Exact solutions of Fractional Maxwell hybrid nanofluid flow model using Integral transforms

In this paper, we obtain exact solutions of a system of fractional partial differential equations (FPDEs) which describe natural convection heat transfer of a specific engine oil in oscillating vertical cylinder. The closed form solutions for the velocity and temperature profiles are obtained using Laplace and finite Hankel transforms. A closed form formula for the Nusselt number is obtained. The effects of the Prandtl number and the order of the fractional derivative on the temperature profile and the Nusselt number are discussed using some figures. The change in the velocity profile with the Prandtl number, the Grashof number, and the order of the fractional derivative is investigated.