Vol.:(0123456789) 1 3
Journal of Thermal Analysis and Calorimetry
https://doi.org/10.1007/s10973-020-09589-9
Numerical investigation of entropy production in SWCNT/H
2
O
nanofuid fowing through inwardly corrugated tube in turbulent fow
regime
Olatomide G. Fadodun
1
· Adebimpe A. Amosun
1
· Nonso L. Okoli
3,4
· David O. Olaloye
2
· Johnson A. Ogundeji
1
·
Solomon S. Durodola
5
Received: 7 September 2019 / Accepted: 17 March 2020
© Akadémiai Kiadó, Budapest, Hungary 2020
Abstract
This work numerically investigates the entropy production rate in single-walled carbon nanotubes (SWCNTs)/H
2
O nanofuid
fowing through an inwardly corrugated pipe in turbulent fow regime. The governing equations (continuity, momentum,
energy, rate of turbulent production and specifc turbulent dissipation) were solved using (SST k - ) model. Parametric study
was carried out on the efect of Reynolds number (5000–40,000), nanoparticle concentration (0–0.25%) and dimensionless
amplitude (e/d = 0, 0.08, 0.12 and 0.16) on entropy production rate and Bejan number. The results show the feld profle of
the Bejan number and the thermal and viscous entropy production rate for various amplitudes of the corrugated pipe. The
study also observed that an increment in concentration of SWCNT–water nanofuid and dimensionless amplitude of the
corrugation reduced the thermal entropy production but enhanced viscous entropy production. For instance, the change in
thermal and viscous entropy production rate at Re = 20,000 and vol = 0.25% between corrugation amplitude 0.12 and 0.16
was − 1.27% and 53.15%, respectively.
Keywords Nanofuid · Entropy · Reynolds number · Bejan number · Corrugated pipe
List of symbols
Re Reynolds number
T Temperature of base fuid (K)
Nu Nusselt number
S Rate of entropy production (W m
−1
K
−1
)
c
p
Specifc heat capacity at constant pressure
(J kg
−1
K
−1
)
Pr Prandtl number of base fuid
u
r
, u
x
Component velocity (m s
−1
)
I Turbulence intensity
h Coefcient of heat transfer (W m
−2
K
−1
)
f Friction factor
k Turbulence kinetic energy (m
2
s
−2
)
D
h
Diameter of the pipe (m)
G
k
Rate of production of turbulent kinetic energy
(J kg
−1
)
S Modulus of the rate of strain tensor
C
μ
Turbulent constant
t
Turbulent constant
k
Turbulent Prandtl number for k
u
t
Frictional velocity (m s
−1
)
Greek symbols
Specifc dissipation (m
2
s
−2
)
φ Nanoparticle volume fraction
μ Dynamic viscosity (kg ms
−1
)
ρ Density of base fuid (kg m
−3
)
Thermal difusivity (m
2
s
−1
)
Thermal conductivity (W m
−1
K
−1
)
Von Karman constant
Subscripts
nf Nanofuid
p Nanoparticle
* Olatomide G. Fadodun
ofadodun@cerd.gov.ng
1
Centre for Energy Research and Development, Obafemi
Awolowo University, Ife, Nigeria
2
Department of Physics, Obafemi Awolowo University, Ife,
Nigeria
3
Department of Physics, Legacy University, Okija, Nigeria
4
Department of Industrial Physics, Chukwuemeka Odumegwu
Ojukwu University, Uli, Nigeria
5
Department of Chemistry, Obafemi Awolowo University, Ife,
Nigeria