Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar's Fractional Derivative-Analytical Solution

The present paper deals with the advancement of non-Newtonian fluid containing some nanoparticles between two parallel plates. A novel fractional operator is used to model memory effects, and analytical solutions are obtained for temperature and velocity fields by the method of Laplace transform. Moreover, a parametric study is elaborated to show the impact of flow parameters and presented in graphical form. As a result, dual solutions are predicted for increasing values of fractional parameters for short and long times. Furthermore, by increasing nanoparticle concentration, the temperature can be raised along with decreasing velocity. A fractional approach can provide new insight for the analytical solutions which makes the interpretation of the results easier and enable the way of testing possible approximate solutions.

Automated summary

The study focuses on the impact of nanoparticles in non-Newtonian fluid flow between two parallel plates, using a fractional operator to model memory effects and obtaining analytical solutions for temperature and velocity fields. A parametric study shows the influence of flow parameters and predicts dual solutions for different timescales. Increasing nanoparticle concentration raises temperature and lowers velocity, while the fractional approach provides new insights for analytical solutions.