Analysis of constant proportional Caputo operator on the unsteady Oldroyd-B fluid flow with Newtonian heating and non-uniform temperature

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Author listMuhammad Arif, Poom Kumam, Wiboonsak Watthayu

PublisherWiley-VCH Verlag

Publication year2024

Volume number104

Issue number2

Start pagee2023000

ISSN0044-2267

eISSN1521-4001

URLhttps://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.202300048

LanguagesEnglish-Canada (EN-CA)


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Abstract

The Caputo operator has recently gained popularity as a widely used operator in fractional calculus. The purpose of this current research is to develop a new operator by combining the Caputo and proportional derivatives, resulting in the constant proportional Caputo (CPC) fractional operator. To demonstrate the dynamic behavior of this newly defined operator, it was applied to the unsteady Oldroyd-B fluid model. Additionally, the research considered an Oldroyd-B fluid in a generalized Darcy medium, considering non-uniform temperature, radiation, and heat generation. Analytical solutions for the proposed model were obtained and presented in graphical form using the computational software MATHCAD. The impact of various physical parameters was also examined through graphical analysis of velocity and temperature profiles, as well as a comparison between isothermal and non-uniform temperature. In conclusion, this research found that the CPC fractional operator effectively explains the dynamics of the Oldroyd-B fluid model with stable and strong memory effects, compared to the classical model.


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Last updated on 2024-10-04 at 11:05