This paper presents a Caputo-Fabrizio fractional derivatives approach to the thermal analysis of a second grade fluid over an infinite oscillating vertical flat plate. Together with an oscillating boundary motion, the heat transfer is caused by the buoyancy force induced by temperature differences between the plate and the fluid. Closed form solutions of the fluid velocity and temperature are obtained by means of the Laplace transform. The solutions of ordinary second grade and Newtonian fluids corresponding to time derivatives of integer and fractional orders are obtained as particular cases of the present solutions. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter α, the material parameter α 2 , and the Prandtl and Grashof numbers on the velocity field. A comparison for time derivative of integer order versus fractional order is shown graphically for both Newtonian and second grade fluids. It is found that fractional fluids (second grade and Newtonian) have highest velocities. This shows that the fractional parameter enhances the fluid flow.

Increasing knowledge of hybrid nanofluid can be traced to its unique improvement of thermal performance and enhancement of heat transfer rate as applicable in the dynamics of fuel and coolant in automobiles. However, the case of water-based nanofluid conveying three kinds of nanoparticles (i.e., ternary-hybrid nanofluid) with various shapes and densities is far-fetched. The transport phenomena of water conveying smaller densities nanoparticles (i.e., copper nanotubes, graphene, and aluminum oxide) and substantial large densities of nanoparticles (i.e., copper oxide, copper, and silver) of various types through a rectangular closed domain with major emphasis on the significance of suction and dual stretching was investigated. The dimensional equation that model the aforementioned transport phenomenon, for the two cases, were non-dimenzionalized using appropriate similarity variables, parameterized, and solved numerically using shooting techniques together with fourth-order Runge-Kutta integration scheme and in-built bvp4c package of MATLAB. Enhancement in suction and stretching ratio causes the vertical velocity of the motion along x-direction and Nusselt number to be an increasing function. Due to an increase in suction and stretching ratio, fluid flow along (x, y)-directions, temperature distribution, and the local skin friction coefficients are decreasing functions. At all the levels of suction and stretching ratio, higher Nusselt numbers were found in the case of water conveying Copper oxide, Copper, and Silver nanoparticles due to their heavy densities.

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