Application of Successive Linearisation Method on Mixed Convection from an Exponentially Stretching Surface with Magnetic Field Effect

A.A. Khidir¹ , W.I. Alfaifi²

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.6 , pp.13-19, Dec-2021

Online published on Dec 31, 2021

Copyright © A.A. Khidir, W.I. Alfaifi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, a numerical solution has been obtained to solve the problem of the MHD boundary layer flow of heat and mass transfer with magnetic field effect. The partial differential equations governing the problem consideration were to a system of boundary value problem of ordinary differential equations by using a similarity transformation. The transformed governing equations in the present study were solved numerically by using the successive linearization method (SLM). The Velocity, temperature and concentration profiles are considered as exponential function. The effect of magnetic field parameter M on the flow profiles were obtained and discussed as well as the numerical values of the skin friction and the rate of heat transfer are entered in tables and compared with other study in the literature. The accuracy of the obtained solution has been checked using comparison with previously published work and excellent agreement is observed. It has been found that in the magnetic field reduced the Velocity of the fluid , whereas the temperature and concentration in fluid is enhanced.

Key-Words / Index Term :
Mixed convection; Boundary layer flow; Exponentially stretching surface; Successive linearisation method

References :
[1] S. J. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method,” CRC Press, Boca Raton 2003.
[2] Geng, F, “Modified variational iteration method for second order initial value problems,” Appl Appl Math, ,1(1), pp. 73–81, 2010.
[3] E. Magyari, B. Keller, “Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface,” J. Phys. D. Appl. Phy. (32) pp. 577-585, 1999,
[4] M. E. Ali, F. Al-Youself , “Laminar mixed convection boundary layers induced by a linearly stretching permeable surface,”Int. J. Heat Mass Transfer,(45), pp. 4241-4250, 2002,
[5] M. K. Partha, P. V. S. N. Murthy and GP. Rajasekhar, “Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface,” Heat Mass Transfer, (41), pp. 360-366, 2005.
[6] M. A. El-Aziz,
“Thermal-diffusion and diffusion-thermo effects on combined heat mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation, “ Physics Letter A, (372) , pp. 263-272, 2008.
[7] Ahmed A. Khidir, “Similarity solution in MHD, Effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection, “ Commun Nonlinear Sci. Numer. Simulat.
(14), pp. 2202-2214, 2009.
[8] D. Pal and H. Mondal, “Effects of Soret Dufour, chemical reaction and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretching sheet, “Commun Nonlinear Sci. Numer. Simulat. , (16), pp. 1942-1958, 2011.
[9] I. Wainia, and I .Pop,” Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid”, Alexandria Engineering Journal, 59 (3), pp. 1881-1891, 2020.
[10] M. Bidyut, B. Krishnendu, B. Astick, K. Ajeet and K. Anil. “MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions”, Nonlinear Engineering, 9 (1), pp. 457-469, 2020.

[11] SS. Pawar, Sachin K. Kamble, “Characterization of Hydraulic Fluids and Development of Heat Transfer Correlation in Helical Coil using New Dimensionless Number M” International Journal of Computer Sciences and engineering, 5 (1), pp.1-3, 2017.
[12] Anil Kumar, G.C. Sharma, “Performance and Analysis of Flow between Annular Space Surrounded by a Rotating Coaxial cylinder with Co-axial Cylindrical Porous Medium” International Journal of Scientific Research in Computer Science and engineering, 5 (3), pp.1-6, 2017.
[13] D. Srinivasacharya and Ch. RamReddy, “Soret and Dufour Effects on Mixed Convection from an Exponentially Stretching Surface, “, International Journal of Nonlinear Science, (12), pp. 60-68, 2011.
[14] 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, “Boundary Value Problems, ID 471793 (2010).
[15] Z. Makukula and S. S. Motsa, “On new solutions for heat transfer in a visco-elastic fluid between parallel plates, “Internationl Journal of Mathematical Models and Method in Applied Sciences, (4), pp. 221-230, 2010.
[16] S. S. Motsa, P. Sibanda and S. Shateyi, “On a new quasi-linearization method for systems of nonlinear boundary value problems, “Mathematical Methods in the Applied Sciences , (34), pp. 1406–1413, 2011.
[17] 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 & Mathematics with Applications, (61), pp. 1431-1441, 2011.
[18] 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. of the Physical Sciences, 6(21), pp. 4910–4923, 2011.
[19] Yassir Daoud, M. A. Mohammed and Ahmed A. Khidir, “On magneto-hydrodynamics threedimensional flow due to a stretching sheet in a porous medium using the successive linearization, method,”Chines Journal of Physics, (73), 2021, pp. 232-238, 2021.
[20] M. A. Mohammed, M. E. Mohammed and Ahmed A. Khidir, “The effects of cross-diffusion and radiation on mixed convection from a vertical flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation, “Journal of Propulsion and Power Research, 5(2), pp. 149-163 2016.
[21] Ahmed A. Khidir and A. F. Abdulrahman, “On successive linearization method for differential equations with nonlinear conditions, “ International Journal of Nonlinear Sciences and Numerical Simulation, vol. 2021, pp. 000010151520190278.
[22] Ahmed A. Khidir and Salihah L. Alsharari, “Application of Successive Linearisation Method on the Boundary Layer Flow Problem of Heat and Mass Transfer with Radiation Effect, “Int. J. Anal. Appl., 19 (5) , pp. 725-742, 2021.
[23] M. A. Mohammed, M. E. Mohammed and Ahmed A. Khidir, “On Linearization Method to MHD Boundary Layer Convective Heat Transfer with Low Pressure Gradient, “ Journal of Propulsion and Power Research, 4(2), pp. 105–113, 2015.
[24] M. A. Mohammed, M. E. Mohammed and Ahmed A. Khidir, “A successive linearization method approach for solving general boundary layer problems, “Int. J. of Appl. Math and Mech. 10 (4), pp. 55–72, 2014.
[25] C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, “Spectral Methods in Fluid Dynamics, “Springer Verlag, Berlin 1988.
[26] L. N. Trefethen, “Spectral Methods in MATLAB, “ SIAM., 2000.