Application of Successive Linearisation Method on the Boundary Layer Flow Problem of Heat and Mass Transfer with Radiation Effect

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Ahmed A. Khidir
Salihah L. Alsharari


In this paper, we applied the successive linearization method (SLM) in solving highly system of nonlinear boundary value problem. The method is presented in detail by solving the problem of free convective heat and mass transfer of an incompressible fluid past a moving vertical plate in the presence of radiation effect. The governing partial differential equations are converted into system of non linear ordinary differential equations by a similarity transformation, which are converted into system of linear ordinary differential equations using SLM. The linear system is solved using the Chebyshev spectral method to find solutions that are accurate and converge rapidly to the full numerical solution. Comparison with previously published works are performed to test the validity of the obtained results with focus on the accuracy and convergence of the solution. The effects of selected fluid parameters on the velocity as well as the temperature and concentration distribution are determined and discussed.

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  1. P. O. Olanrewaju, O. D. Makinde, Effects of thermal diffusion and diffusion thermo on chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction/injection, Arab. J. Sci. Eng. 36 (2011), 1607-1619.
  2. M. S. Alam, M. M Rahman, Dufour and Soret effects on mixed convection flow past a vertical porous flat plate with variablesuction, Nonlinear Anal.: Model. Control, l1 (1) (2006), 3-12.
  3. A. Bejan, I. Dincer, S. Lorente, A. F. Miguel, A. H. Reis, Porous and complex flow structures in modern technologies. Springer, New York, (2004).
  4. A. Chakrabarti, A. S. Gupta, Hydromagnetic flow and heat transfer over a stretching sheet. Quart. Appl. Math. 37 (1979), 73-78.
  5. S. Y. Ibrahim, O. D. Makinde, Chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction. Sci. Res. Essay. 5 (19) (2010), 2875-2882.
  6. D. B. Ingham, A. Bejan, E. Mamut, I. Pop, Emerging technologies and techniques in porous media, Kluwer, Dordrecht, (2004).
  7. D. B. Ingham, I. Pop, Transport phenomena in porous media, vol. III. Pergamon, Oxford, (2005).
  8. N. G. Kafoussias, E. W. Williams, Thermal-diffusion and diffusion-thermo effects on mixed free convective and mass transfer boundary layer flow with temperature dependent viscosity. Int. J. Eng. Sci. 33 (1995), 1369-1384.
  9. O. M. Makinde, MHD steady flow and heat transfer on the sliding plate. AMSE Model. Meas. Control B. 70(1) (2001), 61-70.
  10. O. D. Makinde, On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux. Int. J. Numer. Meth. Heat Fluid Flow, 19 (3/4) (2009), 546-554.
  11. D. A. Nield, A. Bejan, Convection in porous media, 3rd edn. Springer, New York, (2006).
  12. N. Nithyadevi, R. J. Yang, Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects. Int. J. Heat Fluid Flow, 30 (5) (2009), 902-910.
  13. E. Osalusi, J. Side, R. Harris, Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating. Int. Commun. Heat Mass Transfer. 35 (2008), 908-915.
  14. I. Pop, D. B. Ingham, Convective heat transfer: mathematical and computational modeling of viscous fluids and porous media. Pergamon, Oxford, (2001).
  15. E. M. Sparrow, R. D. Cess, The effect of a magnetic field on free convection heat transfer, Int. J. Heat Mass Transfer. 3 (1961), 267-274.
  16. P. Vadasz, Emerging topics in heat and mass transfer in porous media. Springer, New York (2008).
  17. K. Vafai, Handbook of porous media. Taylor & Francis, New York (2005).
  18. K. A. Yih, Free convection effect on MHD coupled heat and mass transfer of a moving permeable vertical surface. Int. Commun. Heat Mass Transf. 26(1), 95-104 (1999).
  19. C. Canuto, M. Y. Hussaini, A. Quarteroni, T. A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin (1998).
  20. L. N. Trefethen, Spectral Methods in MATLAB, SIAM, 2000.
  21. Z. G. Makukula, P. Sibanda and S. S. Motsa, A note on the solution of the Von Karman equations using series and chebyshev spectral methods, Bound. Value Probl. 2010 (2010), 471793.
  22. Z. Makukula and S. S. Motsa, On new solutions for heat transfer in a viscolastic fluid between parallel plates, Int. J. Math. Models Meth. Appl. Sci. 4 (2010), 221-230.
  23. S. S. Motsa, P. Sibanda and S. Shateyi, On a new quasi-linearization method for systems of nonlinear boundary value problems. Math. Meth. Appl. Sci. 34 (2011), 1406-1413.
  24. F. G. Awad, P. Sibanda, S. S. Motsa and O. D. Makinde, Convection from an inverted cone in a porous medium with cross-diffusion effects, Computers Math. Appl. 61 (2011), 1431-1441.
  25. F. G. Awad, P. Sibanda, M. Narayana and S. S. Motsa, Convection from a semi-finite plate in a fluid saturated porous medium with cross-diffusion and radiative heat transfer, Int. J. Phys. Sci. 6 (21) (2011), 4910-4923.