Abstract
Laminar mixed convective buoyancy assisting flow through a two-dimensional vertical duct with a backward-facing step using nanofluids as a medium is numerically simulated using finite volume technique. Different types of nanoparticles such as Au, Ag, Al2O3, Cu, CuO, diamond, SiO2 and TiO2 with 5 % volume fraction are used. The wall downstream of the step was maintained at a uniform wall temperature, while the straight wall that forms the other side of the duct was maintained at constant temperature equivalent to the inlet fluid temperature. The walls upstream of the step and the backward-facing step were considered as adiabatic surfaces. The duct has a step height of 4.9 mm and an expansion ratio of 1.942, while the total length in the downstream of the step is 0.5 m. The downstream wall was fixed at uniform wall temperature 0 ≤ ΔT≤ 30 °C, which was higher than the inlet flow temperature. The Reynolds number in the range of 75 ≤ Re ≤ 225 was considered. It is found that a recirculation region was developed straight behind the backward-facing step which appeared between the edge of the step and few millimeters before the corner which connect the step and the downstream wall. In the few millimeters gap between the recirculation region and the downstream wall, a U-turn flow was developed opposite to the recirculation flow which mixed with the unrecirculated flow and traveled along the channel. Two maximum and one minimum peaks in Nusselt number were developed along the heated downstream wall. It is inferred that Au nanofluid has the highest maximum peaks while diamond nanofluid has the highest minimum peak. Nanofluids with a higher Prandtl number have a higher peak of Nusselt numbers after the separation and the recirculation flow disappeared.
Similar content being viewed by others
References
H.I. Abu-Mulaweh, A review of research on laminar mixed convection flow over backward- and forward-facing steps, Int. J. Thermal Sciences, 2003, Vol. 42, P. 897–909.
M.K. Denhum and M.A. Patrick, Laminar flow over a downstream-facing step in a two-dimensional flow channel, Trans. Instn. Chem. Engrs., 1974, Vol. 52, P. 361–367.
B.F. Armaly, F. Durst, J.C.F. Pereira, and B. Schonung, Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 1983, Vol. 127, P. 473–496.
B.F. Armaly, F. Durst, and V. Kottke, Momentum heat and mass transfer in backward-facing step flows, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
C. Shih and C.M. Ho, Three-dimensional recirculation flow in a backward-facing step, J. Fluids Engng., 1994, Vol. 116, P. 228–232.
T.P. Chiang, T.W.H. Sheu, and S.F. Tsai, Topological flow structures in backward-facing step channels, Computers and Fluids, 1997, Vol. 26, P. 321–337.
V. de Brederode and P. Bradshaw, Three-dimensional flow in normally two-dimensional separation bubbles. I. Flow behind a rearward-facing step, I.C. Aero Report, 1972, No. 72-19.
J. Hertzberg and C.M. Ho, Vortex dynamics in a rectangular sudden expansion, AIAA J., 1992, Vol. 30, No. 10, P. 2420–2425.
N. Tylli, L. Kaiktsis, and B. Ineichen, Sidewall effect in flow over a backward-facing step: experiments and numerical simulations, American Institute of Physics, 2002, Vol. 14, P. 3835–3845.
B.F. Armaly, A. Li, and J.H. Nie, Measurements in three-dimensional laminar separated flow, Int. J. Heat Mass Transfer, 2003, Vol. 46, P. 3573–3582.
J.H. Nie and B.F. Armaly, Reverse flow regions in three-dimensional backward-facing step flow, Int. J. Heat Mass Transfer, 2004, Vol. 47, P. 4713–4720.
W. Aung, An experimental study of laminar heat transfer downstream of back-step, J. Heat Transfer, 1983, Vol. 105, P. 823–829.
E.M. Sparrow and W. Chuck, PC solutions for the heat transfer and fluid flow downstream of an abrupt, asymmetric enlargement in a channel, Numerical Heat Transfer, 1987, Vol. 12, P. 19–40.
K. Khanafer, B. Al-Azmi, A. Al-Shammari, and L. Pop, Mixed convection analysis of laminar pulsating flow and heat transfer over a backward-facing step, Int. J. Heat Mass Transfer, 2008, Vol. 51, P. 5785–5793.
Y.T. Chen, J.H. Nie, B.F. Armaly, and H. Hsieh, Turbulent separated convection flow adjacent to backward-facing step-effects of step height, Int. J. Heat Mass Transfer, 2006, Vol. 49, P. 3670–3680.
H. Iwai, K. Nakabe, and K. Suzuki, Flow and heat transfer characteristics of backward-facing step laminar flow in a rectangular duct, Int. J. Heat Mass Transfer, 2000, Vol. 43, P. 457–471.
J.H. Nie and B.F. Armaly, Three-dimensional convective flow adjacent to backward-facing step-effects of step height, Int. J. Heat Mass Transfer, 2002, Vol. 45, P. 2431–2438.
B.F. Armaly, A. Li, and J.H. Nie, Three-dimensional forced convection flow adjacent to backward-facing step, J. Thermophysics Heat Transfer, 2002, Vol. 16, P. 222–227.
J.G. Barbosa Saldana and N.K. Anand, Forced convection over a three-dimensional horizontal backward-facing step, Int. J. Computational Engng. Sci., 2004, Vol. 11, P. 150–162.
J.G. Barbosa Saldana, N.K. Anand, and V. Sarin, Numerical simulation of mixed convective flow over a three-dimensional horizontal backward-facing step, J. Heat Transfer, 2005, Vol. 127, P. 1027–1036.
H. Lan, B.F. Armaly, and J.A. Drameier, Three-dimensional simulation of turbulent forced convection in a duct with backward-facing step, Int. J. Heat Mass Transfer, 2009, Vol. 52, P. 1690–1700.
J.T. Lin, B.F. Armaly, and T.S. Chen, Mixed convection heat transfer in inclined backward-facing step flows, Int. J. Heat Mass Transfer, 1991, Vol. 34, No. 6, P. 1568–1571.
J.T. Lin, B.F. Armaly, and T.S. Chen, Heat transfer in buoyancy-assisted, vertical backward-facing step flow, Int. J. Heat Mass Transfer, 1990, Vol. 33, P. 2121–2132.
B. Hong, B.F. Armaly, and T.S. Chen, Laminar mixed convection in a duct with a backward-facing step: the effects of inclination angle and Prandtl number, Int. J. Heat Mass Transfer, 1993, Vol. 36, No. 12, P. 3059–3067.
H.I. Abu-Mulaweh, B.F. Armaly, and T.S. Chen, Measurements of laminar mixed convection in boundary-layer flow over horizontal and inclined backward-facing steps, Int. J. Heat Mass Transfer, 1993, Vol. 36, No. 7. P. 1883–1895.
H. Iwai, K. Nakabe, K. Suzuki, and K. Matsubara, The effects of duct inclination angle on laminar mixed convective flows over a backward-facing step, Int. J. Heat Mass Transfer, 2000, Vol. 43, P. 473–485.
J.T. Lin, B.F. Armaly, and T.S. Chen, Mixed convection in buoyancy-assisting, vertical backward-facing step flows, Int. J. Heat Mass Transfer, 1990, Vol. 43, No. 10, P. 2121–2132.
W. Aung and G. Worku, Theory of fully developed, combined convection including flow reversal, J. Heat Transfer, 1985, Vol. 108, P. 485–488.
B. Hong, B.F. Armaly, and T.S. Chen, Mixed convection in a vertical duct with a backward-facing step: uniform wall heat flux case, in: Fundamental of Mixed Convection, ASME Winter Annual Meeting, HTD 1992, Vol. 213, P. 73–78.
B.J. Baek, B.F. Armaly, and T.S. Chen, Measurements in buoyancy-assisting separated flow behind a vertical backward-facing step, J. Heat Transfer, 1993, Vol. 115, P. 403–408.
H.I. Abu-Mulaweh, B.F. Armaly, and T.S. Chen, Measurements in buoyancy-assisting laminar boundary layer flow over a vertical backward-facing step-uniform wall heat flux case, Experimental Thermal Fluid Sci., 1993, Vol. 7, P. 39–48.
H.I. Abu-Mulaweh, B.F. Armaly, and T.S. Chen, Measurements in buoyancy-opposing laminar flow over a vertical backward-facing step, J. Heat Transfer, 1994, Vol. 116, P. 247–250.
H.I. Abu-Mulaweh, B.F. Armaly, and T.S. Chen, Effects of upstream wall heating on mixed convection in separated flows, J. Thermophys. Heat Transfer, 1995, Vol. 9, P. 715–721.
H. Iwai, K. Nakabe, K. Suzuki, and K. Mastubara, Numerical simulation of buoyancy-assisting backward-facing step flow and heat transfer in a rectangular duct, Heat Transfer Asian Res., 1999, Vol. 28, P. 58–76.
E. Abu-Nada, Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward-facing step, Int. J. Heat Mass Transfer, 2008, Vol. 29, P. 242–249.
A.A. Al-aswadi, H.A. Mohammed, N.H. Shuaib, and A. Campo, Laminar forced convection flow over a backward-facing step using nanofluids, Int. Communications Heat Mass Transfer, 2010, Vol. 37, P. 950–957.
H. A. Mohammed, A. A. Al-aswadi, H. I. Abu-Mulaweh, and N.H. Shuaib, Influence of nanofluids on mixed convective heat transfer over a horizontal backward facing step, Heat Transfer Asian Res., 2011, Vol. 27, P. 480–495.
H. A. Mohammed, A. A. Al-Aswadi, N.H. Shuaib, and R. Saidur, Convective heat transfer and fluid flow study over a step using nanofluids: A review, Renewable and Sustainable Energy Reviews, 2011, Vol. 15, P. 2921–2939.
S. Kakac and A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer, 2009, Vol. 52, P. 3187–3196.
V. Velagapudi, R.K. Konijeti, and C.S.K. Aduru, Empirical correlations to predict thermophysical and heat transfer characteristics of nanofluids, Thermal Sci., 2008, Vol. 12, No. 2, P. 27–37.
M. Corcione, Heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the sidewalls, Int. J. Thermal Sciences, 2010, Vol. 49, P. 1536–1546.
K. Khanafer, K. Vafai, and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 2003, Vol. 46, P. 3639–3653.
J.D. Anderson, Computational Fluid Dynamics: The Basic with Applications, Mc Graw-Hill, New York, 1995.
S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Corp., New York, 1980.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mohammed, H.A., Al-aswadi, A.A., Yusoff, M.Z. et al. Buoyancy-assisted mixed convective flow over backward-facing step in a vertical duct using nanofluids. Thermophys. Aeromech. 19, 33–52 (2012). https://doi.org/10.1134/S0869864312010040
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0869864312010040