Sains Malaysiana 46(9)(2017): 1667–1674

http://dx.doi.org/10.17576/jsm-2017-4609-40

 

Unsteady Flow of a Nanofluid Past a Permeable Shrinking Cylinder using Buongiorno’s Model

(Aliran Tak Mantap Nanobendalir melalui Silinder Telap Mengecut menggunakan model Buongiorno)

 

KHAIRY ZAIMI^1*, ANUAR ISHAK² & IOAN POP³

 

¹Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis Indera Kayangan, Malaysia

 

²Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

³Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

 

Diserahkan: 28 Jun 2016/Diterima: 18 April 2017

 

ABSTRACT

The unsteady laminar boundary layer flow of a nanofluid and heat transfer over a permeable shrinking cylinder using the Buongiorno’s nanofluid model is investigated. Using a similarity transformation, the governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically using a shooting method. The numerical results are obtained for velocity, temperature and concentration profiles as well as the skin friction coefficient, the local Nusselt number and the local Sherwood number. Dual solutions are found to exist in a certain range of the suction and unsteadiness parameters. It is observed that suction parameter increase both the skin friction coefficient and the heat transfer rate at the surface, whereas the opposite trend is obtained for the Sherwood number. It is also observed that suction widens the range of the unsteadiness parameter for which the solution exists.

 

Keywords: Nanofluids; shrinking cylinder; suction; unsteady flow

 

ABSTRAK

Aliran lapisan sempadan lamina tak mantap nanobendalir dan pemindahan haba terhadap silinder telap mengecut menggunakan model nanobendalir Buongiorno dikaji. Menggunakan penjelmaan keserupaan, persamaan menakluk dalam bentuk persamaan pembezaan separa dijelmakan kepada persamaan pembezaan biasa dan diselesaikan secara berangka menggunakan kaedah tembakan. Keputusan berangka diperoleh bagi profil-profil halaju, suhu dan pecahan isi padu nanozarah serta pekali geseran kulit, nombor Nusselt setempat dan nombor Sherwood setempat. Penyelesaian dual didapati wujud bagi julat-julat tertentu parameter sedutan dan parameter ketakmantapan. Didapati parameter sedutan meningkatkan pekali geseran kulit dan kadar pemindahan haba pada permukaan, manakala telatah bertentangan diperoleh bagi nombor Sherwood. Didapati juga sedutan meluaskan julat parameter ketakmantapan yang penyelesaian wujud.

 

Kata kunci: Aliran tak mantap; nanobendalir; sedutan; silinder mengecut

RUJUKAN

Bejan, A. 2013. Convection Heat Transfer. 4th ed. New York: Wiley.

Buongiorno, J. 2006. Convective transport in nanofluids. ASME Journal of Heat Transfer 128: 240-250.

Choi, S.U.S. 1995. Enhancing thermal conductivity of fluids with nanoparticles. In Developments and Application of Non- Newtonian Flows FED-vol. 231/MD 66: 99-105.

Das, S.K., Choi, S.U.S., Yu, W. & Pradeep, T. 2007. Nanofluids: Science and Technology. New Jersey: Wiley-Interscience.

Dhanai, R., Rana, P. & Kumar, L. 2016. MHD mixed convection nanofluid flow and heat transfer over an inclined cylinder due to velocity and thermal slip effects: Buongiorno’s model. Powder Technology 288: 140-150.

Duangthongsuk, W. & Wongwises, S. 2008. Effect of thermophysical properties models on the predicting of the convective heat transfer coefficient for low concentration nanofluid. International Communications in Heat and Mass Transfer 35: 1320-1326.

Fang, T., Zhang, J., Zhong, Y. & Tao, H. 2011. Unsteady viscous flow over an expanding stretching cylinder. Chinese Physics Letters 28. Article ID. 124707.

Fang, T., Zhang, J. & Zhong, Y. 2012. Note on unsteady viscous flow on the outside of an expanding or contracting cylinder. Communications in Nonlinear Science and Numerical Simulation 17: 3124-3128.

Harris, S.D., Ingham, D.B. & Pop, I. 2009. Mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport in Porous Media 77: 267-285.

Ishak, A., Nazar, R. & Pop, I. 2008a. Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder. Applied Mathematical Modelling 32: 2059-2066.

Ishak, A., Nazar, R. & Pop, I. 2008b. Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder. Energy, Conversion and Management 49: 3265-3269.

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

Jaluria, Y. & Torrance, K.E. 2003. Computational Heat Transfer. 2nd ed. New York: Taylor & Francis.

Kuznetsov, A.V. & Nield, D.A. 2010. Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences 49: 243-247.

Merkin, J.H. 1985. On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics 20: 171-179.

Mohamed, M.K.A., Noar, N.A.Z.M., Salleh, M.Z. & Ishak, A. 2016. Free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation. Sains Malaysiana 45(2): 289-296.

Mukhopadhyay, S. 2012. Mixed convection boundary layer flow along a stretching cylinder in porous medium. Journal of Petroleum Science and Engineering 96-97: 73-78.

Paullet, J. & Weidman, P.D. 2007. Analysis of stagnation point flow towards a stretching sheet. International Journal of Nonlinear Mechanics 42: 1084-1091.

Postelnicu, A. & Pop, I. 2011. Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge. Applied Mathematics and Computation 217: 4359-4368.

Rosca, A.V. & Pop, I. 2013. Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. International Journal of Heat and Mass Transfer 60: 355-364.

Simal, S., Rosselló, C., Berna, A. & Mulet, A. 1998. Drying of shrinking cylinder-shaped bodies. Journal of Food Engineering 37: 423-435.

Trisaksri, V. & Wongwises, S. 2007. Critical review of heat transfer characteristics of nanofluids. Renewable, Sustainable Energy Review 11: 512-523.

Wan Zaimi, W.M.K.A., Ishak, A. & Pop, I. 2013. Unsteady viscous flow over a shrinking cylinder. Journal of the King Saud University-Science 25: 143-148.

Wang, C.Y. 1988. Fluid flow due to a stretching cylinder. Physics of Fluids 31: 466-468.

Wang, C.Y. & Ng, C. 2011. Slip flow due to a stretching cylinder. International Journal of Non-Linear Mechanics 46: 1191- 1194.

Wang, C.Y. 2012. Natural convection on a vertical stretching cylinder. Communications in Nonlinear Science and Numerical Simulation 17: 1098-1103.

Wang, X.Q. & Mujumdar, A.S. 2008. A review on nanofluids - Part I: Theoretical and numerical investigations. Brazilian Journal of Chemical Engineering 25: 613-630.

Weidman, P.D., Kubitschek, D.G. & Davis, A.M.J. 2006. The effect of transpiration on selfsimilar boundary layer flow over moving surfaces. International Journal of Engineering Science 44: 730-737.

*Pengarang untuk surat-menyurat; email: khairy@unimap.edu.my