Abstract
The two-dimensional, laminar, unsteady natural convection flow of a micropolar nanofluid (Al2O3-water) in a square enclosure under the influence of a magnetic field, is solved numerically using the Chebyshev spectral collocation method (CSCM). The nanofluid is considered as Newtonian and incompressible, and the nanoparticles and water are assumed to be in thermal equilibrium. The governing equations in nondimensional form are given in terms of stream function, vorticity, micrototaion and temperature. The coupled and nonlinear equations are solved iteratively in the time direction, and an implicit backward difference scheme is employed for the time integration. The boundary conditions of vorticity are computed within this iterative process using a CSCM discretization of the stream function equation. The main advantages of CSCM, such as the high accuracy and the ease of implementation, are made used of to obtain solutions for very high values of Ra and Ha, up to 107 and 1000, respectively.
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References
G. Bourantas, V. Loukopoulos, MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid. Int. J. Heat Mass Transf. 79, 930–944 (2014)
G. Bourantas, V. Loukopoulos, Modeling the natural convective flow of micropolar nanofluids. Int. J. Heat Mass Transf. 68 (0), 35–41 (2014)
J.P. Boyd, Chebyshev and Fourier Spectral Methods (Dover, New York, 2000)
A.C. Eringen, Simple microfluids. Int. J. Eng. Sci. 2 (2), 205–217 (1964)
D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, vol. 26 (SIAM, Philadelphia, 1977)
R.U. Haq, S. Nadeem, N.S. Akbar, Z.H. Khan, Buoyancy and radiation effect on stagnation point flow of micropolar nanofluid along a vertically convective stretching surface. IEEE Trans. Nanotechnol. 14 (1), 42–50 (2015)
S.T. Hussain, S. Nadeem, R. Ul Haq, Model-based analysis of micropolar nanofluid flow over a stretching surface. Eur. Phys. J. Plus 129 (8), 1–10 (2014)
S.K. Jena, S. Bhattacharyya, The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below. Int. J. Eng. Sci. 24 (1), 69–78 (1986)
L.N. Trefethen, Spectral Methods in Matlab (SIAM, Philadelphia, 2000)
Ö. Türk, M. Tezer-Sezgin, Chebyshev spectral collocation method for unsteady MHD flow and heat transfer of a dusty fluid between parallel plates. Numer. Heat Transf. Part A: Appl. 64 (7), 597–610 (2013)
Ö. Türk, M. Tezer-Sezgin, Fem solution to natural convection flow of a micropolar nanofluid in the presence of a magnetic field. Meccanica (2015, in press). doi:10.1007/s11012–016–0431–1
K.F.V. Wong, T. Kurma, Transport properties of alumina nanofluids. Nanotechnology 19 (34), 345702 (2008)
M. Zadravec, M. Hribersek, L. Skerget, Natural convection of micropolar fluid in an enclosure with boundary element method. Eng. Anal. Bound. Elem. 33 (4), 485–492 (2009)
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Türk, Ö. (2016). Chebyshev Spectral Collocation Method for Natural Convection Flow of a Micropolar Nanofluid in the Presence of a Magnetic Field. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_43
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DOI: https://doi.org/10.1007/978-3-319-39929-4_43
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