# Determination of Heat Transfer Coefficient from Housing Surface of a Totally Enclosed Fan-Cooled Machine during Passive Cooling

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analytical Background of Heat-Transfer Coefficient

_{0}). This coefficient indicates the effect of the heat transfer by radiation and the convection phenomena, and is described as:

_{c}and h

_{r}are convection and radiation coefficients (W/m

^{2}/K), respectively.

#### 2.1. Natural Convection

^{2}), ΔT is the temperature difference between the surface and the ambiance (°C), ρ is the fluid density (kg/m

^{3}), μ is the dynamic fluid viscosity (kg/s/m), and c

_{p}is the fluid specific heat capacity (kJ/kg/°C).

- Horizontal cylinder as a fin channel base.
- Horizontal U-shaped fin channels as semi-open fin channels on the top and bottom of the housing.
- Horizontal flat plate (upper and lower) as semi-open fin channels on the side of the housing.
- Horizontal and vertical flat plates as fin tips; and
- Vertical plates as end caps.

^{5}< Gr·Pr < 10

^{8}) and turbulent mode (Gr·Pr > 10

^{8}) are, respectively, as [19,20]:

^{4}< Gr·Pr < 10

^{9}) and turbulent (Gr·Pr > 10

^{9}) modes are defined based on McAdams’ research, respectively, as [20]:

^{4}< Gr·Pr < 10

^{9}) and turbulent (Gr·Pr > 10

^{9}) are, respectively, [20]:

#### 2.2. Radiation

_{r}) is defined as [25,26,27]:

^{−8}(W/m

^{2}/K

^{4})], F is the view factor, and T

_{1}and T

_{2}are the radiating surface temperature and absorbing surfaces temperature (K), respectively.

## 3. Analytical Analysis Approach

_{0}) of TEFC housing is calculated by the area-based composite method as:

_{1}is the heat transfer coefficient from primary form one (W/m

^{2}/K), A

_{1}is the primary form one area (m

^{2}), h

_{2}is the heat transfer coefficient primary form two (W/m

^{2}/K), A

_{2}is the primary form two area (m

^{2}), and A

_{T}is the total TEFC housing surface (m

^{2}).

## 4. Experimental Methodology and Analysis Method of Experimental Data

#### 4.1. Experimental Methodology

#### 4.2. Collected Data Analysis Approach

_{T}) was determined. In the DC test, the total heat equalled DC stator copper losses, which was easily determined by the collected value of current and voltage as:

#### 4.3. Uncertainty Analysis

_{QT}) was determined as:

_{V}and w

_{I}are the measurement accuracy of voltage and current, respectively.

_{T}is the measurement accuracy of K-type thermocouple.

## 5. Validation and Discussion

_{T}) value was calculated by (16). Then, the convection coefficient value (h

_{0}) was determined using (17). In the analytical calculation stage, the TEFC housing was divided into several primary shapes (Table 2), and the convection coefficient of each primary body was calculated using appropriate correlations. For the radiation calculation, the hypothesis proposed by Staton was used to determine the view factor. Finally, using the area-based composite approach, the total heat transfer coefficient was calculated (15).

_{0}). Table 3 shows the analytical results, including the radiation phenomenon, and Table 4 shows the analytical results, which excluded the radiation phenomenon. Finally, Table 5 demonstrates the experimental results of the DC stator test.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Horizontal fin channel schematic [23].

**Figure 6.**Analytical and experimental results of the heat-transfer coefficient versus temperature difference of TEFC housing and ambient.

Mean Fin’s Length (mm) | Mean Fin’s Height (mm) | Mean Fin’s Spacing (mm) | Number of Fins | |
---|---|---|---|---|

Fins on the top of the housing | 34.38 | 24.37 | 11.86 | 12 |

Fins on the underside of the housing | 184.25 | 24.37 | 11.86 | 12 |

Fins on the sides of the housing | 180.75 | 24.83 | 9.70 | 30 |

Component | Convection Correlation | Emissivity | View Factor | Area (m ^{2}) |
---|---|---|---|---|

Fin base | Horizontal cylinder | 0.8 | 1 | 0.0918 |

Fins on top of the housing | Horizontal fin channel | 0.8 | 0 | 0.0201 |

Fins on undersides of the housing | Horizontal fin channel | 0.8 | 0 | 0.1078 |

Fins on the sides of the housing | Horizontal flat plate (upper and lower faces) | 0.8 | 0 | 0.2692 |

Fin tips | Horizontal and vertical flat plate | 0.8 | 1 | 0.0209 |

End caps | Vertical flat plate | 0.8 | 1 | 0.0831 |

V (v) | T_{s}(°C) | T_{a}(°C) | h_{0}(W/m ^{2}/K) |
---|---|---|---|

15 | 42 | 20.5 | 6.91 |

17 | 47 | 21.6 | 7.14 |

19 | 51.5 | 20.8 | 7.39 |

22 | 61 | 21.6 | 7.78 |

25 | 64.5 | 21.2 | 7.93 |

V (v) | T_{s}(°C) | T_{a}(°C) | h_{0}(W/m ^{2}/K) |
---|---|---|---|

15 | 42 | 20.5 | 4.95 |

17 | 47 | 21.6 | 5.13 |

19 | 51.5 | 20.8 | 5.34 |

22 | 61 | 21.6 | 5.62 |

25 | 64.5 | 21.2 | 5.73 |

V (v) | I (A) | T_{s}(°C) | T_{a}(°C) | Q_{T}(W) | h_{0}(W/m ^{2}/K) |
---|---|---|---|---|---|

15 | 6.45 | 42 | 20.5 | 96.75 | 6.37 |

17 | 7.12 | 47 | 21.6 | 121.04 | 6.76 |

19 | 7.79 | 51.5 | 20.8 | 148.01 | 6.93 |

22 | 8.71 | 61 | 21.6 | 191.62 | 7.47 |

25 | 9.57 | 64.5 | 21.2 | 239.25 | 7.65 |

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**MDPI and ACS Style**

Shams Ghahfarokhi, P.; Podgornovs, A.; Kallaste, A.; Cardoso, A.J.M.; Belahcen, A.; Vaimann, T.; Asad, B.; Tiismus, H.
Determination of Heat Transfer Coefficient from Housing Surface of a Totally Enclosed Fan-Cooled Machine during Passive Cooling. *Machines* **2021**, *9*, 120.
https://doi.org/10.3390/machines9060120

**AMA Style**

Shams Ghahfarokhi P, Podgornovs A, Kallaste A, Cardoso AJM, Belahcen A, Vaimann T, Asad B, Tiismus H.
Determination of Heat Transfer Coefficient from Housing Surface of a Totally Enclosed Fan-Cooled Machine during Passive Cooling. *Machines*. 2021; 9(6):120.
https://doi.org/10.3390/machines9060120

**Chicago/Turabian Style**

Shams Ghahfarokhi, Payam, Andrejs Podgornovs, Ants Kallaste, Antonio J. Marques Cardoso, Anouar Belahcen, Toomas Vaimann, Bilal Asad, and Hans Tiismus.
2021. "Determination of Heat Transfer Coefficient from Housing Surface of a Totally Enclosed Fan-Cooled Machine during Passive Cooling" *Machines* 9, no. 6: 120.
https://doi.org/10.3390/machines9060120