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Conservation Law of Energy Using Fractional Taylor Series

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Abstract:

Customary conservation law of energy is commonly derived using first-order Taylor series, which is only valid for situation of linear changes in the flow of energy in control volume. It is shown that using high-order Taylor series will approximate non-linear changes in the flow of energy but in fact some error remains. We used fractional Taylor series which exactly represent non-linear flow of energy in control volume. By replacing the customary integer-order Taylor series approximation with the fractional-order Taylor series approximation, limitation of the linear flow of energy in the control volume and the restriction that the control volume must be infinitesimal is omitted. The innovation of this paper is we show that as long as the order of fractional differentiation is equal with flow power-law, the fractional conservation law of energy will be exact and it can be used for fluid in a porous medium.

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Periodical:

Applied Mechanics and Materials (Volume 841)

Pages:

105-109

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.841.105

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Online since:

June 2016

Authors:

Ali Soroush*, Farzam Farahmand

Keywords:

Caputo Fractional Derivative, Conservation Law of Energy, Fractional Taylor Series

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© 2016 Trans Tech Publications Ltd. All Rights Reserved

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