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The Fractal Calculus for Fractal Materials

Authors :
Fakhri Khajvand Jafari
Mohammad Sadegh Asgari
Amir Pishkoo
Source :
Fractal and Fractional, Vol 3, Iss 1, p 8 (2019)
Publication Year :
2019
Publisher :
MDPI AG, 2019.

Abstract

The major problem in the process of mixing fluids (for instance liquid-liquid mixers) is turbulence, which is the outcome of the function of the equipment (engine). Fractal mixing is an alternative method that has symmetry and is predictable. Therefore, fractal structures and fractal reactors find importance. Using F α -fractal calculus, in this paper, we derive exact F α -differential forms of an ideal gas. Depending on the dimensionality of space, we should first obtain the integral staircase function and mass function of our geometry. When gases expand inside the fractal structure because of changes from the i + 1 iteration to the i iteration, in fact, we are faced with fluid mixing inside our fractal structure, which can be described by physical quantities P, V, and T. Finally, for the ideal gas equation, we calculate volume expansivity and isothermal compressibility.

Details

Language :
English
ISSN :
25043110
Volume :
3
Issue :
1
Database :
Directory of Open Access Journals
Journal :
Fractal and Fractional
Publication Type :
Academic Journal
Accession number :
edsdoj.fc3513f9763c4062b2e27d11d83311bb
Document Type :
article
Full Text :
https://doi.org/10.3390/fractalfract3010008