Investigation of heat and mass transfer performance in Jeffrey fluid: impact of Prabhakar fractional operator

This theoretical study seeks to extend the concept of fractional Jeffrey fluid and heat transfer near an infinite vertical plate, governed by generalized boundary conditions, using a time-fractional Prabhakar operator. Initially, the momentum equation incorporating the fractional Jeffrey model is developed to examine the unsteady flow, focusing on pressure dynamics within the boundary layer. Additionally, the energy equation, along with convective heat and mass transfer under generalized conditions, is formulated using the extended Fourier’s law. The Prabhakar fractional operator is utilized to represent the fluid’s transport mechanisms. The study presents fractional governing equations to describe heat, mass, and flow transfer processes influenced by magnetic fields and radiation effects. A Prabhakar fractional derivative is applied to model the fractional system, and analytical solutions are derived using the Laplace transform technique. The accuracy and validity of the results are confirmed by comparing them with previous work and exact solutions. Furthermore, the strong agreement between our analytical solutions and earlier studies reinforces the method’s reliability. The effects of various parameters on the fluid’s velocity, mass, and temperature distribution are demonstrated graphically. Changes in the model’s parameters result in varying trends in the velocity, mass, and temperature profiles, highlighting the critical impact of each parameter on the behavior of fluid flow, mass, and heat transfer.