Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell
This problem deals with the thermo-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic orthotropic spherical shell in the context of a new consideration of heat conduction with fractional order generalized thermoelasticity. Using the Lapl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014000700005&lng=en&tlng=en |
| _version_ | 1818291488395624448 |
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| author | A. Sur M. Kanoria |
| author_facet | A. Sur M. Kanoria |
| author_sort | A. Sur |
| collection | DOAJ |
| description | This problem deals with the thermo-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic orthotropic spherical shell in the context of a new consideration of heat conduction with fractional order generalized thermoelasticity. Using the Laplace transformation, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by eigen value approach and operator theory analysis. The inversion of the transformed solution is carried out by applying a method of Bellman et al (1966). Numerical estimates for thermophysical quantities are obtained for copper like material for weak, normal and strong conductivity and have been depicted graphically to estimate the effects of the fractional order parameter. Comparisons of the results for different theories (TEWED (GN-III), three-phase-lag model) have also been presented and the effect of viscosity is also shown. When the material is isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature. |
| first_indexed | 2024-12-13T02:44:52Z |
| format | Article |
| id | doaj.art-eba3a0da0b2f4ad9b61b4e84616029a0 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-13T02:44:52Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-eba3a0da0b2f4ad9b61b4e84616029a02022-12-22T00:02:13ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-78251171132116210.1590/S1679-78252014000700005S1679-78252014000700005Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shellA. Sur0M. Kanoria1University of CalcuttaUniversity of CalcuttaThis problem deals with the thermo-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic orthotropic spherical shell in the context of a new consideration of heat conduction with fractional order generalized thermoelasticity. Using the Laplace transformation, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by eigen value approach and operator theory analysis. The inversion of the transformed solution is carried out by applying a method of Bellman et al (1966). Numerical estimates for thermophysical quantities are obtained for copper like material for weak, normal and strong conductivity and have been depicted graphically to estimate the effects of the fractional order parameter. Comparisons of the results for different theories (TEWED (GN-III), three-phase-lag model) have also been presented and the effect of viscosity is also shown. When the material is isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014000700005&lng=en&tlng=enGeneralized thermo-visco-elasticityThree-phase-lag modelFractional order heat equationEigen value approachVector-matrix differential equationStep input temperatures |
| spellingShingle | A. Sur M. Kanoria Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell Latin American Journal of Solids and Structures Generalized thermo-visco-elasticity Three-phase-lag model Fractional order heat equation Eigen value approach Vector-matrix differential equation Step input temperatures |
| title | Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell |
| title_full | Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell |
| title_fullStr | Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell |
| title_full_unstemmed | Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell |
| title_short | Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell |
| title_sort | fractional heat conduction with finite wave speed in a thermo visco elastic spherical shell |
| topic | Generalized thermo-visco-elasticity Three-phase-lag model Fractional order heat equation Eigen value approach Vector-matrix differential equation Step input temperatures |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014000700005&lng=en&tlng=en |
| work_keys_str_mv | AT asur fractionalheatconductionwithfinitewavespeedinathermoviscoelasticsphericalshell AT mkanoria fractionalheatconductionwithfinitewavespeedinathermoviscoelasticsphericalshell |