt number (Nu) and the modified Rayleigh number (Ra*) of the heating section.

**Figure 7.**Relationship between the thermal resistance of the working fluid flow (${R}_{flow}$) and Ra*.

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**MDPI and ACS Style**

Yu, C.-W.; Huang, C.S.; Tzeng, C.T.; Lai, C.-M.
Effects of the Aspect Ratio of a Rectangular Thermosyphon on Its Thermal Performance. *Energies* **2019**, *12*, 4014.
https://doi.org/10.3390/en12204014

**AMA Style**

Yu C-W, Huang CS, Tzeng CT, Lai C-M.
Effects of the Aspect Ratio of a Rectangular Thermosyphon on Its Thermal Performance. *Energies*. 2019; 12(20):4014.
https://doi.org/10.3390/en12204014

**Chicago/Turabian Style**

Yu, Chia-Wang, C. S. Huang, C. T. Tzeng, and Chi-Ming Lai.
2019. "Effects of the Aspect Ratio of a Rectangular Thermosyphon on Its Thermal Performance" *Energies* 12, no. 20: 4014.
https://doi.org/10.3390/en12204014