Abstract
The objective of this article is to apply the Atangana-Baleanu derivative fractional in Caputo sense to convective flow of Carboxy-Methyl-Cellulose (CMC) based Carbon nanotubes (CNT's) nanofluid in a vertical microchannel. The magnetohydrodynamic (MHD) flow through a porous medium together with heat transfer is considered. The Atangana-Baleanu fractional derivative without singular and the non-local kernel is used in the mathematical formulation to get the time fractional governing equations subject to physical initial and boundary conditions. The Laplace transform technique is used to obtain the exact analytical solutions for velocity and temperature distributions. Finally, the influence of parameters of interest is studied through plots and discussed physically. (c) 2018 Elsevier Ltd. All rights reserved.