Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

Abstract

It is well established fact that the functional effects, such as relaxation and retardation of materials, can be measured for magnetized permeability based on relative increase or decrease during magnetization. In this context, a mathematical model is formulated based on slippage and non-slippage assumptions for Oldroyd-B fluid with magnetized permeability. An innovative definition of Caputo-Fabrizio time fractional derivative is implemented to hypothesize the constitutive energy and momentum equations. The exact solutions of presented problem, are determined by using mathematical techniques, namely Laplace transform with slipping boundary conditions have been invoked to tackle governing equations of velocity and temperature. The Nusselt number and limiting solutions have also been persuaded to estimate the heat emission rate through physical interpretation. In order to provide the validation of the problem, the absence of retardation time parameter led the investigated solutions with good agreement in literature. Additionally, comprehensively scrutinize the dynamics of the considered problem with parametric analysis is accomplished, the graphical illustration is depicted for slipping and non-slipping solutions for temperature and velocity. A comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

Thermophysical Study of Oldroyd-B Hybrid Nanofluid with Sinusoidal Conditions and Permeability: A Prabhakar Fractional Approach

“…The interchanging of both curves of the numerical scheme and the obtained results of Riaz et al [42] validate this study's solutions.…”

“…The results from both curves have a slight overlap. In Figure 2d, a comparison of both numerical models and strategies for velocity fields using the Prabhakar fractional method is displayed with the work of Riaz et al [42]. The calculations gained by using the Prabhakar fractional framework have an adequate accuracy compared to the exploration of Riaz et al [42].…”

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

“…Fractional differential equations are massively applied to model various daily life physical problems because fractional calculus has memory effects, such as problems in fluid flow, diffusion, relaxation, reaction, oscillation, dynamical processes, and retardation processes in complex systems and many more engineering processes, wherefore ordinary models can not anticipate the preceding processes state. In the literature, most of the studies are focused on flow problems relative to several fractional operators with local kernels, as well as non-local kernels such as Marchaud-Caputo, Atangana-Baleanu, Caputo-Fabrizio, Prabhakar fractional derivative, and others [28][29][30]. These indicate the current state but also the future state of a system.…”

Effect of Magnetic Field with Parabolic Motion on Fractional Second Grade Fluid

“…Khan et al [40] discussed the precise answers for quickened flow behavior of a pivoting SGF in a permeable space. Bilal et al [41] and Ali et al [42] analyzed the SGF with a swaying plate under different conditions. The literature shows more interest developed in the numerical and approximate solutions on the convection flow of SGF [43][44][45][46][47][48][49].…”

“…MHD free convection radiative stream with different conditions has been considered by researchers [56][57][58][59]. Ali et al [42] considered SGF with porous surface and determined the exact solutions. Some recent and useful work has also been done for SGF with fractional differential operators [60][61][62][63][64][65].…”