Time fractional analysis of Casson fluid with Rabotnov exponential memory based on the generalized Fourier and Fick...s law

Abstract

A new approach to investigates the analytical solutions of the mathematical fractional Casson fluid model that is described by the Yang-Abdel-Cattani fractional operator having Rabotnov exponential kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of Casson fluid, developed a fractional model by applying the new definition of Yang-Abdel-Cattani fractional derivative operator having Rabotnov exponential kernel that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler functions, for fluid velocity, concentration and temperature, Laplace integral transformation method is used to solve the fractional model. For several physical significance of various fluid parameters such as α, β, Pr, Gr, Gm, Sc on velocity, concentration and temperature distributions are demonstrated through various graphs and it is noticed that the Yang-Abdel-Cattani fractional parameter portrayed the retardation effect on momentum and energy profile, but it is visualized that for small values of Casson fluid parameter the velocity profile is higher. Furthermore, for being validated the acquired solutions, some limiting models such as ordinary Newtonian model had recovered from Yang-Abdel-Cattani fractional Casson fluid. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.