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# Influence of Single- and Multi-Wall Carbon Nanotubes on Magnetohydrodynamic Stagnation Point Nanofluid Flow over Variable Thicker Surface with Concave and Convex Effects

by 2,*, 4,5 and
1
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
3
School of Mathematical Sciences, Yuquan Campus, Zhejiang University, Hangzhou 310027, China
4
Center of Excellence for Research in Engineering Materials (CEREM), King Saud University, P.O. Box, 800, Al-Riyadh 11421, Saudi Arabia
5
Electrochemistry and Corrosion Laboratory, Department of Physical Chemistry, National Research Centre, El-Behoth St. 33, Dokki, Cairo 12622, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 104; https://doi.org/10.3390/math8010104
Received: 8 December 2019 / Revised: 31 December 2019 / Accepted: 2 January 2020 / Published: 8 January 2020
This paper reports a theoretical study on the magnetohydrodynamic flow and heat exchange of carbon nanotubes (CNTs)-based nanoliquid over a variable thicker surface. Two types of carbon nanotubes (CNTs) are accounted for saturation in base fluid. Particularly, the single-walled and multi-walled carbon nanotubes, best known as SWCNTs and MWCNTs, are used. Kerosene oil is taken as the base fluid for the suspension of nanoparticles. The model involves the impact of the thermal radiation and induced magnetic field. However, a tiny Reynolds number is assumed to ignore the magnetic induction. The system of nonlinear equations is obtained by reasonably adjusted transformations. The analytic solution is obtained by utilizing a notable procedure called optimal homotopy analysis technique (O-HAM). The impact of prominent parameters, such as the magnetic field parameter, Brownian diffusion, Thermophoresis, and others, on the dimensionless velocity field and thermal distribution is reported graphically. A comprehensive discussion is given after each graph that summarizes the influence of the respective parameters on the flow profiles. The behavior of the friction coefficient and the rate of heat transfer (Nusselt number) at the surface (y = 0) are given at the end of the text in tabular form. Some existing solutions of the specific cases have been checked as the special case of the solution acquired here. The results indicate that MWCNTs cause enhancement in the velocity field compared with SWCNTs when there is an increment in nanoparticle volume fraction. Furthermore, the temperature profile rises with an increment in radiation estimator for both SWCNT and MWCNT and, finally, the heat transfer rate lessens for increments in the magnetic parameter for both types of nanotubes. View Full-Text
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Shafiq, A.; Khan, I.; Rasool, G.; Sherif, E.-S.M.; Sheikh, A.H. Influence of Single- and Multi-Wall Carbon Nanotubes on Magnetohydrodynamic Stagnation Point Nanofluid Flow over Variable Thicker Surface with Concave and Convex Effects. Mathematics 2020, 8, 104.