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 AtanganaBaleanu 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 MittageLeffler function My 5(T) and generalized M-function M (IP (F) satisfying initial and boundary conditions. In order to have vivid Theological 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.