Unsteady natural convection flow due to fractional thermal transport and symmetric heat source/sink

Unsteady natural convection flow of viscous fluids in a circular cylinder, due to a generalized fractional thermal transport is analytically studied. The considered mathematical model is based on a new fractional differential constitutive equation of the thermal flux suitable to describe the thermal memory effects. To develop the mathematical model, the time-fractional Caputo-Fabrizio derivative is used. The generalized constitutive equation becomes equivalent to the classical Fourier's law for the zero value of the fractional order of derivative. Analytical solutions for the fluid temperature and velocity are determined using the Laplace and finite Hankel transforms. The influence of the memory parameter on heat transfer and fluid motion is discussed by numerical simulations and graphical illustrations.