Fractional Modeling of Non-Newtonian Casson Fluid between Two Parallel Plates

• Published in: Journal of mathematics (Hidawi) Vol. 2023; pp. 1 - 12
• Main Authors: Qayyum, Mubashir, Afzal, Sidra, Ahmad, Efaza
• Format: Journal Article
• Language: English
• Published: Cairo Hindawi 2023; Hindawi Limited; Wiley
• Subjects: Algorithms; Continuity equation; Finite element analysis; Fractals; Fractional calculus; Heat; Laplace transforms; Mathematical models; Mathematics; Modelling; Nanoparticles; Non-Newtonian fluids; Parallel plates; Parameter modification; Partial differential equations; Perturbation; Radial velocity; Radiation
• ISSN: 2314-4629; 2314-4785
• DOI: 10.1155/2023/5517617

In this manuscript, fractional modeling of non-Newtonian Casson fluid squeezed between two parallel plates is performed under the influence of magneto-hydro-dynamic and Darcian effects. The Casson fluid model is fractionally transformed through mixed similarity transformations. As a result, partial differential equations (PDEs) are transformed to a fractional ordinary differential equation (FODE). In the current modeling, the continuity equation is satisfied while the momentum equation of the integral order Casson fluid is recovered when the fractional parameter is taken as α=1. A modified homotopy perturbation algorithm is used for the solution and analysis of highly nonlinear and fully fractional ordinary differential equations. Obtained solutions and errors are compared with existing integral order results from the literature. Graphical analysis is also performed at normal and radial velocity components for different fluid and fractional parameters. Analysis reveals that a few parameters are showing different behavior in a fractional environment as compared to existing integer-order cases from the literature. These findings affirm the importance of fractional calculus in terms of more generalized analysis of physical phenomena.