An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers
The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9139135 |
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| author | Vasyl Chekurin Yurij Boychuk |
| author_facet | Vasyl Chekurin Yurij Boychuk |
| author_sort | Vasyl Chekurin |
| collection | DOAJ |
| description | The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed) one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer. |
| format | Article |
| id | doaj-art-07e74b30f8c94fc5b7e7676dcd439569 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-07e74b30f8c94fc5b7e7676dcd4395692025-02-03T06:00:14ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/91391359139135An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric LayersVasyl Chekurin0Yurij Boychuk1Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Academy of Sciences of Ukraine, 3-b Naukova Str., Lviv 79060, UkrainePidstryhach Institute for Applied Problems of Mechanics and Mathematics, Academy of Sciences of Ukraine, 3-b Naukova Str., Lviv 79060, UkraineThe mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed) one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.http://dx.doi.org/10.1155/2017/9139135 |
| spellingShingle | Vasyl Chekurin Yurij Boychuk An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers Advances in Mathematical Physics |
| title | An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers |
| title_full | An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers |
| title_fullStr | An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers |
| title_full_unstemmed | An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers |
| title_short | An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers |
| title_sort | iterative method for solving of coupled equations for conductive radiative heat transfer in dielectric layers |
| url | http://dx.doi.org/10.1155/2017/9139135 |
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