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Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method. (English) Zbl 1137.76453
Summary: The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviour of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] Bert, C.W.; Malik, M., Differential quadrature method in computational mechanics, a review, Appl. mech. rev., 49, 1, 1-28, (1996)
[2] Carabineanu, A.; Dinu, A.; Oprea, I., The application of the boundary element method to the MHD duct flow, Zamp, 46, 971-981, (1995) · Zbl 0836.76053
[3] Chen, W.; Wang, X.; Zhong, T., The structure of weighting coefficients matrices of harmonic differential quadrature and its application, Commun. numer. methods eng., 12, 455-460, (1996) · Zbl 0860.65012
[4] Chen, W.; Yu, Y.; Wang, X., Reducing the computational requirement of differential quadrature method, Numer. methods part. differen. equat., 12, 5, 565-577, (1996) · Zbl 0868.65014
[5] Chen, W.; Zhong, T.; Liang, S., On the DQ analysis of geometrically nonlinear vibration of immovably simply supported beams, J. sound vib., 206, 5, 745-748, (1997)
[6] Chen, W.; Zhong, T.; Shu, C., A Lyapunov formulation for efficient solution of the Poisson and convection-diffusion equations by the differential quadrature method, J. comput. phys., 139, 1-7, (1998)
[7] Gardner, L.R.T.; Gardner, G.A., A two-dimensional bi-cubic B-spline finite element used in a study of MHD duct flow, Comput. methods appl. mech. eng., 124, 365-375, (1995) · Zbl 0844.65073
[8] Shercliff, A., The motion of conducting fluids in pipes under transverse fields, Proc. camb. philos. soc, 49, 136, (1953) · Zbl 0050.19404
[9] Shu, C., Differential quadrature and its applications in engineering, (2000), Springer-Verlag
[10] Shu, C.; Chen, W., On optimal selection of interior points for applying discretized boundary conditions in DQ vibration analysis of beams and plates, J. sound vib., 222, 2, 239-257, (1999) · Zbl 1235.74372
[11] Shu, C.; Richards, B.E., Application of generalized differential quadrature to solve two-dimensional incompressible navier – stokes equations, Int. J. numer. methods fluids, 15, 791-798, (1992) · Zbl 0762.76085
[12] Singh, B.; Lal, J., MHD axial flow in a triangular pipe under transverse magnetic field, Indian J. pure appl. maths, 9, 101-115, (1978) · Zbl 0383.76094
[13] Singh, B.; Lal, J., MHD axial flow in a triangular pipe under transverse magnetic field parallel to a side of the triangle, Indian J. technol., 17, 184-189, (1979) · Zbl 0413.76094
[14] Singh, B.; Lal, J., Finite element method for MHD channel flow with arbitrary wall conductivity, J. math. phys. sci., 18, 501-516, (1984) · Zbl 0574.76117
[15] Tezer-Sezgin, M., BEM solution of MHD flow in a rectangular duct, Int. J. numer. methods fluids, 18, 937-952, (1994) · Zbl 0814.76063
[16] Tezer-Sezgin, M.; Aydın, S.H., Dual reciprocity BEM for MHD flow using radial basis functions, Int. J. comput. fluid dynam., 16, 1, 49-63, (2002) · Zbl 1082.76580
[17] Tezer-Sezgin, M.; Köksal, S., FEM for solving MHD flow in a rectangular duct, Int. J. numer. meth. fluids, 28, 445-459, (1989) · Zbl 0669.76140
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