A Numerical Examination of an Unsteady Nonlinear MHD Flow in the Presence of Thermal Radiation and Heat Generation
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Institute of Systems Science, Durban University of Technology, P O Box 1334 Durban 4000, South Africa
Online publication date: 2021-01-29
Publication date: 2021-03-01
International Journal of Applied Mechanics and Engineering 2021;26(1):1-17
In this study, the spectral perturbation method and the spectral relaxation method are used to solve the nonlinear differential equations of an unsteady nonlinear MHD flow in the presence of thermal radiation and heat generation. The SPM is mainly based on series expansion, generating series approximation coupled with the Chebyshev spectral method. The numerical results generated using the spectral perturbation method were compared with those found in the literature, and the two results were in good agreement.
Hayat T., Qasim M. and Abbas Z. (2010): Homotopy solution for the unsteady three dimensional MHD flow and mass transfer in a porous space.– Communications in Nonlinear Science and Numer. Simu., vol.15, No.9, pp.2375-2387.
Kumari M. and Nath G. (2009): Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface.– Communications in Nonlinear Science and Numer. Simu., vol.14, No.8, pp.3339-3350.
Takhar H.S., Chamkha A.J. and Nath G. (2001): Unsteady three-dimensional MHD boundary-layer flow due to the impulsive motion of a stretching surface.– Acta Mechanica, vol.146, No.1-2, pp.59-71.
Olanrewaju P.O., Olanrewaju M.A. and Ajadi D.A. (2012): Unsteady three dimensional MHD flow and mass transfer in a porous space in the presence of thermal radiation.– Int. Research J. of Petroleum and Gas Exploration Research, vol.2. No.2, pp.044-051.
Makinde O.D., Olanrewaju P.O. and Charles M.W. (2011): Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture.– Afrika Matematika, vol.22, No.1, pp.65-78.
Abbas Z., Hayat T., Pop I. and Ashgar S. (2010): Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium.– Int. J. of Heat and Mass Transfer, vol.53, No.1, pp.466-474.
Seshadri R., Sreeshylan N. and Nath G. (2002): Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion.– Int. J. of Heat and Mass Transfer, vol.45, No.6, pp.1345-1352.
Nazar R., Amin N. and Pop I. (2004): Unsteady boundary layer flow due to a stretching surface in a rotating fluid.– Mechanics Research Commu., vol.31, No.1, pp.121-128.
Liao S. (2006): An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate.– Communications in Nonlinear Sci. and Num. Simulation, vol.11, No.3, pp.326-339.
Mehmood A., Ali A., Takhar H.S. and Shah T. (2008): Unsteady three-dimensional MHD boundary-layer flow due to the impulsive motion of a stretching surface.– Journal of Applied Fluid Mech., vol.199, No.1-4, pp.241-249.
Xu H., Liao S. and Pop I. (2007): Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate.– European J. of Mech.-B/Fluids, vol.26, No.1, pp.15-27.
Awad F.G., Motsa S.S. Makukula Z.G. and Sibanda P. (2014): The Spectral Homotopy Analysis Method Extended to Systems of Partial Differential Equations.– Abstract and Applied Analysis, vol.2014, Article ID 241594, 11 pages, doi:10.1155/2014/241594.
Agbaje T.M. and Motsa S.S. (2015): Comparison between spectral perturbation and spectral relaxation approach for unsteady heat and mass transfer by MHD mixed convection ow over an impulsively stretched vertical surface with chemical reaction effect.– Journal of Interpolation and Approximation in Scientific Computing, vol.2015, No.1, pp.48-83.
Motsa S.S. (2015): On Efficient Spectral Perturbation Method for Unsteady Boundary-Layer Flows Caused by an Impulsively Stretching Plate.– Journal of Applied Fluid Mechanics, vol. 9, No. 2, pp. 999-1011.
Agbaje T.M., Motsa S.S, Mondal S. and Sibanda P. (2017): A large parameter spectral perturbation method for nonlinear systems of partial differential equations that models boundary layer flow problems. – Frontiers in Heat and Mass Transfer, vol. 9, No.1, pp.1-13.
Agbaje T.M., Mondal S., Makukula Z.G., Motsa S.S. and Sibanda P. (2018): A new numerical approach to MHD stagnation point flow and heat transfer towards a stretching sheet. – Ain Shams Engineering Journal, vol.9, No.2, pp.233-243.
Williams J.C. and Rhyne T.B. (1980): Boundary layer development on a wedge impulsively set into motion.– SIAM J. on App. Math., vol.38, No.2, pp.215-224.
Karcher C. and Müller U. (1994): Bénard convection in a binary mixture with a nonlinear density-temperature relation.– Physical Review E, vol.49, No.5, pp.4031-4043.
Partha M.K. (2010): Nonlinear convection in a non-Darcy porous medium.– Applied Math. and Mech., vol.31, No.5, pp.565-574.
Don W.S. (1995): Accuracy and speed in computing the Chebyshev collocation derivative.– SIAM J. on Scientific Comp., vol.16, No.6, pp.1253-1268.
Hussaini M.Y. and Zang T.A. (1987): Spectral methods in fluid dynamics.– Annual Review of Fluid Mechanics, vol.19, No.1, pp.339-367.
Trefethen L.N. (2000): Spectral Methods in MATLAB.– SIAM, 1 st Edition.
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