title: Power generalization of the linear constitutive equations of heat and mass transfer and the variants of writing the equations of momentum transfer, heat and diffusion arising from them
metadata.name: dc.contributor.author
metadata.value: Pavlovsky, Valery A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T13:49:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T13:49:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Pavlovsky, V. A. (2023). Power generalization of the linear constitutive equations of heat and mass transfer and the variants of writing the equations of momentum transfer, heat and diffusion arising from them. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 18(4), 527-534.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39310
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Currently, when solving problems of heat and mass transfer, linear constitutive equations are used - in hydrodynamics, the viscous stress tensor is proportional to the strain rate tensor (Newton's rheological ratio), in heat transfer, the heat flux density is linearly related to the temperature gradient (Fourier's heat conduction law), in mass transfer, the diffusion flux density proportional to the concentration gradient (Fick's law). When writing these linear governing equations, proportionality coefficients are used, which are called the viscosity coefficient, thermal conductivity coefficient and diffusion coefficient, respectively. Such constitutive equations are widely used to describe the processes of heat and mass transfer in a laminar flow regime. For turbulent flows, these equations are unsuitable, it is necessary to introduce into consideration the empirical turbulent coefficients of viscosity μt, thermal conductivity λt and diffusion Dt. However, to describe turbulent flows, it is possible to go in another way - to modify the linear constitutive relations by giving them a nonlinear power-law form. Two-parameter power-law generalizations of Newton's, Fourier's and Fick's formulas for shear stress, heat flux density and diffusion, which, depending on the value of the exponents, can be used to describe the processes of heat and mass transfer both in laminar and turbulent fluid flow. Also, this generalization can be used to describe the behavior of power-law fluids and flows of polymer solutions exhibiting the Toms effect.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This study was carried out within the framework of the state task by Ministry of Science and Higher
  Education of the Russian Federation for the implementation of research works N 075-03-2020-094/1 of
  June 10, 2020.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: hydrodynamics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: heat transfer
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: diffusion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Newton's
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Fourier's
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Fick's formulas
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: power generalizations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: turbulence
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Power generalization of the linear constitutive equations of heat and mass transfer and the variants of writing the equations of momentum transfer, heat and diffusion arising from them
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15528-Текст статьи-52260-1-10-20230308.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39310/1/15528-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-52260-1-10-20230308.pdf
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