Time fractional analysis of channel flow of couple stress Casson fluid using Fick's and Fourier's Laws

Shafiq Ahmad; Sami Ul Haq; Farhad Ali; Ilyas Khan; Kottakkaran Sooppy Nisar

doi:10.1038/s41598-022-06897-y

Time fractional analysis of channel flow of couple stress Casson fluid using Fick's and Fourier's Laws

Sci Rep. 2022 Feb 22;12(1):2956. doi: 10.1038/s41598-022-06897-y.

Authors

Shafiq Ahmad¹, Sami Ul Haq¹, Farhad Ali², Ilyas Khan³, Kottakkaran Sooppy Nisar⁴

Affiliations

¹ Department of Mathematics, Islamia College Peshawar, 25000, Peshawar, Pakistan.
² Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan. farhadali@cusit.edu.pk.
³ Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majma'ah, 11952, Saudi Arabia.
⁴ Department of Mathematics, College of Arts and Science, Prince Sattam Bin Abdulaziz University, Wadi Al-Dawasir, 11991, Saudi Arabia.

Abstract

This study aim to examine the channel flow of a couple stress Casson fluid. The flow is generated due to the motion of the plate at [Formula: see text], while the plate at [Formula: see text] is at rest. This physical phenomenon is derived in terms of partial differential equations. The subjected governing PDE's are non-dimensionalized with the help of dimensionless variables. The dimensionless classical model is generalized by transforming it to the time fractional model using Fick's and Fourier's Laws. The general fractional model is solved by applying the Laplace and Fourier integral transformation. Furthermore, the parametric influence of various physical parameters like Casson parameter, couple stress parameter, Grashof number, Schmidt number and Prandtl number on velocity, temperature, and concentration distributions is shown graphically and discussed. The heat transfer rate, skin friction, and Sherwood number are calculated and presented in tabular form. It is worth noting that the increasing values of the couple stress parameter [Formula: see text] deaccelerate the velocity of Couple stress Casson fluid.