Magneto‐hydrodynamics natural convection flows of viscous carbon nanotubes nanofluids with generalized Fourier's law in a vertical cylinder

In this article, we consider the natural (free) convection flows of viscous carbon nanotubes nanofluids in the presence of transverse magnetic field in a vertical cylinder. The fractional derivative is introduced by means of generalized Fourier's law (Caputo–Fabrizio and Atangana–Baleanu fractional derivatives) in the thermal equation. The solutions of the equations are found by means of the Laplace and finite Hankel transforms, which satisfied all imposed initial and boundary conditions. The effects of fractional and physical parameters are graphically underlined.