Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis

In this work, a generalized unsteady magnetohydrodynamic transport of a rate type fluid near an unbounded upright plate is analyzed under Newtonian heating and non-uniform velocity conditions. The vertical plate is suspended in a porous medium and is encountering the radiation effects. Three different fractional models for Maxwell fluid are established by using the modern definitions of Atangana–Baleanu, Caputo–Fabrizio, and Caputo fractional operators. Triple fractional analysis is conducted to reach out to the solutions of consequent flow and energy equations. Laplace transform and Stehfest’s numerical algorithm are jointly applied to solve each fractional model. Shear stress and heat transfer rate are measured at the solid–fluid interface in the form of skin friction coefficient and Nusselt number respectively. The physical significance of associated parameters in velocity and energy boundary layers is investigated and graphs are provided to discuss the relevant physical arguments. A tabular analysis is performed to demonstrate the influence of physical parameters on shear stress and heat transfer rate. An empirical comparison between fractional and classical solutions indicates that fractional operators provide a better explanation of the physical features of the model. It is also analyzed that for Newtonian heating and non-uniform velocity conditions, the Atangana–Baleanu fractional operator is the finest fractional model to describe the memory effect of velocity and energy distribution. The velocity of a Maxwell fluid is always higher for constant velocity condition as compared to the ramped velocity condition. Furthermore, the heat transfer rate declines for increasing values of the fractional parameter α and a minimum value is witnessed for the classical model but, it follows an inverse trend when the radiation parameter Rd increases.