Abstract
This research looked at the unsteady free convection flows of an incompressible viscous fluid with heat/sink in a vertical cylinder containing a mixture of 47 nm alumina nanoparticles in water. The flow direction is subjected to a perpendicular magnetic field. The generalization entails taking into account a new version of the constitutive equation for thermal flux, known as the generalized Atangana-Baleanu derivative, which is based on the generalized time-fractional derivative with Mittag-Leffler kernel. Using the Laplace transform and the finite Hankel transform, closed forms of analytical solutions for temperature and velocity fields, represented with Bessel and generalized G–function of Lorenzo and Hartley functions, are determined. The generalized solutions are appropriate for particularizations to yield solutions corresponding to fractional derivatives with power-law kernel and exponential kernel. The Mittag-Leffler function is a one-parametric function. It is also possible to acquire the usual situation, which corresponds to classical Fourier's law. To compare models based on generalized Atangana-Baleanu, Atangana-Baleanu, Caputo, and Caputo-Fabrizio time fractional derivatives, numerical simulations produced with the program Mathcad are carried out and visually depicted.