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
Mengufuk Diisi dalam Bendalir Jeffrey dengan Kesan Pelesapan Likat)

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

Received: 20 July 2017/Accepted: 27 February 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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*Corresponding author; email: zuki@ump.edu.my