A comparative analysis of three distinct fractional derivatives for a second grade fluid with heat generation and chemical reaction

This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. Th...

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Bibliographic Details
Published in:Scientific reports 2024-02, Vol.14 (1), p.4482-16, Article 4482
Main Authors: Sehra, Sadia, Haleema, Haq, Sami Ul, Alhazmi, Hadil, Khan, Ilyas, Niazai, Shafiullah
Format: Article
Language:English
Subjects:
639/705
639/766
ABC
Boundary layers
Chemical reactions
Comparative analysis
CPC
Differential equations
Fluid flow
Fractional operators
Humanities and Social Sciences
Laplace transforms
Mass transfer
multidisciplinary
Non-Newtonian fluid
Partial differential equations
Science
Science (multidisciplinary)
Second grade fluid
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Summary:This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. The heat mass transfer is observed during the flow past a vertical porous plate that is accelerated exponentially under the effects of the Magneto hydro dynamics. The effects of the heat generation and exponential heating in the temperature boundary layer and chemical reaction at the concentration boundary layer are also analyzed in this article. The flow model is described by three partial differential equations and the set of non-dimensional PDE’s is transformed into ODE’s by utilization of the integral transform technique (Laplace transform). For the better understanding of the rheological properties of the Second Grade fluid we used the CF, ABC and CPC operators to describe the memory effects. The analytical exact solution of the problem is obtained in the form of G-functions and Mittag Leffler functions. For the physical significance of flow parameters, different parameters are graphed. From this analysis it is concluded that the CPC is the most suitable operator to describe the memory effects.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-024-55059-9