Role of single slip assumption on the viscoelastic liquid subject to non‐integer differentiable operators

Abstract

The main focus of this study is to investigate the impact of heat generation/absorption with single slip assumptions based on Newtonian heating on magnetohydrodynamic (MHD) time‐dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. The mathematical modeling based on fractional treatment of governing equation subject to the temperature distribution, shearing stress, and velocity field is developed. The fractionalized analytical solutions have been traced out separately through Atangana‐Baleanu (AB) and Caputo‐Fabrizio (CF) fractional differential operators. These differential operators with and without non‐locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. For the sake of physical investigation of the considered problem, the effective Prandtl number and fractional parameter have been invoked on temperature with and without single slip assumption. Our results suggest that the velocity profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Additionally, the magnetic field and relaxation phenomenon have been analyzed on the profile of velocity with and without single slip assumption.