Main Article Content
In this paper, the problem of boundary layer ﬂow and heat transfer of MHD power-law ﬂuid over a porous sheet in the presence of partial slip is investigated numerically. We assume a temperature dependent thermal conductivity and slip conditions are employed in terms of shear stress. The suitable similarity transformations are used, to transform the governing partial dif- ferential equations (PDEs) into a system of nonlinear ordinary diﬀerential equations (ODEs). The resulting system of ODEs is solved numerically using Matlab bvp4c solver. The numerical values obtained for the velocity and temperature depend on power-law index, slip parameters, permeability, suction/injection parameter, Prandlt number and Nusselt number. The eﬀects of various parameters on the ﬂow and heat transfer characteristics are presented through graphs and tables and discussed from physical point of view.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.
The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.
Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.
 H. Blasius, “Grenzschichten in ﬂu¨ssigkeiten mit kleiner reibung,” Zeitschrift fu¨r angewandte Mathematik und Physik (ZAMP), vol. 56, pp. 1–37, 1908.
 J. Pascal and H. Pascal, “Some similarity solutions to shear ﬂows of non-newtonian power law ﬂuids,” Acta Mechanica, vol. 112, pp. 229–236, 1994.
 A. Abussita, “A note on a certain boundary layer equation,” Applied Mathematics and Computation, vol. 64, pp. 73–77, 1994.
 A. Ishak, “Similarity solutions for fow and heat transfer over a permeable surface with convective boundary conditions,” Applied Mathematics and Computation, vol. 217, pp. 837– 842, 2010.
 E. Magyari, “Comment on similarity solution for laminar thermal boundary layer ﬂow over a ﬂat plate with a convective surface boundary condition by a. aziz,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, pp. 599–601, 2011.
 K. Vafai, Handbook of Porous Media. New York: Marcel Dekker, 2000.
 D. Ingham and I. Pop, Transport Phenomena in Porous Media. New York: Pergamon, Elsevier, 1998.
 M. Kumari, I. Pop, and G. Nath, “Non-darcian eﬀects on forced convection heat transfer over a ﬂat plate in a highly porous medium,” Acta Mechanica, vol. 84, pp. 201–207, 1990.
 N. Luna and F. Mndez, “Forced convection on a heated horizontal ﬂat plate with ﬁnite thermal conductivity in a non-darcian porous medium,” International Journal of Thermal Sciences, vol. 44, pp. 656–664, 2005.
 A. Khaled and K. Vafai, “The role of porous media in modeling ﬂow and heat transfer in biological tissues,” International Journal of Heat and Mass Transfer, vol. 46, pp. 4989–5003, 2003.
 O. Makinde, “Free convection ﬂow with thermal radiation and mass transfer past a moving porous plate.,” International Communications in Heat Mass Transfer, vol. 32, pp. 1411– 1419, 2005.
 F. Ibrahim, A. Elaiw, and A. Bakr, “Inﬂuence of viscous dissipation and radiation on unsteady mhd mixed convection ﬂow of micropolar ﬂuids.,” Applied Mathematics and Information Sciences, vol. 2, pp. 143–162, 2008.
 M. A. P. Datti and N.Mahesha, “Flow and heat transfer in a power-law ﬂuid over a stretching sheet with variable thermal conductivity and non-uniform heat source,” International Journal of Heat and Mass Transfer, vol. 52, pp. 2901–2913, 2009.
 J. Luk, R. Mutharasan, and D. Apelian, “Experimental observations of wall slip: tube and packed bed ﬂow,” Industrial and Engineering Chemistry Research, vol. 26, p. 16091616, 1987.
 D. Kalyon, “Apparent slip and viscoplasticity of concentrated suspensions,” Journal of Rheology, vol. 49, p. 621640, 2005.
 G. Beavers and D. Joseph, “Boundary conditions at a naturally permeable wall,” Journal of Fluid Mechanics, vol. 30, pp. 197–207, 1967.
 H. Andersson, “Slip ﬂow past a stretching surface,” Acta Mechanica, vol. 158, pp. 121–125, 2002.
 A. Farhad, M. Norzieha, S. Sharidan, and I. Khan, “On accelerated mhd ﬂow in a porous medium with slip condition,” European Journal of Scientific Research, vol. 57, pp. 293–304, 2011.
 M. Martin and I. Boyd, “Momentum and heat transfer in laminar boundary layer with slip ﬂow,” Journal of Thermophysics and Heat Transfer, vol. 20, pp. 710–719, 2006.
 A. Aziz, J. Siddique, and T. Aziz, “Steady boundary layer slip ﬂow along with heat and mass transfer over a ﬂat porous plate embedded in a porous medium,” PLOS ONE, 2014.
 C. Cheng, “Soret and dufour eﬀects on free convection boundary layers of non-newtonian power law ﬂuids with yield stress in porous media over a vertical plate with variable wall heat and mass ﬂuxes,” International Communications in Heat and Mass Transfer, vol. 38, pp. 615–619, 2011.
 J. Loureiro and A. Freire, “Asymptotic analysis of turbulent boundary-layer ﬂow of purely viscous non-newtonian ﬂuids,” Journal of Non-Newtonian Fluid Mechanics, vol. 199, pp. 20–28, 2013.
 I. Baoku, B. Olajuwon, and A. Mustapha, “Heat and mass transfer on a mhd third grade ﬂuid with partial slip ﬂow past an inﬁnite vertical insulated porous plate in a porous medium,” International Journal of Heat and Fluid Flow, pp. 81–88, 2013.
 A. Acrious, M. Shah, and E. Peterson, “Momentum and heat transfer in laminar boundary layer ﬂow on non-newtonian ﬂuids past external surfaces,” AIChE Journal, vol. 6, pp. 312– 316, 1960.
 W. Schowalter, “The application of boundary layer theory to power law pseudo plastic ﬂuids: similar solutions,” AIChE Journal, vol. 6, 1960.
 H. Andersson, K. Bech, and B. Dandapat, “Magnetohydrodynamic ﬂow of a power law ﬂuid over a stretching sheet,” International Journal of Non-Linear Mechanics, vol. 72, no. 4, pp. 929–936, 1992.
 M. Hajmohammadi and S. Nourazar, “On the insertion of a thin gas layer in micro cylindrical couette ﬂows involving power-law liquids,” International Journal of Heat and Mass Transfer, vol. 75, pp. 97–108, 2014.
 M. Hajmohammadi, S. Nourazar, and A. Campo, “Analytical solution for two-phase ﬂow between two rotating cylinders ﬁlled with power law liquid and a micro layer of gas,” Journal of Mechanical Science and Technology, vol. 28, pp. 1849–1854, 2014.
 D. Pal and S. Chatterjee, “Soret and dufour eﬀects on MHD convective heat and mass transfer of a power-law ﬂuid over an inclined plate with variable thermal conductivity in a porous medium,” Applied Mathematics and Computation, vol. 219, pp. 7556–7574, 2013.
 T. Hayat, M. Hussain, A. Alsaedi, S. Shehzad, and G. Chen, “Flow of power-law nanoﬂuid over a stretching surface with newtonian heating,” Journal of Applied Fluid Mechanics, vol. 8, pp. 273–280, 2015.
 H. Duwairi and R. Damseh, “Mhd-buoyancy aiding and opposing ﬂows with viscous dissipation eﬀects from radiate vertical surfaces,” Canadian Journal of Chemical Engineering, vol. 82, p. 613, 2004.
 M. Alam, M. Rahman, and M. Sattar, “On the eﬀectiveness of viscous dissipation and joule heating on steady magnetohydrodynamic heat and mass transfer ﬂow over an inclined radiate isothermal permeable surface in the presence of thermophoresis,” Commun Nonlinear Sci Numer Simul, vol. 14, p. 2132, 2009.
 M. Rahman and K. Salahuddin, “Study of hydromagnetic heat and mass transfer ﬂow over an inclined heated surface with variable viscosity and electric conductivity,” Commun Nonlinear Sci Numer Simulat, vol. 15, pp. 2073–2085, 2010.
 K. Das, “Slip eﬀects on heat and mass transfer in mhd micropolar ﬂuid ﬂow over an inclined plate with thermal radiation and chemical reaction,” International Journal of Numerical Methods in Fluids, vol. 70, pp. 96–113, 2012.
 R. Bird, W. Stewart, and E. lightfoot, Transport Phenomena. New York: John Wiley, 1960.
 R. Chhabra and J. Richardson, Non-Newtonian Flow and Applied Rheology: Engineering Applications. Oxford: Butterworth-Heinemann, second edition ed., 2008.
 K. Bhattacharyya, S. Mukhopadhyay, and G. Layek, “Steady boundary layer slip ﬂow and heat transfer over a ﬂat porous plate embedded in a porous media,” Journal of Petroleum Science and Engineering, vol. 78, pp. 304–309, 2011.
 M. Hajmohammadi and S. Nourazar, “On the solution of characteristic value problems arising in linear stability analysis; semi analytical approach,” Applied Mathematics and Computation, vol. 239, pp. 126–132, 2014.