Abstract
In this paper, the Atangana-Baleanu Caputo (ABC) sense is applied on the unsteady MHD bioconvection nanofluid boundary layer flow due to gyrotactic microorganisms. The effects of joule heating, convective boundary conditions and thermal radiation, and were studied. Also, it is focused on the Buongiorno's nanofluid model and two cases of the nanoparticles boundary conditions are assumed, namely, passive control and active control. The solution methodology is starting by an approximation of the time fractional derivatives using ABC and the finite differences method (FDM) of Crank-Nicolson type is applied for the first and second derivatives. The main outcomes revealed that using ABC definitions gives a good approximation of the time fractional derivatives comparing with classical Caputo approximation. Also, values of the velocity and temperature in case of the passive control are higher than those of the active control indicating more physical realistic in this case. Furthermore, there is an enhancement in values of the local Nusselt number up to 0.2% when order of the fractional derivatives is varied from 0.8 to 1. The work finds applications in heat transfer enhancement in bio-inspired nanoparticle-doped fuel cells.