Natural convection simulation of Prabhakar-like fractional Maxwell fluid flowing on inclined plane with generalized thermal flux

Abstract

This study considers the natural convection of viscoelastic fractional-type Maxwell fluid flowing on an inclined oscillating plate with generalized equations for stress-shear and thermal flux of thickness vector. A recent and modified fractional technique, namely Prabhakar fractional derivative, is utilized for the generalized memory effect. The solution of non-dimensional and transformed governed equations is explored by integral transform. Prabhakar-like fractional-Maxwell fluid's energy and momentum profiles are compared with classical Fourier thermal flux and ordinary Maxwell fluid with generalized heat transport. To see insight into the physical behavior of the governed equations, different exceptional cases of momentum profiles are described whose physical significance is well-explained in the existing literature, and also the graphical interpretation is presented for the comparison and influence of all parameters on momentum and energy fields. As a result, we have concluded that the Prabhakar fractional operators signify the possibility of a convenient choice of different fractional constraints, which has good fitting in both experimental and theoretical data. Furthermore, the ordinary-type Maxwell fluid with Fourier thermal flux represents less velocity rate as compared to ordinary Maxwell fluid with fractional thermal flux and fractional Maxwell fluid with fractional thermal flux.