Dogonchi, A.S., Nayak, M.K., Karimi, N., Chamkha, A. J. and Ganji, D.D. (2020) Numerical
simulation of hydrothermal features of Cu-H2O nanofluid natural convection within a porous
annulus considering diverse configurations of heater. Journal of Thermal Analysis and
Calorimetry, 141, pp. 2109-2125. (doi: 10.1007/s10973-020-09419-y)
There may be differences between this version and the published version. You are
advised to consult the publisher’s version if you wish to cite from it.
http://eprints.gla.ac.uk/209482/
Deposited on 5 February 2020
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1
Numerical simulation of hydrothermal features of Cu-H
2
O nanofluid natural
convection within a porous annulus considering diverse configurations of heater
A.S. Dogonchi
1*
, M. K. Nayak
2
, N. Karimi
3
, Ali J. Chamkha
4,5
, D.D. Ganji
6
1
Department of Mechanical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad
Katoul, Iran.
2
Department of Physics, IHSE, Siksha “O” Anusandhan Deemed to be University, Bhubaneswar-
751003, Odisha, India
3
School of Engineering, University of Glasgow, Glasgow, UK
4
Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince
Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia
5
RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab
Emirates
6
Mechanical Engineering Department, Babol Noshirvani University of Technology, Babol, Iran
*
Corresponding author: E-mail: sattar.dogonchi@yahoo.com
Abstract
The purpose of the current study is to numerically investigate the effects of shape factors of
nanoparticles on natural convection in a fluid saturated porous annulus developed between the
elliptical cylinder and square enclosure. A numerical method called the control volume-based
finite element method (CVFEM) is implemented for solving the governing equations. The
modified flow and thermal structures and corresponding heat transfer features are investigated.
Numerical outcomes reveal very good grid independency and excellent agreement with the
existing studies. The obtained results convey that at a certain aspect ratio, increment of
Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt
number. Further, enhancement of Rayleigh number increases the velocity of nanofluid while
that of aspect ratio of the elliptical cylinder shows the opposite trend.
Keywords: Square enclosure; inclined elliptical cylinder; Cu-H
2
O nanofluids; diverse
configurations of heater; CVFEM.
Nomenclature
( , )uv
velocity components in
( , )xy
directions
density
( )
p
C
heat capacity
2
dynamic viscosity
thermal expansion
k
thermal conductivity
K
permeability parameter
T
temperature
p
pressure
m
shape factor
vorticity
stream function
thermal diffusivity
h
T
temperature at the hot side of the enclosure
c
T
temperature at the cold side of the enclosure
Pr
Prandtl number
Ra
Raleigh number
Da
Darcy number
AR
aspect ratio
Subscripts
f base fluid
nf nanofluid
s solid nanoparticle
1. Introduction
Engineers constantly look for innovative methods to improve heat transfer performance by
implementing a wide range of techniques. Natural convection is widely perceived as the
ultimate heat transfer process in numerous engineering devices includes enclosures with heat-
generating elements. Natural Convection in porous media has attracted intensive attention from
3
researchers in the view of its relevance in infiltrating molten metal, transport processes,
extracting crude oil from oil reservoirs, geothermal operations, chemical reactors, thermal
reservoirs, insulating buildings, see for example Nield and Bejan [1], Ingham and Pop [2], Sajid
and Ali [3], Guerrero Martinez et al. [4,5]. In particular, the problem of natural convection of
nanofluids in porous media has already received considerable attention. Here, we briefly
review some of the recent works in this field.
Siavashi et al. [6] have examined the mixed convection within a porous enclosure filled
with non-Newtonian nanoliquid. Izadi et al. [7] discussed the impingement of a jet of air,
hydrogen and Cu-H
2
O nanofluid over a hot surface covered by porous media with non-uniform
input jet velocity. They observed that rise in the volume fraction of nanoliquid augmented the
heat transfer rate. They also perceived that the utilization of non-uniform impingement jet with
diminishing velocity distribution upgrades the thermal performance of the heat sink. Xiong et
al. [8] investigated the influences of nanoparticles with diverse shapes on magnetic radiative
flow within wavy porous space. In their investigation, roles of magnetic parameter, radiation
parameter, nanoparticles' shape and Rayleigh number have been explored. Outputs revealed
that applied magnetic field uplifts the temperature distribution and the Nu
ave
amplifies with Ra
and Da numbers as well as nanoparticles' shape, while magnetic field has the opposite impact.
Bozorg et al. [9] carried out a numerical investigation of heat transfer and oil–
Al
2
O
3
nanoliquid flow inside a parabolic trough solar receiver with internal porous structure.
The results displayed that incremented Reynolds number and volume fraction of nanoparticle
yielded an augmentation in thermal efficiency, pressure drop and heat transfer coefficient.
However, the rise in inlet temperature reduces them. At Re higher than 30×10
4
, concurrent
usage of nanoparticles and porous structure with Da = 0.3 augments pressure drops up to 42.5%
and 42%, exergetic efficiencies by 7% and 15%, thermal efficiencies up to 8% and 15% and
heat transfer coefficients nearly 7%, and 20% for inlet temperature of 500 and 600 K,
respectively. Varol et al. [10] scrutinized entropy generation during natural convection inside
non-evenly heated porous triangular cavity. Lee et al. [11] studied natural convection inside an
annulus among a circular cylinder and enclosure locally heated from the bottom wall. Yoon et
al. [12] examined the role of natural convection within a square enclosure considering two
cylinders as heater and cooler. Sheremet et al. [13] implemented Tiwari and Das nanofluid
model and explored the effects of natural convection inside a square porous cavity.
Selimefendigil and Öztop [14] demonstrated the impacts of internal heat generation and
inclined magnetic field on natural convection in a flexible sided triangular cavity.
4
Mun et al. [15] analyzed the effects of vertical and horizontal equal distance of internal
hot cylinders on natural convection inside a cold enclosure. Bondareva and Sheremet [16]
investigated natural convection melting in a square cavity with a local heater. Rajarathinam
and Nithyadevi [17] showed the heat transfer growth of Cu-H
2
O nanliquid in an inclined porous
cavity with internal heat generation. Dogonchi and Ganji [18] investigated the impact of
Cattaneo-Christov heat flux on magnetic radiative nanoliquid flow and heat transfer among
parallel plates. Further, Dogonchi et al. [19] studied the magnetic natural convection of Cu-
H
2
O nanoliquid in a horizontal semi-cylinder with a local triangular heater. In a separate work,
Dogonchi et al. [20] revealed through numerical analysis the influences of natural convection
of Cu-H
2
O nanoliquid filling triangular enclosure with semicircular bottom wall.
In a numerical study, Nayak [21] worked on magnetic 3D flow and heat transfer
analysis of nanofluid by shrinking surface and declared the effect of thermal radiation and
viscous dissipation there. The same group pf authors [22] discussed natural convection effects
on 3D magnetic flow of nanofluid over permeable stretched surface with thermal radiation.
Malekpour et al. [23] analyzed the effects of magnetic, natural convection and entropy
generation of Cu-H
2
O nanoliquid in an I-shape enclosure. Further, Graphene nanoplatelets
nanoliquids thermal and hydrodynamic performance on integral fin heat sink ( Arshad and Ali
[24]), pressure drop and heat transfer in a straight mini-channel heat sink using TiO
2
nanofluid
( Arshad and Ali [25]), solar dish assisted S-CO
2
Brayton cycle using nanoliquids flow (Khan
et al. [26]) and potential evaluation of ferric oxide and titania nanofluids (Babar and Ali [27]
) were carried out. Many other works have been conducted on natural convection within a
variety of enclosures containing diverse types of inner bodies of various configurations
implementing numerical computations/approaches such as finite volume, finite difference, and
finite element method [28-34].
In order to analyze the problems associated with flow through porous media the models
such as the Darcy, Forchheimer-extended Darcy, and the Brinkman-extended Darcy models
are usually invoked. Choi and Eastman [35] developed nanofluids (nanoscale particles are
suspended in a base fluid) which served as the best medium for an effective and efficient
convective heat transfer process imparting high-performance energy efficient cooling system
needed for many modern applications. According to the thermo-physical features of nanofluids
as well as the particle shapes, sizes, stabilities and volume fractions, nanoliquids with superior
thermal conductivity (compared to the base fluids) augments its heat transfer characteristics
[36]. Further, introduction of porous media upgrades conduction in addition to the existing
convection because of the larger surface contact area occupying among porous structure and
![Fig. 2. Comparison between the a) current work and b) Kim et al. [49] at Ra=105](/figures/fig-2-comparison-between-the-a-current-work-and-b-kim-et-al-edrfgost.webp)
