Analysis of constant proportional Caputo operator on the unsteady Oldroyd-B fluid flow with Newtonian heating and non-uniform temperature
Journal article
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Publication Details
Author list: Muhammad Arif, Poom Kumam, Wiboonsak Watthayu
Publisher: Wiley-VCH Verlag
Publication year: 2024
Volume number: 104
Issue number: 2
Start page: e2023000
ISSN: 0044-2267
eISSN: 1521-4001
URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.202300048
Languages: English-Canada (EN-CA)
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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