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 AJCM  Vol.5 No.1 , March 2015
Influence of Magnetic Field, Viscous Dissipation and Thermophoresis on Darcy-Forcheimer Mixed Convection Flow in Fluid Saturated Porous Media
Abstract: This paper presents an application of the spectral homotopy analysis method (SHAM) to solve a problem of darcy-forcheimer mixed convection flow in a porous medium in the presence of magnetic field, viscous dissipation and thermopherisis. A mathematical model governed the flow is analyzed in order to study the effects of chemical reaction, magnetic field, viscous dissipation and thermophoresis on mixed convection boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. The similarity variable is used to transform the governing equations into a boundary valued problem of coupled ordinary differential equations which are then solved using spectral homotopy Analysis Method. The spatial domains are discretized using Chebyshev-Gauss-Lobatto points and numerical computations are carried out for the non-dimensional physical parameters. A parametric study of selected parameters is conducted and the results for the velocity, temperature and concentration are illustrated graphically and physical aspects of the problem are discussed.
Cite this paper: Fagbade, A. , Falodun, B. and Boneze, C. (2015) Influence of Magnetic Field, Viscous Dissipation and Thermophoresis on Darcy-Forcheimer Mixed Convection Flow in Fluid Saturated Porous Media. American Journal of Computational Mathematics, 5, 18-40. doi: 10.4236/ajcm.2015.51002.
References

[1]   Nield, D.A. (1968) Onset of Thermohaline Convection in a Porous Medium. Water Resources Research, 4, 553-560.
http://dx.doi.org/10.1029/WR004i003p00553

[2]   Bejan, A. and Khair, K.R. (1985) Heat and Mass Transfer by Natural Convection in a Porous Medium. International Journal of Heat and Mass Transfer, 28, 909-918.
http://dx.doi.org/10.1016/0017-9310(85)90272-8

[3]   Yucel, A. (1990) Natural Convection Heat and Mass Transfer along a Vertical Cylinder in a Porous Medium. International Journal of Heat and Mass Transfer, 33, 2265-2274.
http://dx.doi.org/10.1016/0017-9310(90)90125-E

[4]   Lai, F.C. and Kulaki, F.A. (1991) Oscillatory Mixed Convection in Horizontal Porous Layers Locally Heated from Below. International Journal of Heat and Mass Transfer, 34, 887-890.
http://dx.doi.org/10.1016/0017-9310(91)90134-Z

[5]   Rami, Y.J., Fawzi, A. and Abu-Al-Rub, F. (2001) Darcy-Forchheimer Mixed Convection Heat and Mass Transfer in Fluid Saturated Porous Media. International Journal of Numerical Methods for Heat & Fluid Flow, 11, 600-618.
http://dx.doi.org/10.1108/09615530110399503

[6]   Kremer, D.M., Davis, R.W., Moore, E.F., Maslar, J.E., Burgess Jr., D.R. and Ehrman, S.H. (2003) An Investigation of Particle Dynamics in a Rotating Disk Chemical Vapor Deposition Reactor. Journal of the Electrochemical Society, 150, G127-G139.
http://dx.doi.org/10.1149/1.1536180

[7]   Hinds, W.C. (1982) Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles. John Wiley and Sons, New York.

[8]   Goldsmith, P. and May, F.G. (1966) Diffusiophoresis and Thermophoresis in Water Vapour Systems. In: Davies, C.N., Ed., Aerosol Science, Academic Press, London, 163-194.

[9]   Goren, S.L. (1977) Thermophoresis of Aerosol Particles in Laminar Boundary Layer on Flat Plate. Journal of Colloid and Interface Science, 61, 77-85.
http://dx.doi.org/10.1016/0021-9797(77)90416-7

[10]   Chang, Y.P., Tsai, R. and Sui, F.M. (1999) The Effect of Thermophoresis on Particle Deposition from a Mixed Convection Flow onto a Vertical Flat Plate. Journal of Aerosol Science, 30, 1363-1378.
http://dx.doi.org/10.1016/S0021-8502(99)00023-3

[11]   Jayaraj, S., Dinesh, K.K. and Pallai, K.L. (1999) Thermophoresis in Natural Convection with Variable Properties. Heat and Mass Transfer, 34, 469-475.
http://dx.doi.org/10.1007/s002310050284

[12]   Selim, A., Hossain, M.A. and Rees, D.A.S. (2003) The Effect of Surface Mass Transfer on Mixed Convection Flow Past a Heated Vertical Flat Permeable Plate with Thermophoresis. International Journal of Thermal Sciences, 42, 973-982.
http://dx.doi.org/10.1016/S1290-0729(03)00075-9

[13]   Chamkha, A.J. and Pop, I. (2004) Effects of Thermophoresis Particle Deposition in Free Convection Boundary Layer from a Vertical Flat Plate Embedded in a Porous Medium. International Communications in Heat and Mass Transfer, 31, 421-430.
http://dx.doi.org/10.1016/j.icheatmasstransfer.2004.02.012

[14]   Murti, A.S.N., Kameswaran, P.K., Poorna Kantha, T. and Acharyulu, A.A.V.L.A.S. (2012) Numerical Study on MHD Mixed Convection Flow with Dispersion and Chemical Reaction over a Vertical Plate in Non-Darcy Porous Medium. International Journal of Mathematical Archive, 3, 534-549.

[15]   Muhaimin, I., Kandasamy, R., Hashim, I. and Ruhaila, K. (2008) Thermphoresis and Chemical Reaction Effects on Non-Darcy MHD Mixed Convective Heat and Mass Transfer past a Porous Wedge in the Presence of Suction or Injection. Selcuk Journal of Applied Mathematics, 9, 77-95.

[16]   Salem, A.M. (2006) Coupled Heat and Mass Transfer in Darcy-Forchheimer Mixed Convection from a Vertical Flat Plate Embedded in a Fluid-Saturated Porous Medium under the Effects of Radiation and Viscous Dissipation. Journal of the Korean Physical Society, 48, 409-413.

[17]   Srinivasacharya, D. and Swamy Reddy, G. (2012) Chemical Reaction and Radiation Effects on Natural Convective in Porous Medium Saturated with Power-Law Fluid. Frontiers in Heat and Mass Transfer, 3, 1-9.

[18]   Huang, J.S., Tsai, R.Y. and Huang, K.H. (2012) Numerical Study of Thermophoresis on Aerosol Particle Deposition from Hiemenz Flow through Porous Medium onto a Stretching Surface. Journal of Marine Science and Technology, 20, 163-172.

[19]   Postelnicu, A. (2004) Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufor Effects. International Journal of Heat and Mass Transfer, 47, 1467-1472.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2003.09.017

[20]   Ahammad, M.U., Obayedullah, Md. and Rahman, M.M. (2013) Analysis of MHD Free Convection Flow along a Vertical Porous Plate Embedded in a Porous Medium with Magnetic Field and Heat Generation. Journal of Engineering e-Transaction, 8, 10-18.

[21]   Sonth, R.M., Khan, S.K., Abel, M.S. and Prasad, K.V. (2002) Heat and Mass Transfer in a Visco-Elastic Fluid over an Accelerating Surface with Heat Source/Sink and Viscous Dissipation. Heat and Mass Transfer, 38, 213-220.
http://dx.doi.org/10.1007/s002310100271

[22]   Venkateswarlu, M., Ramana Reddy, G.V. and Lakshimi, D.V. (2013) Effects of Chemical Reaction and Heat Generation on MHD Boundary Layer Flow of a Moving Vertical Plate with Suction and Dissipation. Engineering International, 1, 27-38.

[23]   Muhaimin, I., Kandasamy, R., Khamis, A.B. and Roslan, R. (2013) Effect of Thermophoresis Particle Deposition and Chemical Reaction on Unsteady MHD Mixed Convective Flow over a Porous Wedge in the Presence of Temperature Dependent Viscosity. Nuclear Engineering and Design, 261, 95-106.
http://dx.doi.org/10.1016/j.nucengdes.2013.03.015

[24]   Mahdy, A. (2013) Thermophoresis Particle Deposition and Variable Viscosity Effects on Non-Darcy Free Convection in a Fluid Saturated Porous Media with Uniform Suction/Injection. Latin American Applied Research, 43, 113-119.

[25]   Alam, M.S. and Rahman, M.M. (2013) On the Effectiveness of Variable Heat and Mass Fluxes on Hydromagnetic Free Convection and Mass Transfer Flow along an Inclined Permeable Stretching Surface with Thermophoresis. International Journal of Energy and Technology, 5, 1-10.

[26]   RamReddy, Ch., Murthy, P.V.S.N., Chamkha, A.J. and Rashad, A.M. (2013) Influence of Viscous Dissipation on Free Convection in a Non-Darcy Porous Medium Saturated Medium with Nanofluid in the Presence of Magnetic Field. The Open Transport Phenomena Journal, 5, 20-29.

[27]   Kishan, N. and Maripala, S. (2012) Thermophpresis and Viscous Dissipation Effects on Darcy-Forcheimer MHD Mixed Convection in a Fluid Saturated Porous Media. Advances in Applied Science Research, 3, 60-74.

[28]   Shrivastava, U.N. and Usha, S. (1987) Effect of Magnetic Field on Boundary Layer Thickness and Skin Friction at the Surface. Indian Journal of Pure and Applied Mathematics, 18, 741-751.

[29]   Noghrehabadi, A., Ghalambaz, M., Izadpanahi, E. and Pourrajab, R. (2014) Effect of Magnetic Filed on the Boundary Layer Flow, Heat and Mass Transfer of Nanofluids over s Stretching Cylinder. Journal of Heat and Mass Transfer Research, 1, 9-16.

[30]   Ishak, A., et al. (2008) Effect of a Uniform Transverse Magnetic Field on the Stagnation Point Flow over a Stretching Vertical Sheet. Journal of Heat and Mass Transfer, 44, 921-927.

[31]   Isa, S.S.P.M., Arifin, N.M., Nazar, R., Bachok, N., Ali, F.M. and Pop, I. (2014) Effect of Magnetic Field on Mixed Convection Boundary Layer Flow over an Exponentially Shrinking Vertical Sheet with Suction. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 8, 1519.

[32]   Talbot, L., Cheng, R.K., Scheffer, R.W. and Wills, D.R. (1980) Thermophoresis of Particles in a Heated Boundary Layer. Journal of Fluid Mechanics, 101, 737-758.
http://dx.doi.org/10.1017/S0022112080001905

[33]   Batchelor, G.K. and Shen, C. (1985) Thermophoretic Deposition of Particles in Gas Flowing over Cold Surfaces. Journal of Colloid and Interface Science, 107, 21-37.
http://dx.doi.org/10.1016/0021-9797(85)90145-6

[34]   Liao, S.J. (2003) Beyond Perturbation: Introduction to the Homotopy Analysis Method. Chapman and Hall/CRC Press, Boca Raton.
http://dx.doi.org/10.1201/9780203491164

[35]   Liao, S.J. (2012) Homotopy Analysis Method in Nonlinear Differential Equations. Springer and Higher Education Press, Berlin &Beijing.
http://dx.doi.org/10.1007/978-3-642-25132-0

[36]   Motsa, S.S., Sibanda, P. and Shateyi, S. (2010) A New Spectral-Homotopy Analysis Method for Solving a Nonlinear Second Order BVP. Communications in Nonlinear Science and Numerical Simulation, 15, 2293-2302.
http://dx.doi.org/10.1016/j.cnsns.2009.09.019

[37]   Motsa, S.S., Sibanda, P., Awad, F.G. and Shateyi, S. (2010) A New Spectral-Homotopy Analysis Method for the MHD Jeffery-Hamel Problem. Computers & Fluids, 39, 1219-1225.

[38]   Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A. (1988) Spectral Methods in Fluid Dynamics. Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-642-84108-8

[39]   Trefethen, L.N. (2000) Spectral Methods in MATLAB. SIAM, Philadelphia.
http://dx.doi.org/10.1137/1.9780898719598

 
 
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