Numerical Study of the Casson Non-Newtonian Fluid Flow over a Nonlinear Stretching Sheet
Keywords:
Casson fluid, stretched sheet, porous medium, shooting method, porous medium Runge-Kutta methodAbstract
In this paper, numerical study of Casson non-Newtonian fluid over a nonlinear stretching sheet using shooting method will be presented. The governing nonlinear partial differential equation is converted to an ordinary differential equation by using similarity transformations. This ordinary differential equation is handled numerically with the use of well-known shooting technique aided by Runge-Kutta method. For comparison of the results, MATLAB in-built solver BVP4C is used. The discussion of the results is provided in the forms of tables as well as graphically.
References
Boyd, J. P., 2001. Chebyshev and Fourier spectral methods. Courier Corporation.
Shen, J., Tang, T. and Wang, L. L., 2011. Spectral methods: algorithms, analysis and applications (Vol. 41). Springer Science and Business Media.
Shen, J. and Wang, L. L., 2009. Some recent advances on spectral methods for unbounded domains. J. Commun. Comput. Phys, 5, pp.195-241.
Mehdi Rashidi, M. and Erfani, E., 2011. The modified differential transform method for investigating nano boundary-layers over stretching surfaces. International Journal of Numerical Methods for Heat and Fluid Flow, 21(7), pp.864-883.
Hayat, T., Hussain, Q. and Javed, T., 2009. The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet. Nonlinear Analysis: Real World Applications, 10(2), pp.966-973.
Ghori, Q.K., Ahmed, M. and Siddiqui, A.M., 2007. Application of homotopy perturbation method to squeezing flow of a Newtonian fluid. International Journal of Nonlinear Sciences and Numerical Simulation, 8(2), pp.179-184.
Sajid, M. and Hayat, T., 2008. The application of homotopy analysis method to thin film flows of a third order fluid. Chaos, Solitons and Fractals, 38(2), pp.506-515.
Motsa, S.S., Sibanda, P., Awad, F.G. and Shateyi, S., 2010. A new spectral-homotopy analysis method for the MHD Jeffery–Hamel problem. Computers and Fluids, 39(7), pp.1219-1225.
Siddiqui, A.M., Mahmood, R. and Ghori, Q.K., 2006. Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation, 7(1), pp.7-14.
Abbasbandy, S., Hayat, T., Ghehsareh, H.R. and Alsaedi, A., 2013. MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method. Applied Mathematics and Mechanics, 34(8), pp.921-930.
Marinca, V., Herişanu, N., Bota, C. and Marinca, B., 2009. An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate. Applied Mathematics Letters, 22(2), pp.245-251.
Hayat, T., Hussain, Q. and Javed, T., 2009. The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet. Nonlinear Analysis: Real World Applications, 10(2), pp.966-973.
Ganji, D.D., Bararnia, H., Soleimani, S. and Ghasemi, E., 2009. Analytical solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet. Modern Physics Letters B, 23(20n21), pp.2541-2556.
Ghotbi, A.R., 2009. Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet. Communications in Nonlinear Science and Numerical Simulation, 14(6), pp.2653-2663.
Motsa, S.S. and Sibanda, P., 2012. On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi‐analytical technique. International Journal for Numerical Methods in Fluids, 68(12), pp.1524-1537.
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