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

 

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

RUJUKAN

Anwar, I., Amin, N. & Pop, I. 2008. Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder. International Journal of Non-Linear Mechanics 43(9): 814-821.

Baaijens, F.P., Selen, S.H., Baaijens, H.P., Peters, G.W. & Meijer, H.E. 1997. Viscoelastic flow past a confined cylinder of a low density polyethylene melt. Journal of Non-Newtonian Fluid Mechanics 68(2): 173-203.

Das, K., Acharya, N. & Kundu, P.K. 2015. Radiative flow of MHD Jeffrey fluid past a stretching sheet with surface slip and melting heat transfer. Alexandria Engineering Journal 54(4): 815-821.

Ferdows, M., Afify, A. & Tzirtzilakis, E. 2017. Hall current and viscous dissipation effects on boundary layer flow of heat transfer past a stretching sheet. International Journal of Applied and Computational Mathematics 3(4): 3471-3482.

Gaffar, S.A., Prasad, V.R., Reddy, E.K. & Bég, O.A. 2015. Thermal radiation and heat generation/absorption effects on viscoelastic double-diffusive convection from an isothermal sphere in porous media. Ain Shams Engineering Journal 6(3): 1009-1030.

Gebhart, B. 1962. Effects of viscous dissipation in natural convection. Journal of Fluid Mechanics 14(02): 225-232.

George, K.E. 2009. 2 - Non-Newtonian fluid mechanics and polymer rheology. In Advances in Polymer Processing, edited by Thomas, S. & Yang, Weimin. Cambridge: Woodhead Publishing. pp: 13-46.

Geropp, D. 1969. Der turbulente wärmeübergang am rotierenden zylinder. Archive of Applied Mechanics 38(4): 195-203.

Hayat, T., Ashraf, M.B., Shehzad, S.A. & Bayomi, N.N. 2015. Mixed convection flow of viscoelastic nanofluid over a stretching cylinder. Journal of the Brazilian Society of Mechanical Sciences and Engineering 37(3): 849-859.

Kasim, A.R.M., Mohammad, N.F., Shafie, S. & Pop, I. 2013. Constant heat flux solution for mixed convection boundary layer viscoelastic fluid. Heat and Mass Transfer 49(2): 163-171.

Merkin, J. 1977. Mixed convection from a horizontal circular cylinder. International Journal of Heat and Mass Transfer 20(1): 73-77.

Merkin, J. & Pop, I. 1988. A note on the free convection boundary layer on a horizontal circular cylinder with constant heat flux. Heat and Mass Transfer 22(1): 79-81.

Mohamed, M.K.A., Salleh, M.Z., Noar, N. & Ishak, A. 2016. The viscous dissipation effects on the mixed convection boundary layer flow on a horizontal circular cylinder. Jurnal Teknologi 78(4-4): 73-79.

Morini, G.L. 2013. Viscous dissipation. Encyclopedia of Microfluidics and Nanofluidics Boston, MA: Springer US. pp: 1-15.

Nazar, R. 2003. Mathematical models for free and mixed convection boundary layer flows of micropolar fluids.Tesis PhD Universiti Teknologi Malaysia, Malaysia (Unpublished).

Nazar, R., Amin, N. & Pop, I. 2003. Mixed convection boundary-layer flow from a horizontal circular cylinder in micropolar fluids: Case of constant wall temperature. International Journal of Numerical Methods for Heat & Fluid Flow 13(1): 86-109.

Prasad, V.R., Gaffar, S.A., Reddy, E.K. & Bég, O.A. 2014. Flow and heat transfer of Jeffreys non-Newtonian fluid from horizontal circular cylinder. Journal of Thermophysics and Heat Transfer 28(4): 764-770.

Prasad, V.R., Gaffar, S.A., Reddy, E.K. & Bég, O.A. 2015. Numerical study of non-Newtonian Jeffreys fluid from a permeable horizontal isothermal cylinder in non-Darcy porous medium. Journal of the Brazilian Society of Mechanical Sciences and Engineering 37(6): 1765-1783.

Rao, A.S., Nagendra, N. & Prasad, V.R. 2015. Heat transfer in a Non-Newtonian Jeffrey’s fluid over a Non-Isothermal Wedge. Procedia Engineering 127: 775-782.

Rashad, A., Chamkha, A. & Modather, M. 2013. Mixed convection boundary-layer flow past a horizontal circular cylinder embedded in a porous medium filled with a nanofluid under convective boundary condition. Computers & Fluids 86: 380-388.

Rotte, J. & Beek,W. 1969. Some models for the calculation of heat transfer coefficients to a moving continuous cylinder. Chemical Engineering Science 24(4): 705-716.

Salleh, M.Z., Nazar, R. & Pop, I. 2010. Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating. Journal of the Taiwan Institute of Chemical Engineers 41(6): 651-655.

Subba, R.A., Ramachandra, P.V., Rajendra, P., Sasikala, M. & Anwar, B.O. 2017. Numerical study of non-Newtonian polymeric boundary layer flow and heat transfer from a permeable horizontal isothermal cylinder. Frontiers in Heat and Mass Transfer (FHMT) 9(1).

Yirga, Y. & Shankar, B. 2013. Effects of thermal radiation and viscous dissipation on magnetohydrodynamic stagnation point flow and heat transfer of nanofluid towards a stretching sheet. Journal of Nanofluids 2(4): 283-291.

Zin, N.A.M., Khan, I. & Shafie, S. 2017. Exact and numerical solutions for unsteady heat and mass transfer problem of Jeffrey fluid with MHD and Newtonian heating effects. Neural Computing and Applications. doi.org/10.1007/ s00521-017-2935-6.

 

 

*Pengarang untuk surat-menyurat; email: zuki@ump.edu.my

 

 

 

 

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