## Abstract

The aim of the paper is to supply updated air convective coefficients

## 1 Introduction

The attempts to investigate energy exchange by convection in circular and cylindrical bodies wherein the determination of power losses, energy rate, the thermal behavior among a system and its surroundings and the development of thermal models for specific industrial applications are of utmost relevance. Taking into consideration the importance of accurately creating thermal models, convection must be analyzed at a certain level of fidelity. It could appear that heat convection is merely obtained by multiplying an average convection coefficient

Based on the information contained in the preceding paragraph, this article presents an analysis to determine the average convection coefficient of air

## 2 Materials and methods

Explicitly, flow forced convection is generated by external means wherewith air velocity is changed. By the application of three correlations stated by [4–6] the average convection coefficient is determined when air particles are in contact with the surface wall of a steel cylindrical rod as it is shown in Fig. 1.

### 2.1 Heat transfer in a single tube in air cross-flow

As it is previously mentioned, heat is influenced by several factors that are cumbersome to perform analytically. However, on account of the work by Zukauskas, Churchill et al. and Hilpert, [4–6] empirical correlations to determine the Nusselt number were established, thereby average convective coefficients can be calculated.

#### 2.1.1 Zukauskas's correlation

*c*and

*m*are constants that for different Reynolds numbers can be found in [4].

#### 2.1.2 Churchill and Bernstein's correlation

#### 2.1.3 Hilpert's correlation

A range of Reynolds numbers were determined for air flow speeds of

Nusselt vs. Reynolds number at *v* = 0.5–5 m s^{−1}

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Nusselt vs. Reynolds number at *v* = 0.5–5 m s^{−1}

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Nusselt vs. Reynolds number at *v* = 0.5–5 m s^{−1}

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Average convective coefficient

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Average convective coefficient

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Average convective coefficient

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

### 2.2 Lumped heat capacity model LHC

## 3 Results

The average heat convection coefficient of air

Heat convection coefficient,

0.5 | 12.31 | 13.57 | 11.60 |

1.0 | 18.65 | 19.32 | 16.03 |

1.5 | 23.79 | 23.85 | 19.37 |

2.0 | 28.28 | 27.75 | 22.23 |

2.5 | 32.33 | 31.24 | 25.52 |

3.0 | 36.07 | 34.45 | 28.56 |

3.5 | 39.56 | 37.44 | 31.42 |

4.0 | 42.86 | 40.26 | 34.12 |

4.5 | 46.00 | 42.95 | 36.70 |

5.0 | 49.01 | 45.52 | 39.17 |

LHC analysis was performed during a period of time *t* = 30 min until steady state conditions were obtained, i.e.,

Temperature distribution, Zukauskas correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Zukauskas correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Zukauskas correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Churchill correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Churchill correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Churchill correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Hilpert correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Hilpert correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution, Hilpert correlation

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

As it is illustrated in the previous figures, the steady state temperature was reached at the maximum air speed of *v* = 5 m s^{−1}. The final temperature for the three different correlations were compared and evaluated by FEA.

### 3.1 FEA simulation

Finite element analysis using ANSYS Fluent code was performed in a 2D geometry field considering that air velocity

To illustrate, the isothermal behavior at maximum air velocity

Isothermal image at

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Isothermal image at

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Isothermal image at

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Analytical and FEA solutions using edge sizing feature with quadrilateral dominant method performed during a simulation time of

Analytical and FEA comparison a

T(t) [ | T(t) [ | sd | T(t) [ | T(t) [ | sd | T(t) [ | T(t) [ | sd | |

1) Zukauskas C. | 2) Churchill C. | 3) Hilpert C. | |||||||

1.00 | 37.33 | 37.34 | 0.00 | 36.90 | 36.91 | 0.30 | 39.21 | 39.22 | 1.30 |

2.00 | 32.49 | 32.49 | 0.00 | 32.69 | 32.69 | 0.14 | 35.19 | 35.21 | 1.92 |

3.00 | 30.16 | 30.16 | 0.00 | 30.56 | 30.56 | 0.28 | 32.37 | 32.42 | 1.59 |

4.00 | 28.84 | 28.87 | 0.02 | 29.28 | 29.29 | 0.29 | 30.60 | 30.65 | 1.25 |

5.00 | 28.02 | 28.05 | 0.02 | 28.45 | 28.47 | 0.29 | 29.48 | 29.51 | 1.03 |

Temperature distribution at steady state conditions

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution at steady state conditions

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

Temperature distribution at steady state conditions

Citation: Pollack Periodica 18, 2; 10.1556/606.2023.00768

From Table 2 it is clear that more accurate results are obtained using the first correlation since the Standard Deviation

## 4 Conclusions

The determination of sundry convective coefficients of air

The most accurate correlation that can be applied in phenomena with air in cross-flow over cylindrical bodies is Zukauskas correlation since the standard deviation

$sd=0.02$ is lower than the two other correlations;The applicability of the presented average convective coefficients of air are suitable under phenomena with Reynolds numbers in the range from

$1040\le \mathrm{R}\mathrm{e}\le 10400$ . It occurs due to the characteristics of the geometry in study and the air velocity conditions;The findings of this study hold important implications for convective analysis in mechanical systems featuring cylindrical components. Specifically, the insights gained from the present work can be readily applied to a wide range of rotary machinery, including shafts, gears, roller bearings, seals, and other components where heat transfer occurs between the solid body and the surrounding air. This revision provides a clearer explanation of the relevance and scope of the research, and offers a more specific and engaging description of the types of mechanical elements to which the results can be applied.

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