Conduction through a grooved surface and Sierpinsky fractals

A. R. Kacimov, Yu V. Obnosov

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Conduction in a semi-infinite wall with a grooved line of contact between the wall material and convective environment is studied using series expansions. A periodic composition of semicircles is shown to result in a uniform gradient distribution at specific values of the groove radius and the convection heat transfer coefficient. Two fractal parquets exposed to natural thermal gradients are studied by the methods of complex analysis. In double periodic patterns each elementary cell is fractal (Sierpinsky's carpet and Sierpinsky's gasket) in which 'dark' and 'light' phases have arbitrary conductivities. The Maxwell approximation is used to calculate effective characteristics of both fractal structures by 'homogenization' of the environment of an 'inclusion'. Solution of an exact two-dimensional refraction problem within an elementary cell including two components is used for upscaling, i.e. recalculation of effective conductivities and dissipations of subfractals of consequently increasing order.

Original languageEnglish
Pages (from-to)623-628
Number of pages6
JournalInternational Journal of Heat and Mass Transfer
Volume43
Issue number4
DOIs
Publication statusPublished - Feb 2000

Fingerprint

Fractals
fractals
conduction
conductivity
gradients
homogenizing
heat transfer coefficients
Refraction
cells
series expansion
grooves
Thermal gradients
Heat transfer coefficients
refraction
convection
dissipation
inclusions
radii
Chemical analysis
approximation

Keywords

  • Effective conductivity
  • Fractal
  • Homogenization
  • Refraction
  • Upscaling

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Energy(all)
  • Mechanical Engineering

Cite this

Conduction through a grooved surface and Sierpinsky fractals. / Kacimov, A. R.; Obnosov, Yu V.

In: International Journal of Heat and Mass Transfer, Vol. 43, No. 4, 02.2000, p. 623-628.

Research output: Contribution to journalArticle

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