## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Effects of CNTs 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 (SWCNTs and MWCNTs) 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 partial differential equations of nanofluids have been modeled by employing newly defined fractional approaches (derivatives) namely Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives. The comparison of analytical solutions for temperature distribution and velocity field has been established via both approaches i-e (AB) and (CF) 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 (and CF fractional derivatives) are depicted for graphical illustrations. The comparison of three types of fluids (i) pure methanol (ii) methanol with single walls carbon nanotubes and (iii) methanol with multi-walls carbon nanotubes is portrayed via Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives. Finally, the results indicate that, pure methanol moves quicker in comparison with methanol-SWCNTs via Caputo-Fabrizio (CF)and methanol-MWCNTs, while for larger time, methanol-MWCNTs moves more rapidly in comparison with pure methanol and methanol-SWCNTs via Atangana-Baleanu (AB).

**KEYWORDS**

PAPER SUBMITTED: 2018-01-16

PAPER REVISED: 2018-05-14

PAPER ACCEPTED: 2018-05-16

PUBLISHED ONLINE: 2018-06-03

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