Prabhakar fractional simulation for thermal analysis of magnetohydrodynamics flow of Oldroyd-B fluid using slip and Newtonian heating effects

This work critically examines an unsteady magnetized flow of fractionalized Oldroyd-B fluid and the slip and Newtonian heating effects close to an infinitely long plate. No-slip conditions have their importance due to significant applications in pipeline transport, boundary layer investigation, and blood flow modeling to ensure exact estimation of the behavior of fluids on solid boundaries. Slip conditions are used in microfluidics, thin-film coating processes, and boosted oil recovery in which surface interactions have a significant impact on fluid flow. So, the study intends to fulfill the following particular goals: Firstly, to develop governing partial differential equations (PDEs) that define fluid flow while considering the effects of energy and mass transfer. Secondly, investigate how nonlinear thermal radiation affects the temperature profile in the normal direction of the vertical plate. Next, to solve the recommended PDEs, use the Prabhakar time-fractional derivative combined with the Laplace transform, then verify the results with Zakian and Stehfest’s numerical approaches. Further, to find the Nusselt number and the skin friction coefficient for approximation of heat transfer and shear stress on the boundary. Evaluate the physical influence of various factors on fluid flow and display the findings using graphical and numerical methods. In the end, to compare the flow features of the fractional Oldroyd-B model to two limiting models, the second-grade and the Maxwell models, to demonstrate the Prabhakar model’s superiority in modeling memory phenomena.