# Heat Transfer Investigation during Condensation on the Horizontal Pipe

^{*}

## Abstract

**:**

## 1. Introduction

- The heat flux is assumed to equal the rate of heat absorption by the coolant$$q=\frac{{\dot{G}}_{w}({h}_{out}-{h}_{in})}{F},$$
- The heat flux is calculated through direct measurement of the condensate mass flow rate from the heat exchange surface$$q=\frac{{\dot{G}}_{c}{i}_{fg}}{F},$$
- The heat flux is assumed to equal the longitudinal conductive heat flux in the condensing wall$$q=k\frac{\Delta {T}_{w}}{\Delta x},$$
- The heat flux is calculated according to Newton’s cooling law$$q=\frac{{T}_{w}-{T}_{cw}}{R},$$

- The method allows us to determine the heat flux during condensation on various surfaces.
- It allows us to measure the flow of condensate without the need to separate the main one, formed on the experimental model, and the additional one, formed on the setup case.
- The method leads to a decrease in the number of measuring probes.

## 2. Experimental Procedure

#### 2.1. Gradient Heatmetry

#### 2.2. GHFS Type Selection

- The local heat flux by the GHFS (${q}_{GHFS}$) and HGHFS (${q}_{HGHFS}$).
- The temperature of the copper pipe outer surface (${T}_{surf}$) by the L-type thermocouple.
- The temperature difference ($\Delta T$) between inlet and outlet cooling water by the L-type differential thermocouple.
- The cooling water (${\dot{G}}_{w}$) and condensate (${\dot{G}}_{c}$) rate.

#### 2.3. Experimental Setup

- The pipe material must be exchanged for a less thermal conductivity one. The copper’s high thermal conductivity led to temperature equalization over the pipe surface and increased the model thermal inertia which reduced the information content of the temperature measurement;
- The measuring section length must be increased to hydrodynamic flow stabilization;
- The GHFS cross area should be increased to promote the generated thermoEMF, but it is necessary to minimize GHFS width. The purpose of the study is to determine the heat flux distribution over the horizontal pipe surface, and it is necessary to reduce the azimuthal angle $\phi $ at which the heat flux is averaged;
- To eliminate distortions in the natural condensate flow, it is necessary to minimize the number of GHFS and thermocouples and develop a method for removing wires from the heat exchange surface.

#### 2.4. Uncertainty Analysis

## 3. Results

- The experimental conditions do not provide for the organization of film condensation on the surface of a horizontal pipe. According to the fluctuations on the heat flux graphs (Figure 8), the condensate flows down from the pipe surface in the form of separate rivulets. It is necessary to add visual observation of the condensate flow for an explanation of fluctuations in the heat flux recorded using GHFS.
- There is no generally accepted theoretical model for calculating the heat flux during not-filmwise and not-dropwise condensation. Comparison of the results with the Nusselt model for film condensation is irrelevant. Therefore, in continued investigation, the regime conditions should be expanded to achieve film condensation on a horizontal pipe.

## 4. Discussion

- The experiment result indicates that the HTC maximum corresponds to the region of $\phi $ = 30…75${}^{\circ}$.
- The HTC becomes less than the value on the upper generatrix only in the lower pipe region in the range of $\phi $ = 150…180${}^{\circ}$.
- Theoretically, the HTC is equal to zero on the lower pipe generatrix. However, in practice this is not possible because then the thickness of the condensate film is equal to an infinitely large value. The experiment results indicate HTCs decrease in the lower pipe region which is associated with a sub-bottom zone formation.

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Time-dependent heat flux graph by HGHFS for condensation of saturated steam on the upper generatrix of the pipe at the surface temperature: (

**a**)—322 K; (

**b**)—337 K; (

**c**)—354 K; (

**d**)—362 K.

**Figure 4.**Time-dependent heat flux graph by GHFS for condensation of saturated steam on the upper generatrix of the pipe at the surface temperature: (

**a**)—322 K; (

**b**)—337 K; (

**c**)—354 K; (

**d**)—362 K.

**Figure 5.**Time-dependent heat flux graph by GHFS for the regime without cooling (at the ${\dot{G}}_{w}$ = 0).

**Figure 8.**Time-dependent heat flux graph for saturated steam condensation on the horizontal pipe at the azimuthal angle $\phi $ of: (

**a**)—0${}^{\circ}$; (

**b**)—45${}^{\circ}$; (

**c**)—60${}^{\circ}$; (

**d**)—75${}^{\circ}$; (

**e**)—165${}^{\circ}$; (

**f**)—180${}^{\circ}$.

**Figure 9.**Angular heat flux graph for saturated steam condensation on the outer surface of a horizontal pipe.

Sensor Type | Material | Sizes, mm | Volt-Watt Sensitivity S${}_{0}$, $\mathsf{\mu}$V/W Depending on Temperature | |
---|---|---|---|---|

T = 322 K | T = 372 K | |||

GHFS | single-crystal bismuth | 3 × 3 × 0.2 | 2810 | 2810 |

HGHFS | copper–nickel composition | 5 × 5 × 0.2 | 21.5 | 19.3 |

No | ${\mathit{q}}_{\mathit{GHFS}}$ | ${\mathit{q}}_{\mathit{HGHFS}}$ | ${\mathit{T}}_{\mathit{surf}}$ | ${\Delta}\mathit{T}$ | ${\dot{\mathit{G}}}_{\mathit{w}}$ | ${\dot{\mathit{G}}}_{\mathit{c}}$ |
---|---|---|---|---|---|---|

kW/m${}^{2}$ | K | g/s | ||||

1 | 66.4 | 64.8 | 322 | 1.5 | 120 | 0.34 |

2 | 55.9 | 56.6 | 337 | 3.6 | 41 | 0.28 |

3 | 34.4 | 35.7 | 354 | 9.0 | 9.6 | 0.17 |

4 | 24.8 | 23.7 | 362 | 9.5 | 9.0 | 0.13 |

5 | 2.9 | 0 | 372 | 0 | 0 | - |

Sensor Type | Material | Sizes, mm | Volt–Watt Sensitivity ${\mathit{S}}_{0}$, mV/W |
---|---|---|---|

GHFS | single-crystal bismuth | 2.5 × 10 × 0.2 | 2.65 |

Quantity, ${\mathit{X}}_{\mathit{i}}$ | Estimate, ${\mathit{x}}_{\mathit{i}}$ | Standard Uncertainty, $\mathit{u}\left({\mathit{x}}_{\mathit{i}}\right)$ | Uncertainty Contribution, $\mathit{u}\left({\mathit{y}}_{\mathit{i}}\right)$ |
---|---|---|---|

E | 9341 $\mathsf{\mu}$V | 35.0 $\mathsf{\mu}$V | 528 W/m${}^{2}$ |

${S}_{0}$ | 2650 $\mathsf{\mu}$V/W | 67.4 $\mathsf{\mu}$V/W | 3582 W/m${}^{2}$ |

A | 25 × 10${}^{-6}$ m${}^{2}$ | 10.7 × 10${}^{-8}$ m${}^{2}$ | 605 W/m${}^{2}$ |

Quantity, ${\mathit{X}}_{\mathit{i}}$ | Estimate, ${\mathit{x}}_{\mathit{i}}$ | Standard Uncertainty, $\mathit{u}\left({\mathit{x}}_{\mathit{i}}\right)$ | Uncertainty Contribution, $\mathit{u}\left({\mathit{y}}_{\mathit{i}}\right)$ |
---|---|---|---|

q | 141,060 W/m${}^{2}$ | 3670 W/m${}^{2}$ | 142.8 W/(m${}^{2}$ K) |

$\Delta T$ | 25.6 K | 1 K | 215.2 W/(m${}^{2}$ K) |

$\mathit{\phi}$, ${}^{\circ}$ | q, kW/m${}^{2}$ | T, K |
---|---|---|

0 | 117.57 | 350.0 |

15 | 116.32 | 350.5 |

30 | 131.13 | 349.6 |

45 | 176.41 | 348.9 |

60 | 181.13 | 346.9 |

75 | 173.34 | 348.2 |

90 | 156.86 | 346.9 |

105 | 161.15 | 346.9 |

120 | 157.94 | 347.0 |

135 | 137.93 | 346.9 |

150 | 159.04 | 345.5 |

165 | 95.73 | 344.1 |

180 | 94.23 | 344.1 |

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**MDPI and ACS Style**

Zainullina, E.R.; Mityakov, V.Y.
Heat Transfer Investigation during Condensation on the Horizontal Pipe. *Inventions* **2023**, *8*, 2.
https://doi.org/10.3390/inventions8010002

**AMA Style**

Zainullina ER, Mityakov VY.
Heat Transfer Investigation during Condensation on the Horizontal Pipe. *Inventions*. 2023; 8(1):2.
https://doi.org/10.3390/inventions8010002

**Chicago/Turabian Style**

Zainullina, Elza R., and Vladimir Yu. Mityakov.
2023. "Heat Transfer Investigation during Condensation on the Horizontal Pipe" *Inventions* 8, no. 1: 2.
https://doi.org/10.3390/inventions8010002