https://doi.org/10.1140/epjp/s13360-022-03601-x
Regular Article
Investigation of hybrid nanofluid SWCNT–MWCNT with the collocation method based on radial basis functions
1
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran
2
Department of Mechanical Engineering, Babol Noshirvani University of Technology, P. O. Box 484, Babol, Iran
b
torkzadeh@semnan.ac.ir
c
ddg_davood@yahoo.com
Received:
17
August
2022
Accepted:
16
December
2022
Published online:
2
January
2023
In this research, non-Newtonian natural convection of hybrid nanofluid comprising single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) based on methanol fluid between two infinitely parallel vertical flat plates is investigated. The basic partial differential equations are reduced to ordinary differential equations which are solved using the collocation method based on radial basis functions (RBF). The results obtained using the RBF method and numerical method are in good agreement, demonstrating the RBF method’s ability to solve such problems. The hybrid nanofluid has more velocity around the plate with a higher temperature, so it reaches its maximum velocity in 
. Also, it approaches the plate with a lower temperature, and its velocity decreases. As the hybrid nanotubes volume fraction increases, the momentum boundary layer thickness and thermal boundary layer thickness decrease. The maximum velocity profile is related to the hybrid nanotubes volume fraction of 0.05, equal to 0.033. Also, the minimum error in this method for the momentum equation is equal to 
at N = 30 which shows fast convergence of the proposed method.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
