The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base nanofluids containing Copper Oxide (CuO) and Alumina (Al2O3) as nanoparticles is investigated. It is assumed that the nanofluid flows in a channel between two parallel plates with the channel’s upper plate accelerating and exchange heat with the ambient surrounding following the Newton’s law of cooling, while the lower plate is stationary and maintained at a constant temperature. Using appropriate similarity transformation, the governing Navier-Stokes and the energy equations are reduced to a set of nonlinear ordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement technique and numerically by an efficient Runge-Kutta-Fehlberg integration technique coupled with shooting method. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop and Nusselt number are presented graphically, and discussed quantitatively. 1. Introduction Studies related to laminar flow and heat transfer of a viscous fluid in the space between two parallel plates, one of which is moving relative to the other, have received the attention of several researchers due to their numerous industrial and engineering applications. This type of flow is named in honour of Maurice Marie Alfred Couette, a professor of physics at the French University of Angers in the late 19th century [1]. Couette flow has been used to estimate the drag force in many wall driven applications such as lubrication engineering, power generators and pumps, polymer technology, petroleum industry, and purification of crude oil. Literature survey indicates that interest in the Couette flows has grown during the past decades. Jana and Datta [2] examined the effects of Coriolis force on the Couette flow and heat transfer between two parallel plates in a rotating system. Singh [3] studied unsteady free convection flow of an incompressible viscous fluid between two vertical parallel plates, in which one is fixed and the other is impulsively started in its own plane. Kearsley [4] investigated the problem of steady state Couette flow with viscous heating. Jha [5] numerically examined the effects of magnetic field on Couette flow between two vertical parallel plates. The combined effects of variable viscosity and thermal conductivity on generalized Couette flow and heat transfer in the presence of transversely imposed magnetic field have been studied numerically by Makinde and
References
[1]
B. R. Munson, D. F. Young, and T. H. Okiishi, Fundamentals of Fluid Mechanics, John Wiley & Sons, New York, NY, USA, 2002.
[2]
R. N. Jana and N. Datta, “Couette flow and heat transfer in a rotating system,” Acta Mechanica, vol. 26, no. 1–4, pp. 301–306, 1977.
[3]
A. K. Singh, “Natural convection in unsteady Couette motion,” Defence Science Journal, vol. 38, no. 1, pp. 35–41, 1988.
[4]
A. J. Kearsley, “A steady state model of couette flow with viscous heating,” International Journal of Engineering Science, vol. 32, no. 1, pp. 179–186, 1994.
[5]
B. K. Jha, “Natural convection in unsteady MHD couette flow,” Heat and Mass Transfer, vol. 37, no. 4-5, pp. 329–331, 2001.
[6]
O. D. Makinde and O. O. Onyejekwe, “A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity,” Journal of Magnetism and Magnetic Materials, vol. 323, no. 22, pp. 2757–2763, 2011.
[7]
G. S. Seth, M. S. Ansari, and R. Nandkeolyar, “Unsteady hydromagnetic couette flow within a porous channel,” Tamkang Journal of Science and Engineering, vol. 14, no. 1, pp. 7–14, 2011.
[8]
R. K. Deka and A. Bhattacharya, “Unsteady free convective Couette flow of heat generation/absorbing fluid in porous medium,” International Journal of Mathematical Archive, vol. 2, no. 6, pp. 853–863, 2011.
[9]
S. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, FED 231/MD, 66, pp. 99–105, ASME, San Francisco, Calif, USA, 1995.
[10]
J. Lee and I. Mudawar, “Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels,” International Journal of Heat and Mass Transfer, vol. 50, no. 3-4, pp. 452–463, 2007.
[11]
J. Niu, C. Fu, and W. Tan, “Slip-flow and heat transfer of a non-newtonian nanofluid in a microtube,” PLoS ONE, vol. 7, no. 5, Article ID e37274, 2012.
[12]
T. G. Motsumi and O. D. Makinde, “Effects of thermal radiation and viscous dissipation on boundary layer flow of nanofluids over a permeable moving flat plate,” Physica Scripta, vol. 86, no. 4, Article ID 045003, 2012.
[13]
C. J. Choi, S. P. Jang, and S. U. S. Choi, “Electrokinetic effects of charged nanoparticles in microfluidic Couette flow,” Journal of Colloid and Interface Science, vol. 363, no. 1, pp. 59–63, 2011.
[14]
J. C. Maxwell, Electricity and Magnetism, Clarendon Press, Oxford, UK, 3rd edition, 1904.
[15]
H. C. Brinkman, “The viscosity of concentrated suspensions and solutions,” The Journal of Chemical Physics, vol. 20, no. 4, pp. 571–581, 1952.
[16]
H. F. Oztop and E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,” International Journal of Heat and Fluid Flow, vol. 29, no. 5, pp. 1326–1336, 2008.
[17]
S. Kaka？ and A. Pramuanjaroenkij, “Review of convective heat transfer enhancement with nanofluids,” International Journal of Heat and Mass Transfer, vol. 52, no. 13-14, pp. 3187–3196, 2009.
[18]
T. Y. Na, Computational Methods in Engineering Boundary Value Problems, Academic Press, New York, NY, USA, 1979.
[19]
O. D. Makinde, “Thermal criticality in viscous reactive flows through channels with a sliding wall: an exploitation of the Hermite-Padé approximation method,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 312–317, 2008.
