Article
Dimensionless Correlations for Natural Convection Heat
Transfer from a Pair of Vertical Staggered Plates Suspended in
Free Air
Alessandro Quintino
1,
* , Marta Cianfrini
2
, Ivano Petracci
3
, Vincenzo Andrea Spena
1
and Massimo Corcione
1
Citation: Quintino, A.; Cianfrini, M.;
Petracci, I.; Spena, V.A.; Corcione, M.
Dimensionless Correlations for
Natural Convection Heat Transfer
from a Pair of Vertical Staggered
Plates Suspended in Free Air.
Appl. Sci. 2021, 11, 6511. https://
doi.org/10.3390/app11146511
Academic Editor: João Carlos de
Oliveira Matias
Received: 14 June 2021
Accepted: 13 July 2021
Published: 15 July 2021
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4.0/).
1
Dipartimento di Ingegneria Astronautica Elettrica ed Energetica, Sapienza Università di Roma,
Via Eudossiana 18, 00184 Roma, Italy; vincenzo.spena@uniroma1.it (V.A.S.);
massimo.corcione@uniroma1.it (M.C.)
2
Istituto Nazionale di Fisica Nucleare—Laboratori Nazionali di Frascati, Divisione Tecnica,
Via Enrico Fermi 54, 00044 Frascati, Italy; marta.cianfrini@lnf.infn.it
3
Dipartimento di Ingegneria Industriale, Università di Roma Tor Vergata, Via del Politecnico 1,
00133 Roma, Italy; ivano.petracci@uniroma2.it
* Correspondence: alessandro.quintino@uniroma1.it
Abstract:
Buoyancy-induced convection from a pair of staggered heated vertical plates suspended
in free air is studied numerically with the main scope to investigate the basic heat and momentum
transfer features and to determine in what measure any independent variable affects the thermal
performance of each plate and both plates. A computational code based on the SIMPLE-C algorithm
for pressure-velocity coupling is used to solve the system of the governing conservation equations
of mass, momentum and energy. Numerical simulations are carried out for different values of the
Rayleigh number based on the plate length, as well as of the horizontal separation distance between
the plates and their vertical alignment, which are both normalized by the plate length. It is observed
that an optimal separation distance between the plates for the maximum heat transfer rate related
to the Rayleigh number and the vertical alignment of the plates does exist. Based on the results
obtained, suitable dimensionless heat transfer correlations are developed for each plate and for the
entire system.
Keywords:
natural convection in free air; vertical staggered plates; buoyancy-induced convection;
dimensionless correlations
1. Introduction
Buoyancy-induced convection in air from heated vertical parallel plates is of much
interest for a number of thermal engineering applications, such as the electronic equipment
cooling and the solar energy capture to name a few.
The first documented work dealing with this subject was executed experimentally
by Elenbaas [
1
], who, by using a pair of square plates suspended face to face in free air,
obtained the optimal plate spacing for the dissipation of the maximum amount of heat.
Investigations aimed at determining the optimal plate spacing for vertical parallel plate
channels subjected to uniform wall temperature and uniform heat flux conditions were
subsequently conducted theoretically by Bodoia and Osterle [
2
], Levy [
3
], Anand et al. [
4
]
and Bar-Cohen and Rohsenow [
5
], as well as both experimentally and theoretically by
Onur et al. [
6
,
7
] and Baskaya et al. [
8
] for channels consisting of a heated plate and an
unheated plate insulated at the rear.
Other studies dealing with natural convection in vertical parallel plate channels, which
were mostly performed experimentally, were carried out by
Aung et al. [9]
,
Carpenter et al. [10]
,
Sparrow and Bahrami [
11
], Wirtz and Stutzman [
12
], Azevedo and Sparrow [
13
],
Webb and Hill [
14
], Martin et al. [
15
], Straatman et al. [
16
], Qing et al. [
17
] and
Appl. Sci. 2021, 11, 6511. https://doi.org/10.3390/app11146511 https://www.mdpi.com/journal/applsci
