A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law

Abstract

In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative model generalized to fractional model is based on a generalized Fourier law. The solutions for energy and velocity equations are obtained after making the equations dimensionless. To check the insight of the physical parameters, especially the symmetric behavior of fractional parameters, it is found that for small and large values of time, fluid properties show dual behavior. Since the fractional derivative exhibits the memory of the function at the chosen value of time, therefore the present fractional model is more suitable in exhibiting memory than the classical model. Such results can be useful in the fitting of real data where needed. In the limiting case when fractional parameters are taken β=γ = 0 and α = 1 for both velocity and temperature, we get the solutions obtained with ordinary derivatives from the existing literature.

Keywords

• Casson fluid
• oscillating vertical plate
• Prabhakar fractional approach