Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion
The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0< r < R) and a matrix (R < r < ∞) being in perfect thermal contact at r = R is considered. The heat conduction in each region is described by the time-fractional heat conduction equa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/15/10/4122 |
| Summary: | The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0< r < R) and a matrix (R < r < ∞) being in perfect thermal contact at r = R is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 0 < a ≤ 2 and 0 < β ≤ 2, respectively. The Laplace transform with respect to time is used. The approximate solution valid for small values of time is obtained in terms of the Mittag-Leffler, Wright, and Mainardi functions. |
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| ISSN: | 1099-4300 |