Sains Malaysiana 41(12)(2012): 1643–1649

 

Mixed Convection Flow about a Solid Sphere Embedded in a Porous Medium

 Filled with a Nanofluid

(Aliran Olakan Campuran terhadap Sfera Pejal yang Terbenam dalam Medium Berliang

dengan Nanobendalir)

 

Leony Tham

Fakulti Industri dan Asas Tani, Universiti Malaysia Kelantan, 17600 Jeli, Kelantan

Malaysia

 

Roslindar Nazar*

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

43600 UKM Bangi, Selangor, Malaysia

 

Diserahkan: 18 Mei 2012 / Diterima: 31 Julai 2012

 

ABSTRACT

A steady laminar mixed convection boundary layer flow about an isothermal solid sphere embedded in a porous medium filled with a nanofluid has been studied for both cases of assisting and opposing flows. The transformed boundary layer equations were solved numerically using an implicit finite-difference scheme. Three different types of nanoparticles, namely Cu, Al2O3 and TiO2 in water-based fluid were considered. Numerical solutions were obtained for the skin friction coefficient, the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the nanoparticle volume fraction and the mixed convection parameters were analyzed and discussed.

 

Keywords: Boundary layer;mixed convection; nanofluid; porous medium; solid sphere

 

ABSTRAK

Aliran lapisan sempadan olakan campuran berlamina mantap terhadap sfera pejal isoterma yang terbenam dalam medium berliang dengan nanobendalir telah dikaji bagi kes aliran membantu dan aliran menentang. Persamaan lapisan sempadan terjelma diselesaikan secara berangka dengan skema beza terhingga tersirat. Tiga jenis nanozarah dalam bendalir asas air dipertimbangkan, iaitu Cu, Al2O3 and TiO2. Penyelesaian berangka diperoleh bagi pekali geseran kulit, profil halaju dan profil suhu. Ciri-ciri aliran dan pemindahan haba bagi pelbagai nilai parameter pecahan isi padu nanozarah dan parameter olakan campuran dianalisis dan dibincangkan.

 

Kata kunci: Lapisan sempadan; medium berliang; nanobendalir; olakan campuran; sfera pejal

RUJUKAN

Abu-Nada, E. 2008. Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int. J. Heat Fluid Flow 29: 242-249.

Abu-Nada, E. & Oztop, H.F. 2009. Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. Int. J. Heat Fluid Flow 30(4): 669-678.

Ahmad, S. & Pop, I. 2010. Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids. Int. Comm. Heat Mass Transfer 37(8): 987-991.

Arifin, N.M., Nazar, R. & Pop, I. 2011. Viscous flow due to a permeable stretching/ shrinking sheet in a nanofluid. Sains Malaysiana40: 1359-1367.

Bachok, N., Ishak, A., Nazar, R. & Pop, I. 2010. Flow and heat transfer at a general three-dimensional stagnation point in a nanofluid. Physica B: Condensed Matter 405(24): 4914-4918.

Brinkman, H.C. 1952. The viscosity of concentrated suspensions and solutions. J. Chem. Phys. 20: 571-581.

Buongiorno, J. 2006. Convective transport in nanofluids. ASME J. Heat Transfer 128(3): 240-250.

Cebeci, T. & Bradshaw, P. 1988. Physical and Computational Aspects of Convective Heat Transfer. New York: Springer.

Cheng, P. 1982. Mixed convection about a horizontal cylinder and a sphere in a fluid saturated porous medium. Int. J. Heat Mass Transfer 25: 1245-1247.

Choi, S.U.S. 1995. Enhancing thermal conductivity of fluids with nanoparticles. InDevelopment and applications of non-Newtonian Flows.Siginer, D.A. & Wagn, H. P. (eds.).ASME MD-vol. 231 and FED-vol. 66: 99-105.

Das, S.K., Choi, S.U.S., Yu, W. & Pradet, T. 2007. Nanofluids: Science and Technology. New York: Wiley.

Daungthongsuk, W. & Wongwises, S. 2008. Effect of thermophysical properties models on the predicting of the convective heat transfer coefficient for low concentration nanofluid. Int. Comm. Heat Mass Transfer 35: 1320-1326.

Eastman, J.A., Choi, S.U.S., Li, S., Yu, W. & Thompson, L.J. 2010. Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles. J. Appl. Phys. Lett. 78(6): 718-720.

Hady, F.M., Ibrahim, F.S., Abdel-Gaied, S.M. & Eid, M.R. 2012. Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet. Nanoscale Research Letters 7: 229(1-13).

Jou, R.Y. & Tzeng, S.C. 2006. Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures. Int. Comm. Heat Mass Transfer 33(6): 727-736.

Kang, H.U., Kim, S.H. & Oh, J.M. 2006. Estimation of thermal conductivity of nanofluid using experimental effective particle volume. Exp. Heat Transfer 19: 181-191.

Khanafer, K., Vafai, K. & Lightstone, M. 2003. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transfer 46(19): 3639-3653.

Kumar, S., Prasad, S.K. & Banerjee, J. 2010. Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model. Appl. Math. Modelling34(3): 573-592.

Merkin, J.H. 1977. Mixed convection from a horizontal circular cylinder. Int. J. Heat Mass Transfer 20: 73-77.

Nazar, R., Amin, N. & Pop, I. 2003. The Brinkman model for the mixed convection boundary layer flow past a horizontal circular cylinder in a porous medium. Int. J. Heat Mass Transfer 46(17): 3167-3178.

Nazar, R., Tham, L., Pop, I. & Ingham, D.B. 2011. Mixed convection boundary layer flow from a horizontal circular cylinder embedded in a porous medium filled with a nanofluid. Trans. Porous Media 86: 517-536.

Nield, D.A. & Bejan, A. 2006. Convection in Porous Media. New York: Springer.

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

Rosca, N.C., Grosan, T. & Pop, I. 2012. Stagnation-point flow and mass transfer with chemical reaction past a permeable stretching/shrinking sheet in a nanofluid. Sains Malaysiana 41(10): 1271 – 1279.

Tiwari, R.K. & Das, M.K. 2007. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transfer 50(9-10): 2002-2018.

 

 

 

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