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Published in:
2016 | OriginalPaper | Chapter
Chebyshev Spectral Collocation Method for Natural Convection Flow of a Micropolar Nanofluid in the Presence of a Magnetic Field
Author : Önder Türk
Published in: Numerical Mathematics and Advanced Applications ENUMATH 2015
Publisher: Springer International Publishing
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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.