Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform

In this paper, we studied the effect of a magnetic field on the non-isothermal second-grade fluid confined in a vertically oscillating cylinder. The flow solution is magnetized using the perpendicular magnetic field. The resultant fluid flow is due to the oscillating boundary motion and buoyancy force. Here, the MHD flow is modeled using the Caputo-Fabrizio non-integer derivative approach. The exact solution of the governing continuity, momentum and energy equations is obtained by means of Laplace and finite Hankel transforms. The commercial simulation software, Mathematica is used for calculating the roots of the Bessel function. The effects of dimensionless parameters such as Grashof and Prandtl numbers, magnetic field and fractional parameters on the second-grade fluid flow are analyzed. Heat transfer is high at a small Prandtl number. Velocity correlates positively with Grashof number and magnetic field, and negatively with Prandtl number. The heat and mass transfer results obtained from both conventional and fractional models are compared as well.