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Topology of steady heat conduction in a solid slab subject to a nonuniform boundary condition: The Carslaw-Jaeger solutionâ revisited

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dc.contributor.author Kasimova R.
dc.contributor.author Obnosov Y.
dc.date.accessioned 2018-09-18T20:22:39Z
dc.date.available 2018-09-18T20:22:39Z
dc.date.issued 2012
dc.identifier.issn 1446-1811
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/139245
dc.description.abstract Temperature distributions recorded by thermocouples in a solid body (slab) subject to surface heating are used in a mathematical model of two-dimensional heat conduction. The corresponding Dirichlet problem for a holomorphic function (complex potential), involving temperature and a heat stream function, is solved in a strip. The Zhukovskii function is reconstructed through singular integrals, involving an auxiliary complex variable. The complex potential is mapped onto an auxiliary half-plane. The flow net (orthogonal isotherms and heat lines) of heat conduction is compared with the known Carslaw-Jaeger solution and shows a puzzling topology of three regimes of energy fluxes for temperature boundary conditions common in passive thermal insulation. The simplest regime is realized if cooling of a shaded zone is mild and heat flows in a slightly distorted resistor model flow tube. The second regime emerges when cooling is stronger and two disconnected separatrices demarcate the back-flow of heat from a relatively hot segment of the slab surface to the atmosphere through relatively cold parts of this surface. The third topological regime is characterized by a single separatrix with a critical point inside the slab, where the thermal gradient is nil. In this regime the back-suction of heat into the atmosphere is most intensive. The closed-form solutions obtained can be used in assessment of efficiency of thermal protection of buildings. © 2012 Australian Mathematical Society.
dc.relation.ispartofseries ANZIAM Journal
dc.subject complex potential
dc.subject conformal mappings
dc.subject heat lines
dc.subject isotherms
dc.subject Laplace's equation
dc.subject two-dimensional heat conduction
dc.title Topology of steady heat conduction in a solid slab subject to a nonuniform boundary condition: The Carslaw-Jaeger solutionâ revisited
dc.type Article
dc.relation.ispartofseries-issue 4
dc.relation.ispartofseries-volume 53
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 308
dc.source.id SCOPUS14461811-2012-53-4-SID84877997667


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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