Heat Transfer in Water Based Nanofluids (TiO2-H2O, Al2O3-H2O and Cu-H2O) over a Stretching Cylinder
Two-dimensional steady natural convection heat transfer to water based nanofluids (TiO2-water, Al2O3-water, and Cu-water) flowing over a stretching cylinder has been investigated numerically. Using the similarity transformations, the continuity, momentum, and energy equations are reduced to a set of nonlinear, ordinary differential equations. These equations are solved numerically using MATLAB. Because of the algebraic decay of the similarity functions, numerical integration is performed using a compressed coordinate. The axial velocity is the result of forced convection due to stretching, and natural convection induced by the heated cylinder. The results show that the flow velocity with a nanofluid is smaller compared with the velocity of the base fluid for the same stretching and heating conditions, which is basically caused by the increase of viscosity and density. The presence of nanoparticles reduces the thickness of the hydrodynamic boundary layer and enhances the heat transfer rate. The location of the zero shear stress on the surface of the cylinder occurs at shorter and shorter distances (along the cylinder) as the solid volume fraction of nanoparticles increases.
nanofluid, heat transfer, stretching cylinder, convection, similarity solution
 S. Choi, Enhancing thermal conductivity of fluids with nanoparticle, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME FED, vol. 231/MD-Vol. 66, pp. 99-105, 1995.
 H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu. Bussei. Vol. 7, pp. 227-233, 1993.
 S. Lee, S.U.S. Choi, S. Li, and J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, J. Heat Transf. Vol. 121, pp. 280-289, 1999.
 Y. Xuan, and Q. Li, Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Transf. Vol. 21, pp. 58-64, 2000.
 Y. Xuan, and W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transf. Vol. 43, pp. 3701-3707, 2000.
 J. Buongiorno, Convective transport in nanofluids. ASME J. Heat Transf. Vol. 128, pp. 240-250, 2006.
 C. Kleinstreuer, J. Li, and J. Koo, Microfluidics of nano-drug delivery. Int. J. Heat Mass Transf. Vol. 51, pp. 5590-5597, 2008.
 J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, and L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol based nanofluids
containing copper nanoparticles, Appl. Phys. Lett. Vol. 78, pp. 718-720, 2001.
 S.M.S. Murshed, K.C. Leong, and C. Yang, Enhanced thermal conductivity of TiO2-water based nanofluids, Int. J. Thermal Sci. Vol. 44, pp. 367-373, 2005.
 K. Khanafer, K. Vafai, and M. lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transf. Vol. 46, pp. 3639-3653, 2003.
 S.E.B. Maiga, S.J. Palm, C.T. Nguyen, G. Roy, and N. Galanis, Heat transfer enhancement by using nanofluids in forced convection flows, Int. J. Heat Fluid Flow Vol. 26, pp. 530-546, 2005.
 R.Y. Jou, and S.-C. Tzeng, Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures, Int. Commu. Heat Mass Transf. Vol. 33, pp.727–736, 2006.
 K.S. Hang, Ji-H. Lee, and S.P. Jang, Buoyancy-driven heat transfer of water-based nanofluids in a rectangular cavity, Int. J. Heat Mass Transf. Vol. 50, pp. 4003-4010, 2007.
 R.K. Tiwari, and M.K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. Vol. 50, pp. 2002–2018, 2007.
 H.F. Oztop, and E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow Vol. 29, pp. 1326–1336, 2008.
 E. Abu-Nada, and H.F. Oztop, Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid, Int. J. Heat Fluid Flow. Vol. 30, pp. 669–678, 2009.
 M, Muthtamilselvan, P. Kandaswamy, and J. Lee, Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure, Commun. Nonlinear Sci. Numer. Simul. Vol. 15, pp. 1501–1510, 2010.
 A.V. Kuznetsov, and D.A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Thermal Sci. Vol. 49, pp. 243–247, 2010.
 N. Bachok, A. Ishak, and I. Pop, Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, Int. J. Thermal Sci. Vol. 49, pp. 1663–1668, 2010.
 W.A. Khan, and A. Aziz, Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux, Int. J. Thermal Sci. Vol. 50, pp. 1207-1214, 2011.
 A. Aziz, and W.A. Khan, Natural convective boundary layer flow of a nanofluid past a convectively heated vertical plate, Int. J. Thermal Sci. Vol. 52, pp. 83-90, 2012.
 M.M. Rahman, M. A. Al-Lawatia, I.A. Eltayeb, and N. Al-Salti, Hydromagnetic slip flow of water based nanofluids past a wedge with convective surface in the presence of heat generation (or) absorption, Int. J. Thermal Sci. Vol. 57, pp. 172-182, 2012.
 M.M. Rahman, and I.A. Eltayeb, Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition, Meccanica. doi: 10.1007/s11012-012-9618-2.
 S. Kakaç, and A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids. Int. J. Heat Mass Transf. Vol. 52, pp. 3187–3196, 2009.
 S.K. Das, S.U.S. Choi, W. Yu, and T. Pradeep, Nanofluids: Science and Technology. Wiley, New Jersey, 2007.
 V. Trisaksri, and S. Wongwises, Critical review of heat transfer characteristics of nanofluids. Renew. Sustain. Energy Rev. Vol. 11, pp. 512-523, 2007.
 X.Q. Wang, and A.S. Mujumdar, A review on nanofluids—Part I: theoretical and numerical investigations, Braz. J. Chem. Eng. Vol. 25, pp. 613–630, 2008.
 X.Q. Wang, and A.S. Mujumdar, A review on nanofluids—Part II: experiments and applications, Braz. J. Chem. Eng. Vol. 25, pp. 631–648, 2008.
 L.J. Crane, Flow Past a Stretching Plate, Z. Angew Math. Phys. Vol. 21, pp. 645–647, 1970.
 C.Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids Vol. 27, pp. 1915-1917, 1984.
 H.I. Andersson, K.H. Bech, and B.S. Dantapat, Magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Int. J. Nonlinear Mech. Vol. 27, pp. 929–936, 1992.
 E.M.A. Elbashbeshy, Heat transfer over a stretching surface with variable surface heat flux, J. Phys. D: Appl. Phys. Vol. 31, pp. 1951–1954, 1998.
 M.M. Rahman, and M.A. Al-Lawatia, Effects of higher order chemical reaction on micropolar fluid flow on a power law permeable stretched sheet with variable concentration in a porous medium, Can. J. Chem. Eng. Vol. 88, pp. 23–32, 2010.
 M.M. Rahman, Combined effects of internal heat generation and higher order chemical reaction on the non-Darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium, Can. J. Chem. Eng. doi: 10.1002/cjce.20644.
 J.F. Brady, and A. Acrivos, Steady flow in a channel or tube with an accelerating surface velocity, J. Fluid Mech. Vol. 112, pp. 127-150, 1981.
 C.Y. Wang, Fluid flow due to a stretching cylinder, Phys. Fluids Vol. 31, pp. 466-468, 1988.
 A. Ishak, R. Nazar, and I. Pop, Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder, App. Math. Modeling Vol. 2, pp. 2059-2066, 2008.
 C.Y. Wang, Natural convection on a vertical stretching cylinder, Commu. Nonlin. Sci. Numer. Simulat. Vol. 17, pp. 1098-1103, 2012.
 W.A. Khan, and I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat Mass Transf. Vol. 53, pp. 2477–2483, 2010.
 A.A.A. Hamad, and I. Pop, Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects, Transp. Porous Med. Vol. 87, pp. 25–39, 2011.
 S.M. Sebdani, M. Mahmoodi, and S.M. Hashemi. Effect of nanofluid variable properties on mixed convection in a square cavity, Int. J. Thermal Sci. Vol. 52, pp. 112-126, 2012.
 A.V. Kuznetsov, and D.A. Nield, Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Thermal Sci. Vol. 50, pp. 712-717, 2011.
 D.A. Nield, and A.V. Kuznetsov, The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid, Int. J. Heat Mas Transf. Vol. 54, pp. 374-378, 2011.
 K.P. Travis, B.D. Todd, and D.J. Evans. Poiseuille flow of molecular liquids, Physica A Vol. 240, pp. 315-327, 1997.
 B. Straughan. Green-Naghdi fluid with non-thermal equilibrium effects, Proc. Roy. Soc. London A Vol. 466, pp. 2021-2032, 2010.
 H.C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys. Vol. 20, pp. 571–581, 1952.
 Y. Xuan, and Q. Li, Investigation on convective heat transfer and flow features of nanofluids, ASME J. Heat Transf. Vol. 125, pp. 151–155, 2003.
 M.A. Mansour, and S.E. Ahmed, Mixed convection flows in a square lid-driven cavity with heat source at the bottom utilizing nanofluid, The Canadian J. Chem. Eng., doi: 10.1002/cjce.20533.
 R.L. Hamilton, and O.K. Crossner, Thermal conductivity of heterogeneous two-component system, I and EC Fundamentals, Vol. 1, pp. 187-191, 1962.
 C.J. Ho, M.W. Chen, and Z.W. Li, Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity, Int. J. Heat Mass Transf. Vol. 51, pp. 4506–4516, 2008.
 M.K. Das, and P.S. Ohal, Natural convection heat transfer augmentation in a partially heated and partially cooled square cavity utilizing nanofluids, Int. J. Numer. Meth. Heat Fluid Flow Vol. 19, pp. 411-431, 2009.