Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions
This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane hea...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/6439710 |
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| author | Inês Simões António Tadeu Nuno Simões |
| author_facet | Inês Simões António Tadeu Nuno Simões |
| author_sort | Inês Simões |
| collection | DOAJ |
| description | This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensional fundamental solution or 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain. |
| format | Article |
| id | doaj-art-ebd9ca5eef6d406ba0b29d6c30fe0071 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ebd9ca5eef6d406ba0b29d6c30fe00712025-02-03T06:44:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/64397106439710Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain SolutionsInês Simões0António Tadeu1Nuno Simões2ITeCons, Rua Pedro Hispano, s/n, 3030-289 Coimbra, PortugalITeCons, Rua Pedro Hispano, s/n, 3030-289 Coimbra, PortugalITeCons, Rua Pedro Hispano, s/n, 3030-289 Coimbra, PortugalThis paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensional fundamental solution or 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.http://dx.doi.org/10.1155/2016/6439710 |
| spellingShingle | Inês Simões António Tadeu Nuno Simões Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions Journal of Applied Mathematics |
| title | Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions |
| title_full | Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions |
| title_fullStr | Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions |
| title_full_unstemmed | Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions |
| title_short | Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions |
| title_sort | green s functions for heat conduction for unbounded and bounded rectangular spaces time and frequency domain solutions |
| url | http://dx.doi.org/10.1155/2016/6439710 |
| work_keys_str_mv | AT inessimoes greensfunctionsforheatconductionforunboundedandboundedrectangularspacestimeandfrequencydomainsolutions AT antoniotadeu greensfunctionsforheatconductionforunboundedandboundedrectangularspacestimeandfrequencydomainsolutions AT nunosimoes greensfunctionsforheatconductionforunboundedandboundedrectangularspacestimeandfrequencydomainsolutions |