Analysis of fractional natural convection heat transfer of G0-MOS2 engine oil in an oscillating vertical cylinder

In this paper, We show using Laplace and finite Hankel transforms, how to derive exact solutions for the velocity and temperature profiles of a system of fractional differential equations which describe heat transfer by natural convection of a specific engine oil with molybdenum disulphide and graphene oxide (MoS2 + GO) hybrid nano-composites in oscillating vertical cylinder. A few figures are used to illustrate how the temperature profile and the Nusselt number are affected by the Prandtl number and the order of the fractional derivative.