# Thermal Effect of Cylindrical Heat Sink on Heat Management in LED Applications

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. The studies carried out by Salah and Hamida, [13] also adduced a similar pattern and substantiated the finding of Mjallal et al. [12].

## 2. Materials and Methods

#### 2.1. Description of Model

#### 2.2. Materials

#### 2.3. Load and Boundary Conditions

^{2}K) was applied to the surface of the heat sink. The power supplied through the LED chip is as follows: 4.55 W, 9.7 W, 15.03 W, 20.6 W, and 25.75 W, respectively. The simulation time was set at 3600 s (this time is enough for the heat sink to reach steady state temperature), whilst the simulation step increase was determined automatically by the ANSYS simulation machine after the initial start time, number of steps, and end time were specified. In fact, ANSYS Workbench has the capacity to determine the solver steps to ensure the solution converges. However, if the solution does not converge within the specified conditions, it will flag the results obtained to be checked and settings updated.

#### Governing Equation

## 3. Results and Discussion

#### 3.1. Mesh Dependency Study

#### 3.2. Effect of Power on Heat Sink Temperature

#### 3.3. Effect of Thermal Resistance on the Cylindrical Heat Sink

#### 3.4. Thermal Efficiency Analysis

_{f}, the convection coefficient of the cylindrical heat sink fins; ${L}_{f}$ denotes the height of the cylindrical heat sink fin and ${t}_{f}$, the thickness of the cylindrical heat sink fin. In Figure 11, the thermal efficiency at different thicknesses for different power inputs is shown to follow a similar pattern (increasing with power). It is observed that the thermal efficiency increased with the increased power input for the different cylindrical heat sink fin thicknesses. This is valid since the power inputs had no effect on the thermal resistance of the heat sink. This meant that as the power is increased, the heat transfer rate is increased, thereby increasing the thermal efficiency. The thermal efficiency is a factor of how fast heat is removed from the system to the environment. Therefore, a high heat transfer rate will improve the system, whilst a slow heat transfer rate could lead to heat retention and the possible failure of the system. As shown in Figure 12, the comparison between the calculated and simulated thermal efficiencies at a power rating of 25.75 W is presented. The calculated and simulated thermal efficiencies were observed to increase with increased cylindrical heat sink fin thickness (this is a function of the volume). According to Wakefield-Vette [24], the efficiency of fins will increase when the fin thickness increases; this is observed in Figure 11 and Figure 12. At 6 mm, 5 mm, 4 mm, 3 mm, and 2 mm thickness, the calculated thermal efficiency was higher than the simulated thermal efficiency with 15.67%, 14.20%, 12.27%, 8.58%, and 1.2%, respectively. Therefore, the accuracy between the calculated and simulated thermal efficiency ranges from 84.33% to 98.80%. It could be contingent that an increase in the cylindrical heat sink thickness may cause the calculated thermal efficiency to further drift away from the simulated thermal efficiency.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{p} | constant pressure specific heat [J/(kg.°C)] |

g | gravitational acceleration [m/s^{2}] |

h_{f} | the convection coefficient |

k | thermal conductivity [W/(m.°C)] |

L_{f} | the height of fin [m] |

M | mass [kg] |

n | number of fins |

p | pressure [Pa] |

Q | heat flow/power [W] |

R | thermal resistance [°C/W] |

t_{f} | the thickness of fin |

T | temperature [°C] |

T_{∞} | the ambient temperature |

u, v, w | Cartesian velocity components [m/s] |

x, y, z | Cartesian coordinates [m] |

V | the volume [m^{3}] |

Greek symbols | |

α | thermal diffusivity [m^{2}/s] |

β | coefficient of thermal expansion [1/K] |

ρ | density [kg/m^{3}] |

## References

- Todorov, D.G.; Kapisazov, L.G. Led Thermal Management. Electronics
**2008**, 2008, 139–144. [Google Scholar] - Buergel, E. Design of LEDS—Heat Management Challenge. Auto Tech. Rev.
**2012**, 1, 40–43. [Google Scholar] [CrossRef] - Costa, V.A.F.; Lopes, A.M.G. Improved Radial Heat Sink for LED Lamp Cooling. Appl. Therm. Eng.
**2014**, 70, 131–138. [Google Scholar] [CrossRef] - Ekpu, M.; Bhatti, R.; Okereke, M.I.; Mallik, S.; Otiaba, K.C. Prediction and Optimization of Design Parameters of Microelec- tronic Heat Sinks. J. Emerg. Trends Eng. Appl. Sci.
**2013**, 4, 493–500. [Google Scholar] - Barbosa, J.; Simon, D.; Calixto, W. Design Optimization of a High Power LED Matrix Luminaire. Energies
**2017**, 10, 639. [Google Scholar] [CrossRef] - Tang, Y.; Lin, L.; Zhang, S.; Zeng, J.; Tang, K.; Chen, G.; Yuan, W. Thermal Management of High-power LEDs based on Integrated Heat Sink with Vapor Chamber. Energy Convers. Manag.
**2017**, 151, 1–10. [Google Scholar] [CrossRef] - Sobamowo, M.G.; Alaribe, K.C.; Adeleye, A.O. A Study on the Impact of Lorentz Force on the Thermal Behaviour of a Convective-Radiative Porous Fin using Differential Transformation Method. Int. J. Mech. Dyn. Anal.
**2020**, 6, 45–59. [Google Scholar] - Ekpu, M. Effect of Fins Arrangement on Thermal Performance in Microelectronics Devices. J. Appl. Sci. Environ. Manag.
**2018**, 22, 1797–1800. [Google Scholar] [CrossRef] - Staliulionis, Z.; Zhang, Z.; Pittini, R.; Andersen, M.A.E.; Tarvydas, P.; Noreika, A. Investigation of Heat Sink Efficiency for Electronic Component Cooling Applications. Elektron. IR Elektrotechnika
**2014**, 20, 49–54. [Google Scholar] [CrossRef] - Ashad, M.; Karamti, H.; Awrejcewicz, J.; Grzelczyk, D.; Galal, A.M. Thermal Transmission Comparison of Nano-fluids over Stretching Surface under the Influence of Magnetic Field. Micromachines
**2022**, 13, 1296. [Google Scholar] [CrossRef] - Ranjith, P.; Manimaran, A.; Praveen, A.S.; Ramesh, T. Experimental investigation of heat transfer characteristics of LED module using passive heat sinks. Int. J. Ambient. Energy
**2018**, 41, 1209–1213. [Google Scholar] [CrossRef] - Mjallal, I.; Farhat, H.; Hammoud, M.; Ali, S.; Assi, I. Improving the Cooling Efficiency of Heat Sinks through the use of Different Types of Phase Change Materials. Technologies
**2018**, 6, 5. [Google Scholar] [CrossRef] - Salah, S.B.; Hamida, M.B.B. Alternate PCM with air cavities in LED heat sink for transient thermal management. Int. J. Numer. Methods Heat Fluid Flow
**2019**, 29, 4377–4393. [Google Scholar] [CrossRef] - Chu, L.; Chang, W.; Huang, T.H. A Novel Heat Sink Design and Prototyping for LED Desk Lamps. Math. Probl. Eng.
**2015**, 1, 1–8. [Google Scholar] [CrossRef] - Wengang, H.; Lulu, W.; Zongmin, Z.; Yanhua, L.; Mingxin, L. Research on simulation and experimental of thermal performance of LED array heat sink. Procedia Eng.
**2017**, 205, 2084–2091. [Google Scholar] [CrossRef] - Jamil, M.A.; Goraya, T.S.; Rehman, A.U.; Yaqoob, H.; Ikhlaq, M.; Shahzad, M.W.; Zubair, S.M. A comprehensive design and optimization of an offset strip-fin compact heat exchanger for energy recovery systems. Energy Convers. Manag. X
**2022**, 14, 100191. [Google Scholar] - Jamil, M.A.; Din, Z.U.; Goraya, T.S.; Yaqoob, H.; Zubair, S.M. Thermal-hydraulic characteristics of gasketed plate heat exchangers as a preheater for thermal desalination systems. Energy Convers. Manag.
**2020**, 205, 112425. [Google Scholar] [CrossRef] - Ekpu, M.; Bhatti, R.; Okereke, M.I.; Mallik, S.; Otiaba, K. Fatigue life of lead-free solder thermal interface materials at varying bond line thickness in microelectronics. Microelectron. Reliab.
**2014**, 54, 239–244. [Google Scholar] [CrossRef] - Ekpu, M.; Bhatti, R.; Okereke, M.I.; Mallik, S.; Otiaba, K. The effect of thermal constriction on heat management in a microelectronic application. Microelectron. J.
**2014**, 45, 159–166. [Google Scholar] [CrossRef] - Ekpu, M. Finite Element Analysis of the Effect of Fin Geometry on Thermal Performance of Heat Sinks in Microelectronics. J. Appl. Sci. Environ. Manag.
**2019**, 23, 2059–2063. [Google Scholar] [CrossRef] - Okereke, M.I.; Ling, Y. A computational investigation of the effect of three-dimensional void morphology on the thermal resistance of solder thermal interface materials. Appl. Therm. Eng.
**2018**, 142, 346–360. [Google Scholar] [CrossRef] - Jeong, J.; Hah, S.; Kim, D.; Lee, J.H.; Kim, S. Thermal analysis of cylindrical heat sinks filled with phase change material for high-power transient cooling. Int. J. Heat Mass Transf.
**2020**, 154, 119725. [Google Scholar] [CrossRef] - Incropera, F.P.; Dewitt, D.P. Introduction to Heat Transfer, 3rd ed.; John Wiley and Sons: New York, NY, USA, 1996; pp. 1–801. [Google Scholar]
- Wakefield-Vette. Heat Sink Design Facts and Guidelines for Thermal Analysis. Available online: https://www.digikey.com/en/pdf/w/wakefield-thermal-solutions/heat-sink-design-for-thermal-analysis (accessed on 15 February 2022).

**Figure 2.**(

**a**) Mesh dependency study of the present model. (

**b**) Meshed with 108,813 nodes and 27,313 elements.

**Figure 3.**Temperature contour plot at 4.55 W: (

**a**) Isometric view of the heat sink, (

**b**) Back view of the heat sink, and (

**c**) Front view of the heat sink.

Material | Density (kg/m^{3}) | Thermal Conductivity (W/mK) | Specific Heat (J/kgK) |
---|---|---|---|

Aluminium | 2689 | 237.5 | 951 |

Silicon | 2330 | 148 | 712 |

SAC 405 | 7440 | 62 | 236 |

Heat Sink Fin Thickness (mm) | Number of Fins | Density (kg/m^{3}) | Volume of Heat Sink (mm^{3}) | Mass of Heat Sink (g) |
---|---|---|---|---|

2 | 8 | 2689 | 22,301.69 | 59.97 |

3 | 7 | 2689 | 25,117.48 | 67.54 |

4 | 6 | 2689 | 27,202.69 | 73.15 |

5 | 5 | 2689 | 28,698.9 | 77.17 |

6 | 5 | 2689 | 30,171.46 | 81.13 |

^{3}) of the heat sink base is added to the volume of the heat sink.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ekpu, M.; Ogbodo, E.A.; Ngobigha, F.; Njoku, J.E. Thermal Effect of Cylindrical Heat Sink on Heat Management in LED Applications. *Energies* **2022**, *15*, 7583.
https://doi.org/10.3390/en15207583

**AMA Style**

Ekpu M, Ogbodo EA, Ngobigha F, Njoku JE. Thermal Effect of Cylindrical Heat Sink on Heat Management in LED Applications. *Energies*. 2022; 15(20):7583.
https://doi.org/10.3390/en15207583

**Chicago/Turabian Style**

Ekpu, Mathias, Eugene A. Ogbodo, Felix Ngobigha, and Jude E. Njoku. 2022. "Thermal Effect of Cylindrical Heat Sink on Heat Management in LED Applications" *Energies* 15, no. 20: 7583.
https://doi.org/10.3390/en15207583