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Sains Malaysiana 47(7)(2018): 1607–1615
http://dx.doi.org/10.17576/jsm-2018-4707-32
Mathematical Model of Mixed Convection Boundary Layer Flow over a Horizontal Circular Cylinder Filled in a Jeffrey Fluid with Viscous Dissipation Effect (Model
Matematik bagi Aliran Lapisan Sempadan Olakan Campuran melalui
Silinder Bulat
SYAZWANI MOHD
ZOKRI1,
NUR
SYAMILAH
ARIFIN1,
MUHAMMAD
KHAIRUL
ANUAR
MOHAMED1,
ABDUL
RAHMAN
MOHD
KASIM1,
NURUL
FARAHAIN
MOHAMMAD2
& MOHD ZUKI SALLEH1*
1Faculty of Industrial
Sciences & Technology, Universiti Malaysia Pahang, 26300 UMP Kuantan,
Pahang Darul Makmur, Malaysia
2Department of
Computational and Theoretical Sciences, Kulliyyah of Science,
International Islamic
University Malaysia, 25200 Kuantan, Pahang Darul Makmur, Malaysia
Diserahkan: 20 Julai
2017/Diterima: 27 Februari 2018
ABSTRACT
This paper delves into the problem
of mixed convection boundary layer flow from a horizontal circular cylinder
filled in a Jeffrey fluid with viscous dissipation effect. Both cases of cooled
and heated cylinders are discussed. The governing equations which have been
converted into a dimensionless form using the appropriate non-dimensional
variables are solved numerically through the Keller-box method. A comparative
study is performed and authentication of the present results with documented
outcomes from formerly published works is excellently achieved. Tabular and
graphical representations of the numerical results are executed for the
specified distributions, considering the mixed convection parameter, Jeffrey
fluid parameters and the Prandtl and Eckert numbers. Interestingly, boundary
layer separation for mixed convection parameter happens for some positive
(assisting flow) and negative (opposing flow) values. Strong assisting flow
means the cylinder is heated, which causes the delay in boundary layer
separation, whereas strong opposing flow means the cylinder is cooled, which
conveys the separation point close to the lower stagnation point. Contradictory
behaviours of both Jeffrey fluid parameters are observed over the velocity and
temperature profiles together with the skin friction coefficient and Nusselt
number. The increase of the Prandtl number leads to the decrement of the
temperature profile, while the increase of the Eckert number results in the
slight increment of the skin friction coefficient and decrement of the Nusselt
number. Both velocity and temperature profiles of Eckert number show no effects
at the lower stagnation point of the cylinder.
Keywords: Boundary; horizontal circular
cylinder; Jeffrey fluid; layer separation; viscous dissipation
ABSTRAK
Kertas ini membincangkan masalah aliran
lapisan sempadan olakan campuran ke atas silinder bulat mengufuk
dalam bendalir Jeffrey dengan kesan pelesapan likat. Kedua-dua
kes silinder yang disejuk dan dipanaskan dibincangkan. Persamaan
menakluk yang telah ditukarkan kepada bentuk tak bermatra menggunakan
pemboleh ubah penjelmaan tak bermatra yang sesuai diselesaikan
secara berangka melalui kaedah kotak Keller. Kajian perbandingan
dijalankan dan pengesahan keputusan sekarang dengan hasil yang
telah didokumenkan daripada kerja yang diterbitkan sebelum ini
dicapai dengan baik. Perwakilan jadual dan grafik bagi keputusan
berangka dijalankan untuk taburan yang ditentukan, mengambil kira
parameter olakan campuran, parameter bendalir Jeffrey dan nombor
Prandtl dan Eckert. Menariknya, pemisahan lapisan sempadan untuk
parameter olakan campuran berlaku untuk beberapa nilai positif
(aliran membantu) dan negatif (aliran menentang). Aliran membantu
yang kuat bermaksud silinder dipanaskan yang menyebabkan kelewatan
dalam pemisahan lapisan sempadan, manakala aliran menentang yang
kuat bermaksud silinder disejukkan yang membawa titik perpisahan
dekat kepada titik genangan bawah. Tingkah laku yang bercanggah
pada kedua-dua parameter bendalir Jeffrey diperhatikan melalui
profil halaju dan suhu bersama-sama dengan pekali geseran kulit
dan nombor Nusselt. Peningkatan nombor Prandtl menyebabkan pengurangan
profil suhu, manakala peningkatan nombor Eckert menyebabkan sedikit
kenaikan pada pekali geseran kulit dan penurunan nombor Nusselt.
Kedua-dua profil halaju dan suhu nombor Eckert tidak memberi kesan
pada titik genangan bawah silinder.
Kata
kunci: Bendalir Jeffrey; pelesapan likat; pemisahan lapisan sempadan; silinder
bulat mengufuk
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*Pengarang untuk surat-menyurat; email: zuki@ump.edu.my
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