Analysis of the Influences of Parameters in the Fractional Second-Grade Fluid Dynamics

Mehmet Yavuz, Ndolane Sene and Mustafa Yıldız
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Mehmet Yavuz: Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Konya, Turkey
Ndolane Sene: Department of Mathematics, Institut des Politiques Publiques, Dakar Fann BP 5683, Senegal
Mustafa Yıldız: Department of Mathematics, Faculty of Arts and Sciences, Bülent Ecevit University, Incivez, 67100 Zonguldak, Turkey

Mathematics, 2022, vol. 10, issue 7, 1-17

Abstract: This work proposes a qualitative study for the fractional second-grade fluid described by a fractional operator. The classical Caputo fractional operator is used in the investigations. The exact analytical solutions of the constructed problems for the proposed model are determined by using the Laplace transform method, which particularly includes the Laplace transform of the Caputo derivative. The impact of the used fractional operator is presented; especially, the acceleration effect is noticed in the paper. The parameters’ influences are focused on the dynamics such as the Prandtl number ( P r ) , the Grashof numbers ( G r ) , and the parameter η when the fractional-order derivative is used in modeling the second-grade fluid model. Their impacts are also analyzed from a physical point of view besides mathematical calculations. The impact of the fractional parameter α is also provided. Finally, it is concluded that the graphical representations support the theoretical observations of the paper.

Keywords: second-grade fluid; Prandtl number; Grashof number; fractional-order derivative; integral transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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