Effects of carbon nanotubes on magnetohydrodynamic flow of methanol based nanofluids via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives

Abstract

This paper dedicatedly reports the heat transfer analysis of single and multi-walls carbon nanotubes for electrically conducting flow of Casson fluid. Both types of carbon nanotubes are suspended in methanol that is considered as a conventional base fluid. The governing PDE of nanofluids have been modeled by employing newly defined fractional approaches (derivatives) namely Atangana- Baleanu and Caputo-Fabrizio fractional derivatives. The comparison of analytical solutions for temperature distribution and velocity field has been established via both approaches i. e. Atangana-Baleanu and Caputo-Fabrizio fractional operators. The general analytical solutions are expressed in the layout of Mittage- Leffler function Myε,δ(T) and generalized M-function Mpq (F) satisfying initial and boundary conditions. In order to have vivid rheological effects, the general analytical solutions in both cases (Atangana-Baleanu and Caputo-Fabrizio fractional derivatives) are depicted for graphical illustrations. The comparison of three types of fluids: pure methanol, methanol with single walls carbon nano-tubes, and methanol with multi-walls carbon nanotubes is portrayed via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. Finally, the results indicate that, pure methanol moves quicker in comparison with methanol-single-walls carbon nanotubes via Caputo-Fabrizio and methanol-multi-walls carbon nanotubes, while for larger time, these nanotubes move more rapidly in comparison with pure methanol and methanol-single-walls carbon nanotubes via Atangana-Baleanu.