# Unshrouded Plate Fin Heat Sinks for Electronics Cooling: Validation of a Comprehensive Thermal Model and Cost Optimization in Semi-Active Configuration

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis

## 3. Results and Discussion

#### 3.1. Experimental Validation

^{2}, $CB=7.47$ cm and $CH=13.07$ cm), and it dissipates the heat generated by a power transistor. Hence, the heat sink is tested (and it usually operates) in a semi-active configuration, i.e., it takes advantage of an existing fan in the HVAC. The experimental rig used to characterize the heat sink is described in the following.

^{2}and $k=209$ W/m/K. Third, ${R}_{sa}$ is calculated by means of Equations (3)–(7), considering ${c}_{p,a}=1013.4$ J/kg/K, ${k}_{a}=0.0259$ W/m/K, $\rho =1.1794$ kg/m

^{3}, and $\mu =1.8415$ × ${10}^{-5}$ kg/m/s. It is worth mentioning that the lateral area of the baseplate is not involved in the heat transfer phenomenon because the heat sink is flush-mounted on the HVAC wall during the experiments. Consequently, the overall heat transfer area ${A}_{hs}$ can be calculated as:

#### 3.2. Optimization Procedure and Results

^{3}, which is a remarkable 53% less with respect to the actual commercial heat sink volume ($37.4$ cm

^{3}). Therefore, the presented optimization procedure would allow saving $19.8$ cm

^{3}of material and thus reducing production costs, without affecting the overall thermal performances of the heat sink.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

a | air |

app | apparent |

b | baseplate |

bs | side bypass |

bt | top bypass |

ch | channel |

d | approach |

e | experimental |

f | fins |

hs | heat sink |

j | junction |

m | model |

p | spacing |

ref | reference |

s | heat source |

W | working |

## Appendix A: Detailed Model for Pressure Drops

## Appendix B: Genetic Algorithm Settings and Performances

## References

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**Figure 3.**Scheme of the bypass phenomenon. Note that the heat sink is flush-mounted in a duct with $CB\times CH$ section, where $CB$ and $CH$ are channel base and height, respectively.

**Figure 4.**Scheme of heat spreading phenomenon in a PFHS: red and yellow represent high and low temperature regions, respectively; arrows represent heat propagation paths.

L [mm] | W [mm] | ${\mathit{t}}_{\mathit{b}}$ [mm] | N [mm] | H [mm] | t [mm] | p [mm] |
---|---|---|---|---|---|---|

57.2 | 41.4 | 8.4 | 14 | 21.8 | 1 | 2.1 |

$\dot{\mathit{V}}$ [m^{3}/s] | P [W] | ${\mathit{T}}_{\mathit{j}}$ [°C] | ${\mathit{T}}_{\mathit{a}}$ [°C] | ${\mathit{v}}_{\mathit{d}}$ [m/s] | ${\mathit{R}}_{\mathit{j}\mathit{a}\mathbf{,}\mathit{e}}$ [K/W] |
---|---|---|---|---|---|

0.136 | 60.24 | 84.4 | 26.5 | 13.9 | 0.96 |

0.125 | 76.3 | 104.3 | 26.1 | 12.8 | 1.02 |

0.112 | 85.07 | 118 | 25.8 | 11.5 | 1.08 |

0.099 | 87.32 | 121.9 | 25.1 | 10.2 | 1.11 |

0.086 | 82.36 | 118.7 | 24.8 | 8.8 | 1.14 |

0.070 | 71.4 | 111 | 24.2 | 7.2 | 1.22 |

0.054 | 56.64 | 98.1 | 23.8 | 5.6 | 1.31 |

**Table 3.**Comparison between experimental results (${R}_{ja,e}$) and model predictions (${R}_{ja,m}$) for the considered commercial heat sink for different values of approach velocity (${v}_{d}$), with corresponding percent deviations ($\frac{{R}_{ja,m}-{R}_{ja,e}}{{R}_{ja,e}}\xb7100$) between model and experiments.

${\mathit{v}}_{\mathit{d}}$ | ${\mathit{R}}_{\mathit{j}\mathit{c}\mathbf{,}\mathit{m}}$ | ${\mathit{R}}_{\mathit{c}\mathit{s}\mathbf{,}\mathit{m}}$ | ${\mathit{R}}_{\mathit{s}\mathit{p}\mathit{r}\mathbf{,}\mathit{m}}$ | ${\mathit{R}}_{\mathit{s}\mathit{a}\mathbf{,}\mathit{m}}$ | ${\mathit{R}}_{\mathit{j}\mathit{a}\mathbf{,}\mathit{m}}$ | ${\mathit{R}}_{\mathit{j}\mathit{a}\mathbf{,}\mathit{e}}$ | Deviation |
---|---|---|---|---|---|---|---|

[m/s] | [K/W] | [K/W] | [K/W] | [K/W] | [K/W] | [K/W] | [%] |

13.9 | 0.5 | 0.017 | 0.133 | 0.367 | 1.017 | 0.96 | 5.82 |

12.8 | 0.5 | 0.017 | 0.133 | 0.381 | 1.031 | 1.02 | 0.59 |

11.5 | 0.5 | 0.017 | 0.133 | 0.400 | 1.050 | 1.08 | −3.14 |

10.2 | 0.5 | 0.017 | 0.133 | 0.421 | 1.071 | 1.11 | −3.38 |

8.8 | 0.5 | 0.017 | 0.133 | 0.450 | 1.100 | 1.14 | −3.57 |

7.2 | 0.5 | 0.017 | 0.133 | 0.492 | 1.142 | 1.22 | −6.10 |

5.6 | 0.5 | 0.017 | 0.133 | 0.553 | 1.203 | 1.31 | −8.31 |

Boundary type | L [mm] | W [mm] | ${\mathit{t}}_{\mathit{b}}$ [mm] | N | H [mm] | t [mm] |
---|---|---|---|---|---|---|

LB | 10 | 10 | 1 | 2 | 10 | 0.8 |

UB | 100 | 100 | 10 | 22 | 50 | 2 |

Configuration | L | W | ${\mathit{t}}_{\mathit{b}}$ | N | H | t | p | ${\mathit{V}}_{\mathit{b}}$ | ${\mathit{V}}_{\mathit{f}}$ | V |
---|---|---|---|---|---|---|---|---|---|---|

[mm] | [mm] | [mm] | [mm] | [mm] | [mm] | [mm] | [cm^{3}] | [cm^{3}] | [cm^{3}] | |

Initial | 57.2 | 41.4 | 8.4 | 14 | 21.8 | 1 | 2.1 | 19.9 | 17.5 | 37.4 |

Optimized | 20.0 | 40.0 | 4.5 | 22 | 36.4 | 0.9 | 1.0 | 3.6 | 14.0 | 17.6 |

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**MDPI and ACS Style**

Ventola, L.; Curcuruto, G.; Fasano, M.; Fotia, S.; Pugliese, V.; Chiavazzo, E.; Asinari, P.
Unshrouded Plate Fin Heat Sinks for Electronics Cooling: Validation of a Comprehensive Thermal Model and Cost Optimization in Semi-Active Configuration. *Energies* **2016**, *9*, 608.
https://doi.org/10.3390/en9080608

**AMA Style**

Ventola L, Curcuruto G, Fasano M, Fotia S, Pugliese V, Chiavazzo E, Asinari P.
Unshrouded Plate Fin Heat Sinks for Electronics Cooling: Validation of a Comprehensive Thermal Model and Cost Optimization in Semi-Active Configuration. *Energies*. 2016; 9(8):608.
https://doi.org/10.3390/en9080608

**Chicago/Turabian Style**

Ventola, Luigi, Gabriele Curcuruto, Matteo Fasano, Saverio Fotia, Vincenzo Pugliese, Eliodoro Chiavazzo, and Pietro Asinari.
2016. "Unshrouded Plate Fin Heat Sinks for Electronics Cooling: Validation of a Comprehensive Thermal Model and Cost Optimization in Semi-Active Configuration" *Energies* 9, no. 8: 608.
https://doi.org/10.3390/en9080608