Approximation of transient temperatures in complex geometries using fractional derivatives |
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Authors: | Yoshinori Aoki Mihir Sen Samuel Paolucci |
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Affiliation: | (1) Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA;(2) Present address: Japan Patent Office, 3-4-3 Kasumigaseki, Chiyoda-ku, Tokyo, Japan |
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Abstract: | It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system. |
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