Abstract
Theoretically, this work describes the exact solutions of fractional Casson fluid through a channel under the effect of MHD and porous medium. The unsteady fluid motion of the bottom plate, which is confined by parallel but perpendicular sidewalls, supports the flow. By introducing the dimensionless parameters and variables, the momentum equation, as well as the initial and boundary conditions, has been transformed to a dimensionless form. A mix of Laplace and Fourier transformations is used to get the exact solution for the momentum equation. The constitutive equations for Caputo-Fabrizio’s time-fractional derivative are also incorporated for recovering the exact solutions of the flow problem under consideration. After recovering the exact solutions for flow characteristics, three different cases at the surface of the bottom plate are discussed, by addressing the limiting cases under the influence of the side walls. Moreover, these solutions are captured graphically, and the effects of the Reynolds number Re , fractional parameter α , effective permeability K eff , and dimensionless parameter for Casson fluid β on the fluid’s motion are observed.
Highlights
A fraction model correctly depicts the motion of a flow issue when compared to ordinary differential equations (ODEs)
With the influence of MHD and porosity, three distinct forms of motion have been examined for fractional Casson fluid in a
An opposite impact is observed for the dimensionless parameter for Casson fluid ðβÞ upon flow characteristics
Summary
Fractional calculus plays a critical part in the solving of complicated engineering issues. The authors have determined the exact solutions for flow and thermal characteristics by applying Laplace transform The authors of this investigation have carried out a comparative study for the time derivative of fractional and integral order both for Newtonian and second-grade fluids and have highlighted that fractional parameter enhanced the flow characteristics due to augmented velocities of fractional fluid. This work investigates a time-dependent fractional Casson fluid through a channel with porosity and MHD effect; the flow is caused by the bottom plate’s unstable motion, which is confined by sidewalls that are parallel to one another but normal to the bottom plate. The exact solutions for the momentum equation were obtained using integral transforms [22, 23] such as Laplace, finite Fourier, and Fourier transforms, as well as the Caputo-Fabrizio fractional derivative These ideas were addressed for various bottom plate instances. The impact of different parameters involved in the solution of the flow problem has been discussed upon flow characteristics
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