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Conduction through a grooved surface and Sierpinsky fractals

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dc.contributor.author Kacimov A.
dc.contributor.author Obnosov Y.
dc.date.accessioned 2018-09-17T20:14:44Z
dc.date.available 2018-09-17T20:14:44Z
dc.date.issued 2000
dc.identifier.issn 0017-9310
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/133233
dc.description.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. | 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.
dc.relation.ispartofseries International Journal of Heat and Mass Transfer
dc.subject Effective conductivity
dc.subject Fractal
dc.subject Homogenization
dc.subject Refraction
dc.subject Upscaling
dc.title Conduction through a grooved surface and Sierpinsky fractals
dc.type Article
dc.relation.ispartofseries-issue 4
dc.relation.ispartofseries-volume 43
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 623
dc.source.id SCOPUS00179310-2000-43-4-SID0345476320


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  • Публикации сотрудников КФУ Scopus [20180]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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