Analytical and numerical investigation of heat and mass transfer effects on magnetohydrodynamic natural convective flow past a vertical porous plate

Document Type : Full Length Research Article

Authors

1 GITAM University

2 VNR Vignana Jyothi Institute of Engineering and Technology

Abstract

The aim of this investigation is to study the effect of hall current on an unsteady natural convective flow of a viscous, incompressible, electrically conducting optically thick radiating fluid past a vertical porous plate in the presence of a uniform transverse magnetic field. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Analytical and numerical solutions of the coupled governing partial differential equations for the fluid velocity, fluid temperature and fluid concentration profiles are obtained by perturbation and finite element techniques respectively. The effects of the various dimensionless engineering parameters viz., Grashof number for heat and mass transfer, Magnetic field parameter, Prandtl number, Schmidt number, Thermal radiation parameter and Hall parameter entering into the problem on the primary and secondary velocities, temperature and concentration profiles throughout the boundary layer are investigated through graphs. The expressions of skin-friction, Nusselt number and Sherwood number are derived and represented through tabular form. The results reveal that the flow field and the temperature distribution are greatly influenced by thermal radiation parameter. Furthermore, the limiting cases are obtained and are found to be in good agreement with the previously published results.

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References

References
 [1].              R. Srinivasa Raju, G. Jithender Reddy, J. Anand Rao, M. M. Rashidi, Rama Subba Reddy Gorla, ‘‘Analytical and Numerical Study of Unsteady MHD Free Convection Flow over an Exponentially Moving Vertical Plate With Heat Absorption’’, Int. J. Thermal Sci., 107, 303-315 (2016).
 [2].              S. Reddy Sheri, R. Srinivasa Raju, ‘‘Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation’’, Meccanica, 51(5),                               1057-1068, (2016).
 [3].              R. Srinivasa Raju, B. Mahesh Reddy, M.M. Rashidi, Rama Subba Reddy Gorla, ‘‘Application of Finite Element Method to Unsteady MHD Free Convection Flow Past a Vertically Inclined Porous Plate Including Thermal Diffusion And Diffusion Thermo Effects’’, J. Porous Media, 19 (8), 701-722, (2016).
 [4].              R. Srinivasa Raju, G. Jitthender Reddy, J. Anand Rao, M.M. Rashidi, ‘‘Thermal Diffusion and Diffusion Thermo Effects on an Unsteady Heat and Mass Transfer MHD Natural Convection Couette Flow Using FEM’’, J. Comp. Design and Eng., 3 (4), 349-362, (2016).
 [5].              M.V. Ramana Murthy, R. Srinivasa Raju, J. Anand Rao, ‘‘Heat and Mass transfer effects on MHD natural convective flow past an infinite vertical porous plate with thermal radiation and Hall Current’’, Procedia Eng. J., 127, 1330-1337, (2015).
 [6].             S. Sivaiah, R. Srinivasa Raju, "Finite Element Solution of Heat and Mass transfer flow with Hall Current, heat source and viscous dissipation", Appl. Math. Mech., 34 (5), 559-570, (2013).
 [7].              J. Anand Rao, R. Srinivasa Raju, S. Sivaiah, ‘‘Finite Element Solution of heat and mass transfer in MHD Flow of a viscous fluid past a vertical plate under oscillatory suction velocity’’, J. Appl. Fluid Mech., 5 (3), 1-10, (2012).
 [8].              J. Anand Rao, S. Sivaiah, R. Srinivasa Raju, ‘‘Chemical Reaction effects on an unsteady MHD free convection fluid flow past a semi-infinite vertical plate embedded in a porous medium with Heat Absorption’’, J. Appl. Fluid Mech., 5 (3), 63-70, (2012).
 [9].              G. Jitthender Reddy, R. Srinivasa Raju, J. Anand Rao, ‘‘Thermal Diffusion and Diffusion Thermo impact on Chemical reacted MHD Free Convection from an Impulsively Started Infinite Vertical Plate embedded in a Porous Medium using FEM’’, J. Porous Media, 20 (12), 1097-1117, (2017).
[10].             R. Dodda, R. Srinivasa Raju, J. Anand Rao, ‘‘Influence Of Chemical Reaction On MHD boundary Layer flow Of Nano Fluids Over A Nonlinear Stretching Sheet With Thermal Radiation’’, J. Nanofluids, 5 (6), 880-888, (2016).
[11].             R. Dodda, R. Srinivasa Raju, J. Anand Rao, ‘‘Slip Effect of MHD Boundary Layer Flow of Nanofluid Particles over a Nonlinearly Isothermal Stretching Sheet in Presence of Heat Generation/Absorption’’, Int. J. Nanosci. Nanotech., 12(4), 251-268, (2016).
[12].             J. Anand Rao, R. Srinivasa Raju, S. Sivaiah, ‘‘Finite Element Solution of MHD transient flow past an impulsively started infinite horizontal porous plate in a rotating fluid with Hall current’’, J. Appl. Fluid Mech., 5(3), 105-112, (2016).
[13].             V.S. Rao, L. Anand Babu, R. Srinivasa Raju, ‘‘Finite Element Analysis of Radiation and mass transfer flow past semi-infinite moving vertical plate with viscous dissipation’’, J. Appl. Fluid Mech., 6 (3), 321-329, (2013).
[14].             R. Srinivasa Raju, ‘‘Combined influence of thermal diffusion and diffusion thermo on unsteady hydromagnetic free convective fluid flow past an infinite vertical porous plate in presence of chemical reaction’’, J. Inst. Eng.: Series C, 97(4), 505-515, (2016).
[15].             R. Srinivasa Raju, K. Sudhakar, M. Rangamma, ‘‘The effects of thermal radiation and Heat source on an unsteady MHD free convection flow past an infinite vertical plate with thermal diffusion and diffusion thermo’’, J. Inst. Eng.: Series C, 94(2), 175-186, (2013).
[16].             A. Aghaei, H. Khorasanizadeh, G. Sheikhzadeh, Mahmoud Abbaszadeh, ‘‘Numerical study of magnetic field on mixed convection and entropy generation of nanofluid in a trapezoidal enclosure’’, J. Magn. Mater., 403, 133-145, (2016).
[17].             A. Aghaei, A. A. Abbasian Arani, F. Abedi, ‘‘Analysis of Magnetic Field Effects on Distributed Heat Sources in a Nanofluid-Filled Enclosure by Natural Convection’’, J. Appl. Fluid Mech., 9(3), 1175-1187, (2016).
[18].             R. Deka, U. N. Das, V. M. Soundalgekar, ‘‘Effects of mass transfer flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction’’, Forsch. Ingenieurwes., 60, 284-287, (1994).
[19].             R. Muthucumaraswamy, P. Ganesan, ‘‘Effect of the chemical reaction and injection on flow characteristics in an unsteady upward motion of an isothermal plate’’, J. Appl. Mech. Tech. Phys., 42, 665-671, (2001).
[20].             A.J. Chamkha, ‘‘MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction’’, Int. Commun. Heat Mass Transfer, 30, 413-422, (2003).
[21].             F.S. Ibrahim, A.M. Elaiw, A.A. Bakr, ‘‘Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction’’, Commun. Nonlinear Sci. Numer. Simul., 13, 1056-1066, (2008).
[22].             M.M. Rahman, ‘‘Convective flows of micropolar fluids from radiate isothermal porous surfaces with viscous dissipation and Joule heating’’, Commun. Nonlinear Sci. Numer. Simul., 14, 3018-3030, (2009).
[23].            A.C. Cogley, W.E. Vincenty, S.E. Gilles, ‘‘Differential approximation for radiation in a non-gray gas near equilibrium’’, AIAA J., 6, (1968)                 pp. 551-553.
[24].             M.D. Abdus Sattar, Kalim MD. Hamid, ‘‘Unsteady free-convection interaction with thermal radiation in a boundary layer flow past a vertical porous plate’’, J. Math. Phys. Sci., 30, 25-37, (1996).
[25].             K. Vajravelu, ‘‘Flow and heat transfer in a saturated porous medium’’, ZAMM, 74, 605-614, (1994).
[26].             M.A. Hossain, H.S. Takhar, ‘‘Radiation effect on mixed convection along a vertical plate with uniform surface temperature’’, Heat Mass Transf., 31, 243-248, (1996).
[27].             A. Raptis, ‘‘Radiation and free convection flow through a porous medium’’, Int. Commun. Heat Mass Transf., 25, 289-295, (1998).
[28].             O.D. Makinde, ‘‘Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate’’, Int. Commun. Heat Mass Transf., 32, 1411-1419, (2005).
[29].             F.S. Ibrahim, A.M. Elaiw, A.A. Bakr, ‘‘Effect of the chemical reaction and radiation absorption on unsteady MHD mixed convection flow past a semi-infinite vertical permeable moving plate with heat source and suction’’, Commun. Nonlinear Sci. Numer. Simul., 13, 1056-1066, (2008).
[30].             A.A. Bakr, ‘‘Effects of chemical reaction on MHD free convection and mass transfer flow of a micropolar fluid with oscillatory plate velocity and constant heat source in a rotating frame of reference’’, Commun. Nonlinear Sci. Numer. Simul., 16, 698-710, (2011).
[31].             I. Pop, T. Watanabe, ‘‘Hall effect on magneto hydrodynamic free convection about a                       semi-infinite vertical flat plate’’, Int. J. Eng. Sci., 32, 1903-1911, (1994).
[32].             E.M. Abo-Eldahab, E.M.E. Elbarbary, ‘‘Hall current effect on magnetohydrodynamic free-convection flow past a semi-infinite vertical plate with mass transfer’’, Int. J. Eng. Sci., 39, 1641-52, (2001).
[33].             H.S. Takhar, S. Roy, G. Nath, ‘‘Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents’’, Heat Mass Transf., 39, 8258-34, (2003).
[34].             L.K. Saha, S. Siddiqa, M.A. Hossain, ‘‘Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux’’, Appl. Math. Mech. -Engl. Ed., 32(9), 1127-1146, (2011).
[35].             P.V. Satya Narayana B. Venkateswarlu,                      S. Venkataramana, ‘‘Effects of Hall current and radiation absorption on MHD micropolar fluid in a rotating system’’, Ain Shams Eng. J., http://dx.doi.org/10.1016/j.asej.2013.02.002, (2013).
[36].             G.S. Seth, G.K. Mahato, S. Sarkar, ‘‘Effects of Hall current and rotation on MHD natural convection flow past an impulsively moving vertical plate with ramped temperature in the presence of thermal diffusion with heat absorption’’, Int. J. Energy Tech., 5(16), 1-12, (2013).
[37].             B.K. Sharma, R.C. Chaudhary, ‘‘Hydromagnetic unsteady mixed convection and mass transfer flow past a vertical porous plate immersed in a porous medium with Hall Effect’’, Eng. Trans., 56(1), 3-23, (2008).
[38].             K.R. Cramer, S.I. Pai, ‘‘Magnetofluid dynamics for engineers and applied physicists’’, McGraw Hill Book Company, New York (1973).
[39].             M.Q. Brewster, ‘‘Thermal Radiative Transfer and Properties’’, John Wiley & Sons, New York, USA, (1992).
[40].             K.J. Bathe, "Finite Element Procedures", Prentice-Hall, New Jersey, (1996).
[41].             J.N. Reddy, ‘‘An  Introduction  to  the  Finite  Element  Method’’,  McGraw-Hill  Book Company, New York, 3rd  Edition, (2006).

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History

  • Receive Date: 07 January 2017
  • Revise Date: 25 July 2017
  • Accept Date: 03 September 2017

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