Research Article
Effects of Second-Order Slip Flow and Variable Viscosity on
Natural Convection Flow of (CNTs - Fe
3
O
4
)/Water Hybrid
Nanofluids due to Stretching Surface
Ayele Tulu and Wubshet Ibrahim
Department of Mathematics, Ambo University, Ambo, Ethiopia
Correspondence should be addressed to Ayele Tulu; ayeletulu@ymail.com
Received 7 August 2020; Revised 25 October 2020; Accepted 9 March 2021; Published 19 March 2021
Academic Editor: Mostafa S. Shadloo
Copyright © 2021 Ayele Tulu and Wubshet Ibrahim. is is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
is study deals with natural convection unsteady flow of CNTs − Fe
3
O
4
/water hybrid nanofluids due to stretching surface
embedded in a porous medium. Both hybrid nanoparticles of SWCNTs − Fe
3
O
4
and MWCNTs − Fe
3
O
4
are used with water as
base fluid. Effects of hybrid nanoparticles volume friction, second-order velocity slip condition, and temperature-dependent
viscosity are investigated. e governing problem of flow is solved numerically employing spectral quasilinearization method
(SQLM). e results are presented and discussed via embedded parameters using graphs and tables. e results disclose that the
thermal conductivity of (CNTs − Fe
3
O
4
)/H
2
O hybrid nanofluids is higher than that of CNTs − H
2
O nanofluids with higher value
of hybrid nanoparticle volume fraction. Also, the results show that momentum boundary layer reduces while the thermal
boundary layer gros with higher values of temperature-dependent viscosity and second-order velocity slip parameters. e skin
friction coefficient improves, and the local heat transfer rate decreases with higher values of nanoparticle volume fraction,
temperature-dependent viscosity, and second-order velocity slip parameters. Furthermore, more skin friction coefficients and
lower local heat transfer rate are reported in the CNTs − Fe
3
O
4
/H
2
O hybrid nanofluid than in the CNTs − H
2
O nanofluid. us,
the obtained results are promising for the application of hybrid nanofluids in the nanotechnology and biomedicine sectors.
1. Introduction
e broad applications of heat transfer in various sectors of
industry and biomedicine have required the accessibility of
efficient thermal performance techniques. In the past few
decades, several techniques of enhancing the thermal per-
formance of working fluids have been realized by different
researchers. Scattering of nanoparticles of metallic structures
such as copper, carbides, alumina, nitrides, metal oxides,
carbon nanotubes, and graphite in the working fluid is
considered to be one of the innovative and efficient methods
(Mahanthesh et al. [1]). At present, nanofluids are the noble
options for the heat transfer fluids due to their remarkably
higher thermal conductivity, and their use is common in
heat exchangers, cooling systems, solar energy, biomedicine,
and so forth (Aziz et al. [2]). Besides, the porous media have
better dissipation area, which results in improved convective
heat transfer. As a result, Reddy and Sreedevi [3] analyzed
heat and mass transfer characteristics of nanofluid flow over
porous stretching sheet. e non-Newtonian Casson
nanofluid flow and heat transfer over stretching cylinder in a
porous medium were investigated by Tulu and Ibrahim [4].
Furthermore, the effect of temperature and concentration on
the thermal conductivity of ZnO-TiO/EG hybrid nanofluid
using artificial neural network and curve fitting on exper-
imental data was evaluated by Safaei et al. [5].
At present, heat transfer of carbon nanofluids (CNTs)
has received great attention due to their potential applica-
tions in the fields of nanotechnology and biomedicine. CNTs
are allotropes of carbon prepared in cylindrical tubes of
graphite with nanometer in diameter and a few millimeters
in length (Hirlekar et al. [6]). CNTs are generally divided
into single-wall carbon nanotubes (SWCNTs) and multiwall
carbon nanotubes (MWCNTs) depending on their number
Hindawi
Mathematical Problems in Engineering
Volume 2021, Article ID 8407194, 18 pages
https://doi.org/10.1155/2021/8407194