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Abstract 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.

Abstract Nanofluids with their augmented thermal characteristics exhibit numerous implementations in engineering and industrial fields such as heat exchangers, microelectronics, chiller, pharmaceutical procedures, etc. Due to such properties of nanofluids, a mathematical model of non-Newtonian Casson nanofluid is analyzed in this current study to explore the steady flow mechanism with the contribution of water-based Aluminum oxide nanoparticles. A stretchable surface incorporating variable thickness is considered to be the source of the concerning fluid flow in two-dimension. An exponential viscosity of the nanofluid is proposed to observe the fluid flow phenomenon. Different models of viscosity including Brinkman and Einstein are also incorporated in the flow analysis and compared with the present exponential model. The physical flow problem is organized in the boundary layer equations which are further tackled by the execution of the relevant similarity transformations and appear in the form of ordinary nonlinear differential equations. The different three models of nanofluid viscosity exhibit strong graphical and tabulated relations with each other relative to the various aspects of the flow problem. In all concerned models of the viscosity, the deteriorating nature of the velocity field corresponding to the Casson fluid and surface thickness parameters is observed.