Fractional Nadeem trigonometric non-Newtonian (NTNN) fluid model based on Caputo-Fabrizio fractional derivative with heated boundaries.

The fractional operator of Caputo-Fabrizio has significant advantages in various physical flow problems due to the implementations in manufacturing and engineering fields such as viscoelastic damping in polymer, image processing, wave propagation, and dielectric polymerization. The current study has the main objective of implementation of Caputo-Fabrizio fractional derivative on the flow phenomenon and heat transfer mechanism of trigonometric non-Newtonian fluid. The time-dependent flow mechanism is assumed to be developed through a vertical infinite plate. The thermal radiation's effects are incorporated into the analysis of heat transfer. With the help of mathematical formulations, the physical flow system is expressed. The governing equations of the flow system acquire the dimensionless form through the involvement of the dimensionless variables. The application of Caputo-Fabrizio derivative is implemented to achieve the fractional model of the dimensionless system. An exact solution of the fractional-based dimensionless system of the equations is acquired through the technique of the Laplace transform. Physical interpretation of temperature and velocity distributions relative to the pertinent parameters is visualized via graphs. The current study concludes that the velocity distributions exhibit an accelerating nature corresponding to the increasing order of the fractional operator. Moreover, the graphical results are more significant corresponding to the greater time period.