Sains Malaysiana 45(2)(2016): 289–296

 

Free Convection Boundary Layer Flow on a Horizontal Circular Cylinder in a Nanofluid with Viscous Dissipation

(Olakan Bebas Aliran Lapisan Sempadan pada Silinder Bulat Mengufuk dalam Nanobendalir dengan Pelesapan Likat)

 

Muhammad Khairul Anuar Mohamed1, Nor Aida Zuraimi Md Noar1, Mohd Zuki Salleh*1 & Anuar Ishak2

1Applied & Industrial Mathematics Research Group, Faculty of Industrial Sciences and Technology

Universiti Malaysia Pahang, 26300 Kuantan, Pahang Darul Makmur, Malaysia

2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 10 April 2015/Diterima: 2 Julai 2015

 

ABSTRACT

In this paper, the problem of free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation and constant wall temperature is investigated. The transformed boundary layer equations are solved numerically using finite difference scheme namely the Keller-box method. Numerical solutions were obtained for the reduced skin friction coefficient, Nusselt number and Sherwood number as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Brownian motion parameter, thermophoresis parameter, Lewis number and Eckert number were analyzed and discussed.

Keywords: Free convection; horizontal circular cylinder; nanofluid; viscous dissipation

 

ABSTRAK

Dalam kajian ini, masalah olakan bebas aliran lapisan sempadan pada silinder bulat mengufuk dalam nanobendalir dengan pelesapan likat dan suhu permukaan malar dikaji. Persamaan lapisan sempadan terjelma diselesaikan secara berangka dengan menggunakan skim beza terhingga dikenali sebagai kaedah kotak Keller. Penyelesaian berangka diperoleh bagi pekali geseran kulit diturunkan, nombor Nusselt dan nombor Sherwood diturunkan serta profil halaju dan suhu. Ciri aliran dan pemindahan haba bagi pelbagai nilai parameter gerakan Brown, parameter termoforesis, nombor Lewis dan nombor Eckert dianalisis dan dibincangkan.

Kata kunci: Nanobendalir; olakan bebas; pelesapan likat; silinder bulat mengufuk

 

RUJUKAN

 

Anwar, I., Qasim, A.R., Ismail, Z., Salleh, M.Z. & Shafie, S. 2013. Chemical reaction and uniform heat generation/absorption effects on MHD stagnation-point flow of a nanofluid over a porous sheet. World Applied Sciences Journal 24(10): 1390.

Arifin, N.M.¡, Nazar, R. & Pop, I. 2011. Viscous flow due to a permeable stretching/shrinking sheet in a nanofluid. Sains Malaysiana 40(12): 1359-1367.

Azim, N.H.M.A. 2014. Effects of viscous dissipation and heat generation on MHD conjugate free convection flow from an isothermal horizontal circular cylinder. SOP Transactions on Applied Physics 1(3): 1-11.

Bachok, N., Ishak, A. & Pop, I. 2010. Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. International Journal of Thermal Sciences 49(9): 1663-1668.

Blasius, H. 1908. Grenzschichten in Flssigkeiten mit kleiner Reibung. Zeitschrift f¨urangewandte Mathematik und Physik 56: 1-37.

Chen, C.H. 2004. Combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation. International Journal of Engineering Science 42(7): 699-713.

Fr¨ossling, N. 1958. Calculating by series expansion of the heat transfer in laminar, constant property boundary layers at non isothermal surfaces. Archiv f¨or Fysik 14: 143-151.

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

Ishak, A., Nazar, R., Amin, N., Filip, D. & Pop, I. 2007. Mixed convection of the stagnation-point flow towards a stretching vertical permeable sheet. Malaysian Journal of Mathematical Sciences 2: 217-226.

Ishak, A., Nazar, R. & Pop, I. 2006. Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 41(5): 509-518.

Kakaç, S. & Pramuanjaroenkij, A. 2009. Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer 52(13-14): 3187-3196.

Khan, W.A. & Pop, I. 2010. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat and Mass Transfer 53(11-12): 2477-2483.

Merkin, J.H. & Pop, I. 1988. A note on the free convection boundary layer on a horizontal circular cylinder with constant heat flux. Wärme - und Stoffübertragung 22(1-2): 79-81.

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

Merkin, J.H. 1976. Free convection boundary layer on an isothermal horizontal cylinder. ASME/AIChe Heat Transfer Conference, St. Louis, USA.

Molla, M.M., Hossain, M.A. & Paul, M.C. 2006. Natural convection flow from an isothermal horizontal circular cylinder in presence of heat generation. International Journal of Engineering Science 44(13-14): 949-958.

Nazar, R., Jaradat, M., Arifin, N. & Pop, I. 2011. Stagnation-point flow past a shrinking sheet in a nanofluid. Central European Journal of Physics 9(5): 1195-1202.

Nazar, R., Amin, N., Filip, D. & Pop, I. 2004. Stagnation point flow of a micropolar fluid towards a stretching sheet. International Journal of Non-Linear Mechanics 39(7): 1227-1235.

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.

Nazar, R., Amin, N. & Pop, I. 2002. Free convection boundary layer on an isothermal horizontal circular cylinder in a micropolar fluid. Proceedings of Tweifth Int Heat Transfer Conference. Paris, Elsevier. 2: 525-530.

Partha, M.K., Murthy, P. & Rajasekhar, G.P. 2005. Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat and Mass Transfer 41(4): 360-366.

Rosca, A.V., Rosca, N.C. & Pop, I. 2014. Note on dual solutions for the mixed convection boundary layer flow close to the lower stagnation point of a horizontal circular cylinder: Case of constant surface heat flux. Sains Malaysiana 43(8): 1239-1247.

Roşca, N.C. & Pop, I. 2014. Unsteady boundary layer flow of a nanofluid past a moving surface in an external uniform free stream using Buongiorno’s model. Computers & Fluids 95(0): 49-55.

Salleh, M.Z., Nazar, R. & Pop, I. 2011. Numerical solutions of forced convection boundary layer flow on a horizontal circular cylinder with Newtonian heating. Malaysian Journal of Mathematical Sciences 5(2): 161-184.

Salleh, M.Z. & Nazar, R. 2010. Free convection boundary layer flow over a horizontal circular cylinder with Newtonian heating. Sains Malaysiana 39(4): 671-676.

Salleh, M.Z., Nazar, R. & Pop, I. 2009. Forced convection boundary layer flow at a forward stagnation point with Newtonian heating. Chemical Engineering Communications 196: 987-996.

Sarif, N.M., Salleh, M.Z., Tahar, R.M. & Nazar, R. 2014. Numerical solution of the free convection boundary layer flow over a horizontal circular cylinder with convective boundary conditions. AIP Conference Proceedings 1602: 179-185.

Singh, G. & Makinde, O.D. 2014. Axisymmetric slip flow on a vertical cylinder with heat transfer. Sains Malaysiana 43(3): 483-489.

Soundalgekar, V.M. 1972. Viscous dissipation effects on unsteady free convective flow past an infinite, vertical porous plate with constant suction. International Journal of Heat and Mass Transfer 15(6): 1253-1261.

Tahavvor, A.R. & Yaghoubi, M. 2010. Experimental and numerical study of frost formation by natural convection over a cold horizontal circular cylinder. International Journal of Refrigeration 33(7): 1444-1458.

Tham, L., Nazar, R. & Pop, I. 2014. Mixed convection flow from a horizontal circular cylinder embedded in a porous medium filled by a nanofluid: Buongiorno-Darcy model. International Journal of Thermal Sciences 84: 21-33.

Tham, L. & Nazar, R. 2012. Mixed convection flow about a solid sphere embedded in a porous medium filled with a nanofluid. Sains Malaysiana 41(12): 1643-1649.

Tiwari, R. & Das, M. 2007. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50: 2002-2018.

Vajravelu, K. & Hadjinicolaou, A. 1993. Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation. International Communications in Heat and Mass Transfer 20(3): 417-430.

Wong, K.V. & De Leon, O. 2010. Applications of nanofluids: Current and future. Advances in Mechanical Engineering 2: 519659.

Yacob, N.A., Ishak, A., Pop, I. & Vajravelu, K. 2011. Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid. Nanoscale Research Letters 6(1): 1-7.

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.

Yusoff, N.H.M., Uddin, M.J. & Ismail, A.I.M. 2014. Combined similarity-numerical solutions of MHD boundary layer slip flow of non-Newtonian power-law nanofluids over a radiating moving plate. Sains Malaysiana 43(1): 151-159.

 

*Pengarang untuk surat-menyurat; email: zukikuj@yahoo.com

 

 

sebelumnya