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

Saqib Murtaza, Poom Kumam, Zubair Ahmad, Thidaporn Seangwattana, Ibn B.N.E. Ali

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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.

Original languageEnglish
Article number2240151
JournalFractals
Volume30
Issue number5
DOIs
Publication statusPublished - 1 Aug 2022
Externally publishedYes

Keywords

  • Exponential Kernel
  • Finite Difference Scheme
  • Fractal-Fractional Model
  • Heat Generation
  • Numerical Solution

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