### Abstract

In this paper, we consider the heat transfer problems associated with a periodic array of triangular, longitudinal, axisymmetric, and pin fins. The problems are modeled as a wall where the flat side is isothermal and the other side, which has extended surfaces/fins, is subjected to convection with a uniform heat transfer coefficient. Hence, our analysis differs from the classical approach because (i) we consider multidimensional heat conduction and (ii) the wall on which the fins are attached is included in the analysis. The latter results in a nonisothermal temperature distribution along the base of the fin. The Biot number (Bi 1/4 ht=k) characterizing the heat transfer process is defined with respect to the thickness/diameter of the fins (t). Numerical results demonstrate that the fins would enhance the heat transfer rate only if the Biot number is less than a critical value, which, in general, depends on the geometrical parameters, i.e., the thickness of the wall, the length of the fins, and the period. For pin fins, similar to rectangular fins, the critical Biot number is independent of the geometry and is approximately equal to 3.1. The physical argument is that, under strong convection, a thick fin introduces an additional resistance to heat conduction.

Original language | English |
---|---|

Article number | 044502 |

Journal | Journal of Thermal Science and Engineering Applications |

Volume | 9 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2017 |

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### Keywords

- Axisymmetric and pin fins
- Critical Biot number
- Fin effectiveness
- Heat conduction
- Longitudinal
- Triangular
- Uniform heat transfer coefficient

### ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics
- Engineering(all)
- Fluid Flow and Transfer Processes

### Cite this

*Journal of Thermal Science and Engineering Applications*,

*9*(4), [044502]. https://doi.org/10.1115/1.4035971

**Critical biot numbers of periodic arrays of fins.** / Fyrillas, Marios M.; Ospanov, Sayat; Kaibaldiyeva, Ulmeken.

Research output: Contribution to journal › Article

*Journal of Thermal Science and Engineering Applications*, vol. 9, no. 4, 044502. https://doi.org/10.1115/1.4035971

}

TY - JOUR

T1 - Critical biot numbers of periodic arrays of fins

AU - Fyrillas, Marios M.

AU - Ospanov, Sayat

AU - Kaibaldiyeva, Ulmeken

PY - 2017/12/1

Y1 - 2017/12/1

N2 - In this paper, we consider the heat transfer problems associated with a periodic array of triangular, longitudinal, axisymmetric, and pin fins. The problems are modeled as a wall where the flat side is isothermal and the other side, which has extended surfaces/fins, is subjected to convection with a uniform heat transfer coefficient. Hence, our analysis differs from the classical approach because (i) we consider multidimensional heat conduction and (ii) the wall on which the fins are attached is included in the analysis. The latter results in a nonisothermal temperature distribution along the base of the fin. The Biot number (Bi 1/4 ht=k) characterizing the heat transfer process is defined with respect to the thickness/diameter of the fins (t). Numerical results demonstrate that the fins would enhance the heat transfer rate only if the Biot number is less than a critical value, which, in general, depends on the geometrical parameters, i.e., the thickness of the wall, the length of the fins, and the period. For pin fins, similar to rectangular fins, the critical Biot number is independent of the geometry and is approximately equal to 3.1. The physical argument is that, under strong convection, a thick fin introduces an additional resistance to heat conduction.

AB - In this paper, we consider the heat transfer problems associated with a periodic array of triangular, longitudinal, axisymmetric, and pin fins. The problems are modeled as a wall where the flat side is isothermal and the other side, which has extended surfaces/fins, is subjected to convection with a uniform heat transfer coefficient. Hence, our analysis differs from the classical approach because (i) we consider multidimensional heat conduction and (ii) the wall on which the fins are attached is included in the analysis. The latter results in a nonisothermal temperature distribution along the base of the fin. The Biot number (Bi 1/4 ht=k) characterizing the heat transfer process is defined with respect to the thickness/diameter of the fins (t). Numerical results demonstrate that the fins would enhance the heat transfer rate only if the Biot number is less than a critical value, which, in general, depends on the geometrical parameters, i.e., the thickness of the wall, the length of the fins, and the period. For pin fins, similar to rectangular fins, the critical Biot number is independent of the geometry and is approximately equal to 3.1. The physical argument is that, under strong convection, a thick fin introduces an additional resistance to heat conduction.

KW - Axisymmetric and pin fins

KW - Critical Biot number

KW - Fin effectiveness

KW - Heat conduction

KW - Longitudinal

KW - Triangular

KW - Uniform heat transfer coefficient

UR - http://www.scopus.com/inward/record.url?scp=85018513944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018513944&partnerID=8YFLogxK

U2 - 10.1115/1.4035971

DO - 10.1115/1.4035971

M3 - Article

AN - SCOPUS:85018513944

VL - 9

JO - Journal of Thermal Science and Engineering Applications

JF - Journal of Thermal Science and Engineering Applications

SN - 1948-5085

IS - 4

M1 - 044502

ER -