Use of Atangana–baleanu Fractional Derivative in Helical Flow of a Circular Pipe

Abstract

There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe.

Fractional Study for Transient Free Convection Flow in a Channel with Mittag-Leffler Memory

“…Another comparison is drawn to validate our obtained results. Results are compared with [26], in the absence of MHD, radiative heat flux, and chemical reaction. Heat and mass transfer model with three fractional approaches such as (i) Caputo, (ii) Caputo-Fabrizio, and (iii) Atangana-Baleanu is compared graphically and presented in Figures 17-22.…”

“…In this modern era, the study of fractional calculus becomes hot topic because of its huge applications in all disciplines of science and engineering. Researchers have keen interest to formulate the physical problems with noninteger derivatives because fractional-order models provide the much efficient description of model [23][24][25][26][27][28]. Sarwar et al studied the non-Newtonian fractional brinkman type fluid with AB derivative [29].…”