Hindawi Publishing Corporation
Advances in Mechanical Engineering
Volume 2013, Article ID 121943, 8 pages
http://dx.doi.org/10.1155/2013/121943
Research Article
Mixed Convection Boundary Layer Flow Embedded in
a Thermally Stratified Porous Medium Saturated by a Nanofluid
Mohd Hafizi Mat Yasin,
1
Norihan Md. Arifin,
1
Roslinda Nazar,
2
Fudziah Ismail,
1
and Ioan Pop
3
1
Institute for Mathematical Research, Universiti Putra Malaysia (UPM), Selangor, 43400 Serdang, Malaysia
2
School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia (UKM),
Selangor, 43600 Bangi, Malaysia
3
Department of Mathematics, Babes ¸-Bolyai University, 400084 Cluj-Napoca, Romania
Correspondence should be addressed to Norihan Md. Arifn; norihanarifn@yahoo.com
Received 11 June 2013; Revised 12 September 2013; Accepted 15 September 2013
Academic Editor: Guy Lauriat
Copyright © 2013 Mohd Hafzi Mat Yasin et al. Tis 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.
We present the numerical investigation of the steady mixed convection boundary layer fow over a vertical surface embedded
in a thermally stratifed porous medium saturated by a nanofuid. Te governing partial diferential equations are reduced to
the ordinary diferential equations, using the similarity transformations. Te similarity equations are solved numerically for
three types of metallic or nonmetallic nanoparticles, namely, copper (Cu), alumina (Al
2
O
3
), and titania (TiO
2
), in a water-based
fuid to investigate the efect of the solid volume fraction or nanoparticle volume fraction parameter of the nanofuid on the
fow and heat transfer characteristics. Te skin friction coefcient and the velocity and temperature profles are presented and
discussed.
1. Introduction
Te problem of convective fow in a porous medium provides
one of the basic scenarios for heat transfer theory, and thus,
it is of considerable theoretical and practical interest and has
been extensively studied. Excellent reviews of the topic can be
found in the books by Nield and Bejan [1], Pop and Ingham
[2], Ingham and Pop [3], Vafai [4, 5], and Vadasz [6]. Te most
basic and classical problem for natural convection in a porous
medium is that of free convection past a vertical fat plate,
which was frst studied by Cheng and Minkowycz [7]. Tere
are several numerical studies on the mixed convection fow
in a porous medium, and we mention here those by Merkin
[8, 9], Harris et al. [10, 11], Nazar et al. [12, 13], Ping and I-Dee
[14], and Ping [15].
Te problem of convection fow in a thermally stratifed
fuid is also an important problem, and this type of fow arises
in many contexts, ranging from industrial and technological
settings to the oceanic and atmospheric environments. Strat-
ifcation is due to the diference in water density like warm
water is less than cool water and therefore tends to foat on top
of the cooler heavier water so that the thermal stratifcation
refers to a temperature layering efect that occurs in water
and so forth. Termal stratifcation is a characteristic of all
fuid bodies surrounded by diferentially heated side walls.
Hence, the dynamics of fows in thermally stratifed fuid
is gaining attention amongst researchers of both theoretical
and applied felds in the last few decades. In the case of
vertical consideration, thermal stratifcation arises mainly
because of temperature variations, concentration diference,
or presence of diferent fuids of diferent density (Moorthy
and Senthilvadivu [16]). Takar and Pop [17] analysed the
free convection from a vertical plate immersed in a ther-
mally stratifed porous medium under the boundary layer
assumptions. Natural convection in a thermally stratifed
fuid saturated porous medium has been studied by Tiwari