Open Access

ARTICLE

A Fractal-Fractional Model for the MHD Flow of Casson Fluid in a Channel

Nadeem Ahmad Sheikh^1,2, Dennis Ling Chuan Ching¹, Thabet Abdeljawad^3,4,5, Ilyas Khan^6,*, Muhammad Jamil^7,8, Kottakkaran Sooppy Nisar⁹

1 Fundamental and Applied Science Department, Universiti Teknologi PETRONAS, Perak, 32610, Malaysia
2 Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan
3 Department of Mathematics and General Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia
4 Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
5 Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
6 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 72915, Vietnam
7 Department of Geosciences, Universiti Teknologi PETRONAS, Perak, 32610, Malaysia
8 Department of Earth Sciences, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, 22010, Pakistan
9 Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia

* Corresponding Author: Ilyas Khan. Email:

Computers, Materials & Continua 2021, 67(2), 1385-1398. https://doi.org/10.32604/cmc.2021.011986

Received 08 June 2020; Accepted 26 July 2020; Issue published 05 February 2021

Abstract

An emerging definition of the fractal-fractional operator has been used in this study for the modeling of Casson fluid flow. The magnetohydrodynamics flow of Casson fluid has cogent in a channel where the motion of the upper plate generates the flow while the lower plate is at a static position. The proposed model is non-dimensionalized using the Pi-Buckingham theorem to reduce the complexity in solving the model and computation time. The non-dimensional fractal-fractional model with the power-law kernel has been solved through the Laplace transform technique. The Mathcad software has been used for illustration of the influence of various parameters, i.e., Hartman number, fractal, fractional, and Casson fluid parameters on the velocity of fluid flow. Through graphs and tables, the results have been implemented and it is shown that the boundary conditions are fully satisfied. The results reveal that the flow velocity is decreasing with the increasing values of the Hartman number and is increasing with the increasing values of the Casson fluid parameter. The findings of the fractal-fractional model have elucidated that the memory effect of the flow model has higher quality than the simple fractional and classical models. Furthermore, to show the validity of the obtained closed-form solutions, special cases have been obtained which are in agreement with the already published solutions.

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