Finite Difference Technique for Unsteady MHD Periodic Flow of Viscous Fluid through a Planer Channel

Pawan Preet Kaur¹, SP Agrawal² and Anil Kumar^3,

¹Deparment of Applied Mathematics, Lyallpur Khalsa College Engineering Jalandhar Punjab

²Department of Civil Engineering, World Institute of Technology Sohna, Gurgaon, India

³Department of Applied Mathematics, World Institute of Technology Sohna, Gurgaon, India

Cite this paper:
Pawan Preet Kaur, SP Agrawal and Anil Kumar. Finite Difference Technique for Unsteady MHD Periodic Flow of Viscous Fluid through a Planer Channel. American Journal of Modeling and Optimization. 2013; 1(3):47-55. doi: 10.12691/ajmo-1-3-5

Abstract

In the present paper we investigate an unsteady periodic flow of a viscous incompressible fluid through a porous planer channel in the presence of transverse magnetic field. The governing equations have been solved by finite difference method. The analytical expressions for the velocity profiles of the fluid have been obtained and numerical computations involved in the solution have been shown by tables. The effects of various parameters on the flow field have been discussed with the help of graphs and tables.

Keywords:
magnetohydrodynamics planer channel periodic flow viscous fluid Hartmann number Finite difference technique

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Figures

References:

[1]	Sparrow, E.M. and Cess, R.D. (1961): The effect of a magnetic field on a free convective heat transfer, International Journal of Heat and Mass Transfer, 3, 267-274.
[2]	Raptis, A.; Massias, C. and Tzivanidis, G. (1982): Hydromagnetic free convection flow through a porous medium between two parallel plates, Phys. Lett., 90(A), 288-289.
[3]	Pal, D.; Veerbhadraiah, R.; Shivakumar, P.N. and Rudraiah, N. (1984): Longitudinal dispersion of tracer particles in a channel bounded by porous media using slip condition, International Journal of Mathematical science, 7,755-764.
[4]	Singh, K.D. and Kumar, Suresh (1993): Free convective fluctuating flow through a porous medium with variable permeability, Journal of Mathematical and Physical Sciences, 27(2), 141-148.
[5]	Aldoss, T.K.; Al-Nimr, M.A.; Jarrah, M.A. and Al-Shaer, B.(1995): Mixed convection flow from a vertical plate embedded in porous medium in the presence of magnetic field, Heat Transfer, 28(A), 635-645.
[6]	Malcinde, O.D. (1995): Laminar flow in a channel of varying width with permeable boundaries, Romanian Journal of Physics, 40(4-5), 403.
[7]	Soltani, F. and Yilmazar, U. (1998): Slip velocity and slip layer thickness in flow of concentrated suspensions, Journal of Applied Polymer Science, 70, 515-522.
[8]	Jha, B.K. (1998): Effect of applied magnetic field on transient free convective flow in a vertical channel, Indian Journal of Pure and Applied Mathematics, 29(4), 441-445.
[9]	Helmy, K.A. (1998): MHD unsteady free convective flow past a vertical porous plate, Z AMP, Z.Angew Math. Mech., 78(4), 255-270.
[10]	Hossain, M.A.; Das, S.K. and Pop, I.(1998): Heat transfer response of MHD free convective flow along a vertical plate to surface temperature oscillation, International Journal of Non-Linear Mechanics, 33(3), 541-553.
[11]	Kim, Y.J. (2000): Unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction, International Journal of Engineering Science, 38,833-842.
[12]	Yu, S. and Ameel, T.A. (2002): Slip low heat transfer in rectangular micro channels, International Journal of Heat and Mass Transfer, 44, 4225-4234.
[13]	Derek, C.; Tretheway, D.C. and Mainhart, C.D. (2002): Apparent fluid slip at hydrophibic micro channel walls, Physics of Fluids, 14, L9-L12.
[14]	Sharma, G.C.; Jain, M. and Kumar, Anil (2002): The flow between annular space surrounded by coaxial cylindrical porous medium, Published in National Conference on 67th Indian Mathematical Society, AMU, Aligarh, Jan. 27-30, 2002.
[15]	Steinruck, H. (2003): About the physical relevance of similarity solution of the boundary layer flow equation describing mixed convection flow along a vertical plate, Fluid Dynamics Research, 32, 1-13.
[16]	Khaled, A.R.A and Vafai, K. (2004): The effect of slip condition on stokes and coutte flows due to an oscillating wall, International Journal of Nonlinear Mechanics, 39, 795-809.
[17]	Makinde, O.D. and Mhone, P.Y. (2005): Heat transfer to MHD Oscillatory flow in a channel filled with porous medium, Romanian Journal of physics, 50(9-10), 931-938.
[18]	Makinde, O.D. and Osalusi, E. (2006): MHD steady flow in a channel with slip at permeable boundaries, Romanian Journal of Physics, 51(3-4), 319-328.
[19]	Kumar, Anil; Varshney, C.L. and Sajjan Lal (2007): Viscous flow coaxial cylinder in the presence of magnetic field, Published in the 15th International conference on Interdisciplinary Mathematical and Statistical Technique, Shanghai, China, May20-23.
[20]	Mahmood, A. and Ali, A. (2007): The effect of slip condition on unsteady MHD Oscillatory flow of a viscous fluid in a planer channel, Romanian Journal of Physics, 52, Nos. 1-2, 85-91.
[21]	Mishra, J.P.; Shit, G.C. and Rath, H.J. (2008): Flow and heat transfer of a MHD visco-elastic fluid in a channel with stretching walls, Computers and Fluids, 37(1), 1-11.
[22]	Anil Kumar, CL Varshney and Sajjan Lal (2013): Performance Modeling and analysis of Non-Viscous Incompressible Fluid Flow and Convective Temperature Flow in the Magnetic effects, International Journal of Mathematical Modeling and Physical Sciences Vol. 01, ( 01) pp 10-15, March 2013.
[23]	Anil Kumar and S P Agrawal (2013): Mathematical and Simulation of lid driven cavity flow at different aspect ratios using single relaxation time lattice Boltzmann technique, American Journal of theoretical and Applied Statistics, vol 2 (3), pp 87-93.
[24]	Anil Kumar , SP Agrawal and Pawan Preet Kaur (2013)Finite Element Galerkin’s Approach for Viscous Incompressible Fluid Flow through a Porous Medium in Coaxial Cylinders, Journal of Mathematical Sciences and Applications, 2013, Vol. 1, No. 3, 39-42.
[25]	Anil Kumar, CL Varshney and Sajjan Lal (2013): Perturbation Technique of MHD Free Convection Flow through Infinite Vertical Porous Plate with Constant Heat Flux, International Journal of Mathematical Modeling and Physical Sciences Vol. 01, (02) pp 1-5, 2013.
[26]	Anil Kumar, R. K. Saket, C L Varshney and Sajjan Lal : Finite difference technique for reliable MHD steady flow through channels permeable boundaries, International Journal of Biomedical Engineering and Technology (IJBET) UK, Vol. 4(2) pp 101-110, 2010.