THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Matjaz Ramšak

,

Leopold Škerget

HEAT DIFFUSION IN FRACTAL GEOMETRY COOLING SURFACE

ABSTRACT
In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
KEYWORDS
heat transfer, cooling of electronic devices, boundary element method, fractals
PAPER SUBMITTED: 2012-04-04
PAPER REVISED: 2012-06-26
PAPER ACCEPTED: 2012-06-27
DOI REFERENCE: https://doi.org/10.2298/TSCI1204955R
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 4, PAGES [955 - 968]
REFERENCES
  1. Huang, H., Xu, X., Effects of Surface Morphology on Thermal Contact Resistance, Thermal Science 15 (2011), Suppl. 1, pp. S33-S38
  2. Mandelbrot, B., How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, Science, New Series, 156 (1967), 3775, pp. 636-638
  3. Ramsak, M., et al., A Multidomain Boundary Element Method for Unsteady Laminar Flow Using Stream Function-Vorticity Equations, Eng Anal Bound Elem, 29 (2005), 1, pp. 1-14
  4. Ramsak, M., Skerget, L., 3-D Multidomain Bem for Solving the Laplace Equation, Eng Anal Bound Elem, 31 (2007), 6, pp. 528-538
  5. Brebbia, C. A., The Boundary Element Method for Engineers, Pentech Press, London, 1978
  6. Ramsak, M., Skerget, L., Mixed Boundary Elements for Laminar Flows, Int. J Num Meth. Fluids, 31 (1999), 5, pp. 861-877
  7. Grigoriev,M. M., Dargush, G. F., APoly-Region Boundary Elementh Method for Incompressible Viscous Fluid Flows, Int. J. Num. Meth. Fluids, 46 (1999), 7, pp. 1127-1158
  8. Ramsak, M.,
  9. Paige, C. C., Saunders, M. A., LSQR: Sparse Linear Equations and Least-Squares Problems, ACM Transactions on Mathematical Software, 8 (1982), 1, pp. 195-209 Ram{ak, M., et al.: Heat Difussion in Fractal Geometry Cooling Surface THERMAL SCIENCE: Year 2012, Vol. 16, No. 4, pp. 955-968 967
  10. Ramsak, M., Skerget, L., Iterative Least Squares Methods for Solving over-Determined Matrix for Mixed Boundary Elements, ZAMM, 80 (2000), Suppl. 3, pp. S657-S658
  11. Celik, I., Numerical Uncertainty in Fluid Flow Calculations: Needs for Future Research, ASME Journal of Fluids Engineering, 115 (1993), 2, pp. 194-195
PDF VERSION [DOWNLOAD]
Heat diffusion in fractal geometry cooling surface

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence