Helical Estimation of Atangana-Baleanu-Caputo Fractionalized Magnetohydrodynamic Second Grade Fluid for Generalized Boundary Conditions under Porous Environment

Abstract

In the current work, we estimate the flow of helices of the unsteady fractionalized second grade fluid with MHD effect between uniaxial annular cylinders. The analytical outcomes are evaluated for the rotational and longitudinal velocity and the shear stress because of fluid circulation and translating between two infinite coaxial circular cylinders, which are turning their axis. Hardly anyone did this before and applied most modern non-integer Atangana Baleanu Caputo fractional time derivatives on the governing equation of second grade fluid with some natural effects. The outcomes are determined by using some integral transforms such as Laplace and finite Hankel transforms. The acquired outcomes exhibited in integral and series forms with newly defined special $\textbf{M}^{a,b}_{c}(\kappa,t)$ function. The outcome that fulfills both the governing equation and all designated account conditions. Additionally, the respective outcome for Newtonian fluid for the same movement is acquired in limited cases. The impact of material parameter $\alpha$ and kinematic viscosity of the $\alpha$ is also discussed. Last, we examined the behavior of distinct parameters on fluid movement along with graphically analogizing second grade and Newtonian fluids.