MHD Stagnation-Point Flow Past over a Stretching Sheet in the Presence of Non-Darcy Porous Medium and Heat Source/Sink

Abstract:

The steady boundary layer magnetohydrodynamic stagnation- point flow past a stretching sheet through porous media in the presence of heat source /sink has been studied. Dissipative effects such as viscous, Joule and Darcy dissipation are also considered in the present study. The governing nonlinear coupled partial differential equations are modified into self-similar ordinary differential equations by appropriate similarity transformations and then the transmuted equations are numerically solved by Runge-Kutta fourth order method. Particular importance of pertinent physical parameters of interest which cover velocity ratio parameter, magnetic parameter, porous matrix, Prandtl number, Eckert number, temperature index parameter and heat source parameter. The outcomes acquired for velocity, temperature and skin friction has been displayed in tables and graphs. For the verification of the present outcomes with the earlier published results in a particular case is also presented and it is found that the present result is in good agreement.

• Periodical: Defect and Diffusion Forum (Volume 374)
• Pages: 92-105
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.374.92
• Online since: April 2017
• Authors: S.R. Mishra*, B. Nayak, Ram Prakash Sharma
• Keywords: Mhd Flow, Non-Darcy Porous Medium, Runge-Kutta Fourth Order, Stagnation-Point, Stretching Sheet

References

[1] L.J. Crane, Flow past a stretching plate, Z. Angew. Math. Phys. 21 (1970) 645– 647.

[2] P.S. Gupta, A.S. Gupta, Heat and mass transfer on a stretching sheet with suction and blowing, Can J Chem Eng, 55 (1977) 744–6.

DOI: 10.1002/cjce.5450550619

[3] B.K. Dutta, P. Roy, A.S. Gupta, Temperature field in flow over a stretching sheet with uniform heat flux, Int Commun H eat Mass Transfer, 12 (1985) 89–94.

DOI: 10.1016/0735-1933(85)90010-7

[4] J.B. McLeod, K.R. Rajagopal, On the uniqueness of flow of a Navier–Stokes fluid due to a stretching boundary, Analysis and Continuum Mechanics. 98 (1989) 565-573.

DOI: 10.1007/978-3-642-83743-2_31

[5] W.C. Troy, W.A. Overman II, G.B. Ermentrout, Uniqueness of flow of a second-order fluid past a stretching sheet, Quart. Appl. Math. 45 (1987) 753–755.

DOI: 10.1090/qam/872826

[6] C.Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids 27 (1984) 1915-(1917).

DOI: 10.1063/1.864868

[7] E. Magyari, B. Keller, Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls, Eur. J. Mech. B Fluids 19 (2000) 109-122.

DOI: 10.1016/s0997-7546(00)00104-7

[8] E.M. Sparrow, J.P. Abraham, Universal solutions for the stream wise variation of the temperature of a moving sheet in the presence of a moving fluid, Int. J. Heat Mass Transfer 48 (2005) 3047-3056.

DOI: 10.1016/j.ijheatmasstransfer.2005.02.028

[9] L.J. Grubka, K.M. Bobba, Heat transfer characteristics of a continuous, stretching surface with variable temperature, ASME J. Heat Transfer 107 (1985) 248–250.

DOI: 10.1115/1.3247387

[10] T.R. Mahapatra, A.S. Gupta, Magneto hydrodynamic stagnation point flow towards a stretching sheet, Acta Mech, 152 ( 2001) 191–6.

DOI: 10.1007/bf01176953

[11] T.R. Mahapatra, A.S. Gupta, Heat transfer in stagnation-point flow towards a stretching sheet, Heat Mass Transfer 38 (2002) 517–21.

DOI: 10.1007/s002310100215

[12] R. Nazar, N. Amin, D. Filip, I. Pop, Stagnation point flow of a micropolar fluid towards a stretching sheet, Int J Non-Linear Mech 39 (2004) 1227–35.

DOI: 10.1016/j.ijnonlinmec.2003.08.007

[13] T. Hayat, T. Javed, Z. Abbas, MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface, Nonlinear Anal Real World Appl, 10 (2009)1514–26.

DOI: 10.1016/j.nonrwa.2008.01.019

[14] W. Ibrahim, O. D. Makinde, Magnetohydrodynamic stagnation point flow and heat transfer of Casson nanofluid past a stretching sheet with slip and convective boundary condition, Journal of Aerospace Engineering, 29(2) Article number 04015037, (2016).

DOI: 10.1061/(asce)as.1943-5525.0000529

[15] W. Ibrahim, O.D. Makinde, Magnetohydrodynamic stagnation point flow of a power-law nanofluid towards a convectively heated stretching sheet with slip, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 230(5) (2016).

DOI: 10.1177/0954408914550357

[16] Altan T, Oh S, Gegel H (1979) Metal forming fundamentals and applications. American society for metals, Ohio.

[17] Fisherl E (1976) Extrusion of plastics. Wiley, New York.

[18] Karwe M, Jaluria Y (1991) Numerical simulation of thermal transport associated with a continuously moving flat sheet in materials processing. ASME J Heat Transf 113: 612–619.

DOI: 10.1115/1.2910609

[17] Crane L (1970), Flow past a stretching sheet. ZAMP 21: 645–647.

[20] Amkadni M, Azzouzi A, Hammouch Z (2008) On the exact solutions of laminar mhd flow over a stretching flat plate. Commun Nonlinear SciNumer Simul 13: 359–368.

DOI: 10.1016/j.cnsns.2006.04.002

[21] Pop I, Na T (1998) A note on MHD flow over a stretching permeablesurface. J Fluid Eng. 25: 263–269.

[22] Liu I (2005) A note on heat and mass transfer for a hydromagnetic flow over a stretching sheet. IntCommun Heat Mass Transf 32: 1075.

DOI: 10.1016/j.icheatmasstransfer.2005.02.003

[23] Chiam T (1995) Hydromagnetic flow over a surface stretching with power law velocity. Int J Eng. Sci 33: 429.

DOI: 10.1016/0020-7225(94)00066-s

[24] Cortell R (2005) A note on magneto hydrodynamic flow of a power-law fluid over a stretching sheet. Appl Math Comput 168: 557–566.

DOI: 10.1016/j.amc.2004.09.046

[25] Yi-wu Y (1985) One-dimensional non-uniform temperature flow with heat transfer by convection. Appl Math Mech (English Edition 6), 259–268.

DOI: 10.1007/bf01895522

[26] B. Mohanty, S.R. Mishra, H.B. Pattnaik, Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet, Alexandria Engineering Journal, 54(2)(2015)223-232.

DOI: 10.1016/j.aej.2015.03.010

[27] S.R. Mishra, G.C. Dash, P.K. Pattnaik, Flow of heat and mass transfer on MHD free convection in a micropolar fluid with heat source, Alexandria Engineering Journal, 54 (3)(2015)681-689.

DOI: 10.1016/j.aej.2015.04.010

[28] A. Ishak (2011) MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malays 40: 391–395.

[29] W. A. Khan, O. D. Makinde, Z. H. Khan, Non-aligned MHD stagnation point flow of variable viscosity nanofluids past a stretching sheet with radiative heat. International Journal of Heat and Mass Transfer, 96(2016)525-534.

DOI: 10.1016/j.ijheatmasstransfer.2016.01.052

[30] A. M. Olanrewaju, O. D. Makinde, On boundary layer stagnation point flow of a nanofluid over a permeable flat surface with Newtonian heating. Chemical Engineering Communications, 200(6)(2013)836-852.

DOI: 10.1080/00986445.2012.721825

[31] R.S. Tripathy, G.C. Dash, S.R. Mishra, S. Baag, Chemical reaction effect on MHD free convective surface over a moving vertical plane through porous medium, Alexandria Engineering Journal, 54 (3)(2015)673-679.

DOI: 10.1016/j.aej.2015.04.012

[32] R.S. Tripathy, S.R. Mishra, G.C. Dash, M.M. Hoque, Numerical analysis of hydromagnetic micropolar fluid along a stretching sheet with non-uniform heat source and chemical reaction, Engineering Science and Technology, An International Journal, 19(2016).

DOI: 10.1016/j.jestch.2016.05.012

[33] H. A. Attai, Stagnation Point Flow towards a Stretching Surface through a Porous Medium with Heat Generation, Turkish Journal of Engineering & Environmental Sciences, 30 ( 2006) 299-306.

[34] B. Norfifah and I. Anuar, MHD Stagnation-Point Flow of a Micropolar Fluid with Prescribed Wall Heat Flux, European Journal of Scientific Research, 35 (2009) 436-443.

[35] G.C. Dash, R.S. Tripathy, M.M. Rashidi, S.R. Mishra, Numerical approach to boundary layer stagnation-point flow past a stretching/shrinking sheet, Journal of Molecular Liquids, 221(2016) 860-866.

DOI: 10.1016/j.molliq.2016.06.072

[36] H Xu, SJ Liao, I Pop, Series solution of unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Acta Mecc 184 (2006) 87–101.

DOI: 10.1007/s00707-005-0302-7

[37] Y. Lok, Y. Phang, N. Amin, I. Pop, Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface, Int J Eng Sci 41 (2003) 173–186.

DOI: 10.1016/s0020-7225(02)00146-5

[38] D. Pal, Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation, Meccanica, 44 (2009) 145–158.

DOI: 10.1007/s11012-008-9155-1

[39] O. D. Makinde, W. A. Khan, Z. H. Khan, Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet. International Journal of Heat and Mass Transfer, 62(2013)526-533.

DOI: 10.1016/j.ijheatmasstransfer.2013.03.049

[40] S. Baag, S.R. Mishra, G.C. Dash, M.R. Acharya, Numerical investigation on MHD micropolar fluid flow toward a stagnation point on a vertical surface with heat source and chemical reaction, Journal of King Saud Engineering Sciences-(29)(2017).

DOI: 10.1016/j.jksues.2014.06.002

[41] A. Ishak, K. Jafar, R. Nazar, I. Pop, MHD stagnation point flow towards a stretching sheet, Physica A, 388(2009)3377-3383.

DOI: 10.1016/j.physa.2009.05.026