A Mathematical Model of Heat Transfer in Spheroplastic
Spheroplastics are composite materials composed of a polymer or organosilicate binder and hollow spherical inclusions (mostly, of glass, but there are also of carbon, phenol, and epoxy), which are called microspheres and have a diameter within a millimeter with the wall thickness of several micromet...
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MGTU im. N.È. Baumana
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ftdoajarticles:oai:doaj.org/article:ab56406e1ffa492a89d4d644cfe9149e 2023-05-15T17:58:11+02:00 A Mathematical Model of Heat Transfer in Spheroplastic V. S. Zarubin G. N. Kuvyrkin I. Yu. Savelyeva 2017-01-01T00:00:00Z https://doi.org/10.7463/mathm.0416.0846276 https://doaj.org/article/ab56406e1ffa492a89d4d644cfe9149e RU rus MGTU im. N.È. Baumana https://www.mathmelpub.ru/jour/article/view/49 https://doaj.org/toc/2412-5911 2412-5911 doi:10.7463/mathm.0416.0846276 https://doaj.org/article/ab56406e1ffa492a89d4d644cfe9149e Matematika i Matematičeskoe Modelirovanie, Vol 0, Iss 4, Pp 42-58 (2017) spheroplastic microspheres four-phase mathematical model effective thermal conductivity Mathematics QA1-939 article 2017 ftdoajarticles https://doi.org/10.7463/mathm.0416.0846276 2022-12-30T21:27:16Z Spheroplastics are composite materials composed of a polymer or organosilicate binder and hollow spherical inclusions (mostly, of glass, but there are also of carbon, phenol, and epoxy), which are called microspheres and have a diameter within a millimeter with the wall thickness of several micrometers. To reduce the material density in watercraft constructions sometimes are used so called macrospheres of up to 40 mm in diameter and shell thickness of 0,5--1,5 mm from spheroplastic with microspheres.Microspheres may contain inert gases such as nitrogen. Many countries have commercialised quartz microspheres. The USA, in particular, produces Q-Gel microspheres with density of 300 kg / m3, the bulk density - 100 kg / m3 and the average diameter of 75 microns,characterized by a high mechanical strength and low cost. Carbon microspheres having low mechanical properties can absorb radio waves in certain frequency ranges. Spheroplastic with silicone microspheres combine relatively high mechanical and dielectric properties.In virtue of low thermal conductivity spheroplastics are used in various heat-insulating structures. As the thermal insulation coatings, the spheroplastic covers the outer surface of the pipes, in particular oil and gas pipelines in the permafrost zones, regions of swampy ground, and underwater. The effective heat conductivity factor, primarily, determines the specific application of spheroplastic as a thermal insulation material. To quantify the value of this factor is necessary to have a mathematical model describing heat ransfer in spheroplastic.The paper presents a four-phase mathematical model of the heat transfer in a representative element of a spheroplastic structure placed in an unlimited array of homogeneous material, the thermal conductivity of which is to be determined as desired characteristics of spheroplastic. This model in combination with a dual variational formulation of stationary heat conduction problem in the inhomogeneous solid first is used to define the guaranteed two-sided ... Article in Journal/Newspaper permafrost Directory of Open Access Journals: DOAJ Articles Mathematics and Mathematical Modeling 16 04 42 58 |
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spheroplastic microspheres four-phase mathematical model effective thermal conductivity Mathematics QA1-939 |
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spheroplastic microspheres four-phase mathematical model effective thermal conductivity Mathematics QA1-939 V. S. Zarubin G. N. Kuvyrkin I. Yu. Savelyeva A Mathematical Model of Heat Transfer in Spheroplastic |
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spheroplastic microspheres four-phase mathematical model effective thermal conductivity Mathematics QA1-939 |
description |
Spheroplastics are composite materials composed of a polymer or organosilicate binder and hollow spherical inclusions (mostly, of glass, but there are also of carbon, phenol, and epoxy), which are called microspheres and have a diameter within a millimeter with the wall thickness of several micrometers. To reduce the material density in watercraft constructions sometimes are used so called macrospheres of up to 40 mm in diameter and shell thickness of 0,5--1,5 mm from spheroplastic with microspheres.Microspheres may contain inert gases such as nitrogen. Many countries have commercialised quartz microspheres. The USA, in particular, produces Q-Gel microspheres with density of 300 kg / m3, the bulk density - 100 kg / m3 and the average diameter of 75 microns,characterized by a high mechanical strength and low cost. Carbon microspheres having low mechanical properties can absorb radio waves in certain frequency ranges. Spheroplastic with silicone microspheres combine relatively high mechanical and dielectric properties.In virtue of low thermal conductivity spheroplastics are used in various heat-insulating structures. As the thermal insulation coatings, the spheroplastic covers the outer surface of the pipes, in particular oil and gas pipelines in the permafrost zones, regions of swampy ground, and underwater. The effective heat conductivity factor, primarily, determines the specific application of spheroplastic as a thermal insulation material. To quantify the value of this factor is necessary to have a mathematical model describing heat ransfer in spheroplastic.The paper presents a four-phase mathematical model of the heat transfer in a representative element of a spheroplastic structure placed in an unlimited array of homogeneous material, the thermal conductivity of which is to be determined as desired characteristics of spheroplastic. This model in combination with a dual variational formulation of stationary heat conduction problem in the inhomogeneous solid first is used to define the guaranteed two-sided ... |
format |
Article in Journal/Newspaper |
author |
V. S. Zarubin G. N. Kuvyrkin I. Yu. Savelyeva |
author_facet |
V. S. Zarubin G. N. Kuvyrkin I. Yu. Savelyeva |
author_sort |
V. S. Zarubin |
title |
A Mathematical Model of Heat Transfer in Spheroplastic |
title_short |
A Mathematical Model of Heat Transfer in Spheroplastic |
title_full |
A Mathematical Model of Heat Transfer in Spheroplastic |
title_fullStr |
A Mathematical Model of Heat Transfer in Spheroplastic |
title_full_unstemmed |
A Mathematical Model of Heat Transfer in Spheroplastic |
title_sort |
mathematical model of heat transfer in spheroplastic |
publisher |
MGTU im. N.È. Baumana |
publishDate |
2017 |
url |
https://doi.org/10.7463/mathm.0416.0846276 https://doaj.org/article/ab56406e1ffa492a89d4d644cfe9149e |
genre |
permafrost |
genre_facet |
permafrost |
op_source |
Matematika i Matematičeskoe Modelirovanie, Vol 0, Iss 4, Pp 42-58 (2017) |
op_relation |
https://www.mathmelpub.ru/jour/article/view/49 https://doaj.org/toc/2412-5911 2412-5911 doi:10.7463/mathm.0416.0846276 https://doaj.org/article/ab56406e1ffa492a89d4d644cfe9149e |
op_doi |
https://doi.org/10.7463/mathm.0416.0846276 |
container_title |
Mathematics and Mathematical Modeling |
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16 |
container_issue |
04 |
container_start_page |
42 |
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58 |
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1766166746988806144 |