Abstract
In this study, experiments are conducted to measure the thermal resistances of heat sinks with cross-cut branched fins on horizontal cylinders. The experiments were conducted for several numbers of fin, heights of fins, and heat inputs. From the experimental data, the Nusselt number correlation for Rayleigh numbers of 190000–1000000, fin heights of 10–30 mm, and fin numbers of 9–36 is proposed. Using the suggested correlation, the fin thickness and fin number for maximizing the thermal performance are obtained. Finally, it is demonstrated that the optimal heat sink with cross-cut branched fins on a horizontal cylinder has 26 % lower thermal resistance than that of a conventional heat sink with plate fins.
Similar content being viewed by others
Abbreviations
- A b :
-
Heat-sink base area without attached fins [m2]
- A c :
-
Cross-sectional area of repeating unit in fin [m2]
- A f :
-
Surface area of repeating unit in fin [m2]
- B :
-
Bias error
- D :
-
Cylinder diameter [m]
- g :
-
Gravitational acceleration [m/s2]
- H :
-
Fin height [m]
- H 1 :
-
Height of stem side of branched fin [m]
- H 2 :
-
Height of branch side of branched fin [m]
- h :
-
Convective heat-transfer coefficient [W/m2K]
- k f :
-
Thermal conductivity of fluid [W/mK]
- k s :
-
Thermal conductivity of solid [W/mK]
- L :
-
Fin length [m]
- L f :
-
Repeating unit length [m]
- N :
-
Fin number
- N d :
-
Number of data
- N f :
-
Number of repeating units
- Nu :
-
Nusselt number
- Nu cyl :
-
Nusselt number for horizontal cylinder
- P :
-
Perimeter of repeating unit [m]
- Pr :
-
Prandtl number
- q :
-
Power input [W]
- R th :
-
Thermal resistance [K/W]
- Ra :
-
Rayleigh number
- S :
-
Standard deviation
- T :
-
Heat-sink base temperature [K]
- T amb :
-
Ambient temperature [K]
- t :
-
Fin thickness [m]
- t 95% :
-
t distribution for confidence level of 95 %
- U :
-
Uncertainty
- α :
-
Angle between tributary branches [°]
- α f :
-
Thermal diffusivity of fluid [m2/s]
- β f :
-
Volume expansion coefficient of fluid [1/K]
- η :
-
Fin efficiency
- v f :
-
Kinematic viscosity of fluid [m2/s]
- T :
-
Temperature [K]
- q :
-
Power input [W]
- R th :
-
Thermal resistance [K/W]
References
N. Narendran and Y. Gu, Life of LED-based white light sources, Journal of Display Technology, 1 (2005) 167–171.
X. Luo and S. Liu, A microjet array cooling system for thermal management of high-brightness LEDs, IEEE Transactions on Advanced Packaging, 30 (2007) 475–484.
X. Qu, S. C. Wong and K. T. Chi, Color control system for RGB LED light sources using junction temperature measurement, IECON 2007-33rd Annual Conference of the IEEE Industrial Electronics Society (2007) 1363–1368.
X. Qu, S.-C. Wong and K. T. Chi, Temperature measurement technique for stabilizing the light output of RGB LED lamps, IEEE Transactions on Instrumentation and Measurement, 59 (2009) 661–670.
K. E. Starner, An experimental investigation of free convection heat transfer from rectangular fin arrays, ASME Journal of Heat Transfer, 85 (1963) 273–278.
B. H. An, H. J. Kim and D.-K. Kim, Nusselt number correlation for natural convection from vertical cylinders with vertically oriented plate fins, Experimental Thermal and Fluid Science, 41 (2012) 59–66.
Q. Shen et al., Natural convection heat transfer along vertical cylinder heat sinks with longitudinal fins, International Journal of Thermal Sciences, 100 (2016) 457–464.
B. Li and C. Byon, Experimental and numerical study on the heat sink with radial fins and a concentric ring subject to natural convection, Applied Thermal Engineering, 90 (2015) 345–351.
D. Jang, S.-J. Park, S.-J. Yook and K.-S. Lee, The orientation effect for cylindrical heat sinks with application to LED light bulbs, International Journal of Heat and Mass Transfer, 71 (2014) 496–502.
G. Lorenzini and L. A. O. Rocha, Constructal design of Y-shaped assembly of fins, International Journal of Heat and Mass Transfer, 49 (2006) 4552–4557.
K. T. Park, H. J. Kim and D.-K. Kim, Experimental study of natural convection from vertical cylinders with branched fins, Experimental Thermal and Fluid Science, 54 (2014) 29–37.
K. K. Singh and M. K. Sinha, Optimization of design parameters in a cylindrical heat sink with branched fins under natural convection, Journal of Engineering, Design and Technology, 15 (2017) 242–253.
M. Ahmadi, G. Mostafavi and M. Bahrami, Natural convection from rectangular interrupted fins, International Journal of Thermal Sciences, 82 (2014) 62–71.
D. Jang, D. R. Kim and K.-S. Lee, Correlation of cross-cut cylindrical heat sink to improve the orientation effect of LED light bulbs, International Journal of Heat and Mass Transfer, 84 (2015) 821–826.
E. M. Sparrow and S. B. Vemuri, Natural convection/radiation heat transfer from highly populated pin fin arrays, Journal of Heat Transfer, 107(1) (1985) 190–197.
F. P. Incropera, D. P. DeWitt, T. L. Bergman, A. S. Lavine and F. P. Incropera, Foundations of Heat Transfer, Wiley Textbooks (2012).
S. W. Churchill and H. H. Chu, Correlating equations for laminar and turbulent free convection from a horizontal cylinder, International Journal of Heat and Mass Transfer, 18 (1975) 1049–1053.
H. J. Kim, B. H. An, J. Park and D.-K. Kim, Experimental study on natural convection heat transfer from horizontal cylinders with longitudinal plate fins, Journal of Mechanical Science and Technology, 27 (2013) 593–599.
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1070142).
Author information
Authors and Affiliations
Corresponding author
Additional information
Donghyuk Kim is a Ph.D. student in the Department of Mechanical Engineering at Ajou University, Korea. His research interests include heat transfer, photothermal therapy, and air conditioning.
Dong-Kwon Kim is a Professor in the Department of Mechanical Engineering at Ajou University, Korea. His current research interests include various air-cooled heat sinks and deep learning-based design of thermal systems.
Rights and permissions
About this article
Cite this article
Kim, D., Kim, DK. Experimental study on thermal performances of heat sinks with cross-cut branched fins on horizontal cylinders under natural convection. J Mech Sci Technol 35, 3743–3751 (2021). https://doi.org/10.1007/s12206-021-0743-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-021-0743-5