NUMERICAL ANALYSIS OF NEWLY DEVELOPED FRACTAL-FRACTIONAL MODEL OF CASSON FLUID WITH EXPONENTIAL MEMORY

Saqib Murtaza, Poom Kumam, Zubair Ahmad, Thidaporn Seangwattana and Ibn E. Ali
Additional contact information
Saqib Murtaza: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Poom Kumam: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand†Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand‡Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Zubair Ahmad: �Dipartimento di Matematica e Fisica, Universit‘a degli Studi della Campania “Luigi Vanvitelli†, Caserta 81100, Italy
Thidaporn Seangwattana: �Faculty of Science Energy and Environment, King Mongkut’s University of Technology North Bangkok, Rayong Campus (KMUTNB), 21120 Rayong, Thailand
Ibn E. Ali: ��Higher Education Archives & Libraries Department KP, Government Superior Science College, Peshawar, Pakistan

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-10

Abstract: In the current research community, certain new fractional derivative ideas have been successfully applied to examine several sorts of mathematical models. The fractal fractional derivative is a novel concept that has been proposed in recent years. In the presence of heat generation, however, it is not employed for the free convection Couttee flow of the Casson fluid model. The core interest of the present analysis is to examine the Casson fluid under the influence of heat generation and magnetic field. The flow of the Casson fluid has been considered in between two vertical parallel plates. The distance between the plates is taken as l. The linear coupled governing equation has been developed in terms of classical PDEs and then generalized by employing the operator of the fractal-fractional derivative with an exponential kernel. The numerical solution of the proposed problem has been found employing the finite-difference technique presented by Crank–Nicolson. The Crank–Nicolson finite difference scheme has the advantage of being unconditionally stable and can be applied directly to the PDEs without any transformation to ODEs. This technique in sense of exponential memory has been revealed to be unreported in the literature for such a proposed problem. For graphical analysis, the graphs of velocity profile and thermal field have been plotted in response to several rooted parameters. For comparative analysis, the graphs for the parameter of fractal-fractional, fractional, and classical order have also been plotted. From the analysis, it has been found that the fractal-fractional order model has a large memory effect than the fractional-order and classical model due to the fractal order parameter.

Keywords: Fractal-Fractional Model; Exponential Kernel; Finite Difference Scheme; Numerical Solution; Heat Generation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2240151X

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