ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 93–103.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
F. Oueslati and B. Ben-Beya.
INVESTIGATION OF HEAT AND MASS TRANSFER
AND IRREVERSIBILITY PHENOMENA WITHIN
A THREE-DIMENSIONAL TILTED ENCLOSURE
FOR DIFFERENT SHAPES
and B. Ben-Beya
Abstract: Three-dimensional thermosolutal natural convection and entropy generation within an
inclined enclosure is investigated in the current study. A numerical method based on the ﬁnite volume
method and a full multigrid technique is implemented to solve the governing equations. Eﬀects of
various parameters, namely, the aspect ratio, buoyancy ratio, and tilt angle on the ﬂow patterns and
entropy generation are predicted and discussed.
Keywords: natural convection, heat and mass transfer, three-dimensional ﬂow, entropy generation,
Thermosolutal natural convection, which refers to the convection driven by a combination of temperature
and concentration gradients, has continued to be a very active area for researchers during the past few decades
due to its industrial and geophysical applications. Double diﬀusive convection occurs in a wide variety of ﬁelds,
such as astrophysics, oceanography, geology, channel-type solar energy collectors, biology, chemical processes, and
geophysical problems .
The heat and mass transfer and the ﬂuid ﬂow phenomenon were extensively studied within two-
dimensional (2D) conﬁned cavities, and detailed reviews on the 2D investigations are easily available in the lit-
erature [2–5]. For instance, the double diﬀusive natural convection investigation in an inclined enclosure having a
parallelogrammic shape was conducted by Costa  who reported that augmenting the Rayleigh number (Ra) or
buoyancy ratio N always leads to an increase in the heat and mass transfer rates in the 2D cavity. It was also
conﬁrmed that selected combinations of the tilt angle and aspect ratio can provide the maximum heat and mass
transfer rates. Chen et al.  examined 2D thermosolutal convection in an inclined enclosure. They showed that
the critical thermal Grashof number for the onset of stationary instability increases exponentially as the cavity
inclination changes from γ =0to90
, while the critical Grashof number for the onset of oscillatory instability
decreases exponentially. They also stated that the ﬁrst onset of instability is oscillatory rather than stationary
for tilt angles smaller than the critical value. Two-dimensional double diﬀusive convection was also predicted by
Al-Farhany and Turan  for the case of a tilted enclosure ﬁlled with a porous medium. The results showed that
the average Nusselt and Sherwood numbers decrease with increasing aspect ratio and tilt angle. The Nusselt and
Sherwood numbers increase at N>−1 and decrease at N<−1.
Physics Department, Faculty of Science, Albaha University, Al Baha, 6543 Kingdom of Saudi Arabia;
Laboratory of Physics of Fluids, Physics Department, Faculty of Science of Tunis, Tunis
El Manar University, Tunis, 2092 Tunisia; firstname.lastname@example.org. Translated from Prikladnaya Mekhanika i
Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 107–119, January–February, 2018. Original article submitted February
2018 by Pleiades Publishing, Ltd.