Impact of Newtonian Heating via Fourier and Fick’s Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel

Abstract

In this manuscript, a new approach to study the fractionalized Oldroyd-B fluid flow based on the fundamental symmetry is described by critically examining the Prabhakar fractional derivative near an infinitely vertical plate, wall slip condition on temperature along with Newtonian heating effects and constant concentration. The phenomenon has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick’s and Fourier’s law. The fractional model is transfromed into a non-dimentional form by using some suitable quantities and the symmetry of fluid flow is analyzed. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstrations are made to characterize the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, to validate our current results, some limiting models such as fractional and classical fluid models for Maxwell and Newtonian are recovered, in the presence of with/without slip boundary wall conditions. Further, it is observed from the graphs the velocity curves for classical fluid models are relatively higher than fractional fluid models. A comparative analysis between fractional and classical models depicts that the Prabhakar fractional model explains the memory effects more adequately.