<abstract xmlns="http://www.w3.org/1999/xhtml">

The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as <italic>u</italic>0. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as <italic>α</italic>, <italic>β</italic>, <italic>Pr</italic>, <italic>Q, Gr, M</italic>, <italic>Nr</italic> and <italic>K</italic>, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.
</abstract>

The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u0. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as α, β, Pr, Q, Gr, M, Nr and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.

A Fractional Study of MHD Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel

Department of Computer Science and Mathematics

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of...

A Fractional Study of MHD Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel

Publié en ligne: 05 janv. 2024

Pages: 84 - 92

Reçu: 29 avr. 2023

Accepté: 28 juin 2023

DOI: https://doi.org/10.2478/ama-2024-0011

Mots clés
YAC derivative, series solution, heat transfer, Laplace transformation, Rabotnov exponential functions, system parameters

© 2024 Aziz Ur Rehman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Fractional Study of MHD Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel

Publié en ligne: 05 janv. 2024

Pages: 84 - 92

Reçu: 29 avr. 2023

Accepté: 28 juin 2023

DOI: https://doi.org/10.2478/ama-2024-0011

Mots clésYAC derivative, series solution, heat transfer, Laplace transformation, Rabotnov exponential functions, system parameters

© 2024 Aziz Ur Rehman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
YAC derivative, series solution, heat transfer, Laplace transformation, Rabotnov exponential functions, system parameters