Thermo diffusion impacts on the flow of second grade fluid with application of (ABC), (CF) and (CPC) subject to exponential heating

Abstract

The aim of this article is to investigate the exact solution by using a new approach for the thermal transport phenomena of second grade fluid flow under the impact of MHD along with exponential heating as well as Darcy’s law. 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 second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. 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.

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

“…Abouelregal et al [26] developed a fractional heat conduction models with phase lags and Euler-Bernoulli beam theory are used to derive the governing system equations by employing Atangana-Baleanu fractional operator. The ABC, CF and CPC comparative analysis of second-grade fluid under Newtonian heating effect, found the series solution, performed by Rehman et al [27]. Some of the contributions related to fractional integral operators in bioheat transfer models are highlighted in [28][29][30][31][32][33][34].…”

A Fractional Study of MHD Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel

“…Mohammadi et al [29] utilized the Euler method for fractional-order Caputo Fabrizio derivative to approximate the system's solution and analyse the effects of the mumps virus. Rehman et al [30] performed a comparative analysis of ABC, CF and CPC methods for a second-grade fluid under the influence of Newtonian heating, obtaining series solutions. Kumar et al [31] proposed a new generalized fractional derivative that produces different types of singular and nonsingular fractional derivatives based on various kernels.…”

Unsteady MHD Free Convection Flow of a Second Grade Casson Fluid with Ramped Wall Temperature

“…Magnetic fields are also used in a variety of technological applications, such as fast-breeder reactors, controlled thermonuclear fusion, and MHD power generation. To explore intriguing findings on second-grade fluids, one can refer to the citations [33][34][35][36][37]. The purpose of this analysis is to extend the work done by Samiulhaq et al, [33] for Casson fluid flow with variable velocity, radiation and heat source included with ramped wall temperature.…”