Sains Malaysiana 47(7)(2018): 1599–1605

http://dx.doi.org/10.17576/jsm-2018-4707-31

 

Flow and Heat Transfer in a Nanofluid Thin Film over an Unsteady Stretching Sheet

(Aliran dan Pemindahan Haba dalam Filem Nipis Nanobendalir atas Kepingan Meregang Secara tak Mantap)

 

R.C. AZIZ¹, I. HASHIM²* & S. ABBASBANDY³

 

¹Faculty of Science & Technology Open University Malaysia, 50480 Kuala Lumpur, Federal Territory, Malaysia

 

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

 

³Department of Mathematics, Imam Khomeini International University, Ghazvin 34149-16818, Iran

 

Diserahkan: 11 September 2017/Diterima: 27 Februari 2018

 

 

ABSTRACT

This study analyzes the heat transfer of a thin film flow on an unsteady stretching sheet in nanofluids. Three different types of nanoparticles are considered; copper Cu, alumina Al₂O₃ and titania TiO₂ with water as the base fluid. The governing equations are simplified using similarity transformations. The resulting coupled nonlinear differential equations are solved by the Homotopy Analysis Method (HAM). The analytical series solutions are presented and the numerical results obtained are tabulated. In particular, it shows that the heat transfer rate decreases when nanoparticles volume fraction increases.

 

Keywords: Heat transfer; nanofluids; thin film flow

 

ABSTRAK

Kajian ini menganalisis pemindahan haba bagi aliran filem nipis di atas kepingan meregang secara tak mantap dalam nanobendalir. Tiga jenis nanozarah berbeza telah dipertimbangkan; tembaga Cu, alumina Al₂O₃ dan titania TiO₂ dengan air sebagai bendalir asas. Persamaan menakluk dipermudahkan dengan menggunakan persamaan penukaran. Persamaan pembeza tidak linear berangkai yang terhasil diselesaikan melalui Kaedah Analisis Homotopi (KAH). Siri penyelesaian analitik ditunjukkan dan keputusan berangka yang diperoleh dijadualkan. Secara khususnya ditunjukkan bahawa kadar pemindahan haba menurun apabila isi padu pecahan nanozarah meningkat.

 

Kata kunci: Aliran filem nipis; nanobendalir; permindahan haba

RUJUKAN

Abel, M.S., Tawade, J. & Nandeppanavar, M.M. 2009. Effect of non-uniform heat source on MHD heat transfer in a liquid film over an unsteady stretching sheet. International Journal of Non-Linear Mechanics 44(9): 990-998.

Abu-Nada, E. & Oztop, H.F. 2009. Effects of inclination angle on natural convection in enclosures filled with Cu-water

nanofluid. International Journal of Heat and Fluid Flow 30(4): 669-678.

Andersson, H.I., Aarseth, J.B. & Dandapat, B.S. 2000. Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer 43(1): 69-74.

Aziz, R.C. & Hashim, I. 2010. Liquid film on unsteady stretching sheet with general surface temperature and viscous dissipation. Chinese Physics Letters 27(11): 110202.

Aziz, R.C., Hashim, I. & Abbasbandy, S. 2012. Effects of thermocapillarity and thermal radiation on flow and heat transfer in a thin liquid film on an unsteady stretching sheet. Mathematical Problem Engineering 2012: 127320.

Aziz, R.C., Hashim, I. & Alomari, A.K. 2011. Thin film flow and heat transfer on an unsteady stretching sheet with internal heating. Meccanica 46(2): 349-357.

Brinkman, H.C. 1952. The viscosity of concentrated suspensions and solutions. The Journal of Chemial Physics 20: 571-581.

Choi, S.U.S. 1995. Enhancing thermal conductivity of fluids with nanoparticles. The Proceeding of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD 66: 99-105.

Dandapat, B.S., Singh, S.K. & Maity, S. 2017. Thin film flow of bi-viscosity fluid over an unsteady stretching sheet: An analytical solution. International Journal Mechanical Sciences 130: 367-374.

Hayat, T., Ambreen, S., Awais, M. & Mesloub, S. 2012. Soret and Dufour effects for three-dimensional flow in a viscoelastic fluid over a stretching surface. International Journal of Heat and Mass Transfer 55: 2129-2136.

Liao, S.J. 2004. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall. p. 31.

Liao, S.J. 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics. and Computation 147: 449-513.

Liao, S.J. 2009. Notes on the homotopy analysis method: Some definitions and theorems. Communications in. Nonlinear Science and Numerical Simulation 14: 983-997.

Liu, I.C. & Andersson, H.I. 2008. Heat transfer in a liquid film on an unsteady stretching sheet. International Journal of Thermal Sciences 47(6): 766-772.

Maiga, S.E.B., Palm, S.J., Nguyen, C.T., Roy, G. & Galanis, N. 2005. Heat transfer enhancement by using nanofluids in forced convection flows. International Journal of Heat and Fluid Flow 26(4): 530-546.

Maity, S., Ghatani, Y. & Dandapat, B.S. 2016. Thermocapillary flow of a thin nanoliquid film over an unsteady stretching sheet. Journal Heat Transfer 138(4): 042401.

Megahed, A.M. 2015. Effect of slip velocity on Casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation. Applied Mathematics and Mechanics 36(10): 1273-1284.

Narayana, M. & Sibanda, P. 2012. Laminar flow of nanoliquid film over an unsteady stretching sheet. International Journal of Heat and Mass Transfer 55(25-26): 7552-7560.

Noor, N.F.M. & Hashim, I. 2010. Thermocapillarity and magnetic field effects in a thin liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer 53(9-10): 2044-2051.

Noor, N.F.M., Abdulaziz, O. & Hashim, I. 2010. MHD flow and heat transfer in a thin liquid film on an unsteady stretching sheet by the homotopy analysis method. International Journal Numerical Methods in Fluids 63(3): 357-373.

Oztop, H.F. & Abu-Nada, E. 2008. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal Heat Fluid Flow 29(5): 1326-1336.

Santra, A.K., Sen, S. & Chakraborty, N. 2008. Study of heat transfer characteristics of copper-water nanofluid in a differentially heated square cavity with different viscosity models. Journal of Enhanced Heat Transfer 15: 273-287.

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

Vajravelu, K., Prasad, K.V. & Ng, C.O. 2012. Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface. Communication Nonlinear Science and Numerical Simulation 17(11): 4163-4173.

Waheed, S.E. 2016. Flow and heat transfer in a Maxwell liquid film over an unsteady stretching sheet in a porous medium with radiation. SpringerPlus 5(1): 1061.

Wang, C. 2006. Analytic solutions for a liquid film on an unsteady stretching surface. Heat and Mass Transfer 42: 759-766.

Wang, C.Y. 1990. Liquid film on an unsteady stretching surface. Quarterly of Applied Mathematics 48: 601-610.

Xu, H., Pop, I. & You, X.C. 2013. Flow and heat transfer in a nano-liquid film over an unsteady stretching surface. International Journal Heat and Mass Transfer 60(1): 646- 652.

 

 

*Pengarang untuk surat-menyurat; email: ishak_h@ukm.edu.my