Effects of Radiation and Porosity of the Medium on MHD Flow Past an Inclined Plate in the Presence of Hall Current
Department of Mathematics and Astronomy, University of Lucknow, India
E-mail: rajputgauravlko@gmail.com
Received:
Received: 09 January 2017; revised: 10 April 2017; accepted: 24 April 2017; published online: 30 June 2017
DOI: 10.12921/cmst.2017.0000003
Abstract:
The present study deals with an analysis of the effects of radiation and porosity of the medium on unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively started inclined plate under the influence of transversely applied uniform magnetic field and Hall current. The medium of the flow is taken as porous. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The results obtained are discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof Number, Prandtl number, Hall current, radiation, permeability, magnetic field parameter and Schmidt number. The numerical values obtained for skin-friction and Nusselt number have been tabulated. The objective of this study is to analyze radiation and the porosity of the medium in the MHD flow model. In the study we found that the velocity in the boundary layer increases with the values of radiation and porosity of the medium. It is also observed that radiation and porosity of the medium increases the skin-friction at the wall surface. The results of the study are found to be in agreement with the actual flow. The importance of the problem can be seen in cooling of electronic components of a nuclear reactor, bed thermal storage and heat sink in the turbine blades.
Key words:
Hall current, mass diffusion, MHD flow, porous medium, radiation effect
References:
[1] A.N. Armstrong, R. Muthucumaraswamy, MHD flow past a parabolic started vertical plate with variable temperature and mass diffusion, Journal of Mechanical Engineering and Sciences, 7, 1251–1260 (2014).
[2] I.G. Baoku, C.I. Cookey, B.I. Olajuwon, Influence of thermal radiation on a transient MHD Couette flow through a porous medium, Journal of Applied Fluid Mechanics 5(1), 81–87 (2012).
[3] D. Deka, R.K. Deka, Radiation effects on MHD flow past an infinite vertical plate with variable temperature and uniform mass diffusion, JP Journal of Mathematical Sciences, 1(1), 15–29. (2011).
[4] S.K. Guchhait, S. Das, R.N. Jana, Combined effects of Hall current and radiation on MHD free convective flow in a ver- tical channel with an oscillatory wall temperature, Open Journal of Fluid Dynamics 3, 9–22 (2013).
[5] M.A. Hossain, M.A. Alim, D.A.S. Rees, The effect of radi- ation in free convection from a porous vertical plate, Int J Heat and Mass transfer, 42(1), 181–191 (1999).
[6] D. Pal, H. Mondal, Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity, Meccanica, 44 133–144 (2009).
[7] A. Raptis, Radiation and free convection flow through a porous medium, Int Comm. Heat Mass Transfer 25(2), 289– 295 (1998).
[8] A.Raptis,C.Perdikis,Unsteadyflowthroughahighlyporous medium in the presence of radiation, Transport Porous Media 57, 171–179 (2004).
[9] U.S. Rajput, P.K. Sahu, Radiation effects on steady hydro- magnetic flow of a viscous fluid through a vertical channel in a porous medium with heat generation or absorption, Int J of Math Archive 2(10), 1–7 (2011).
[10] U.S.Rajput,G.Kumar,Chemicalreactioneffectonunsteady MHD flow past an impulsively Started oscillating inclined plate with variable temperature and mass diffusion in the presence of Hall current, Applied Research Journal 2(5), 244–253 (2016).
[11] C.S.K.Raju,N.Sandeep,S.Saleem,Effectsofinducedmag- netic field and homogeneous–heterogeneous reactions on stagnation flow of a Casson fluid, Engineering Science and Technology, an International Journal 19, 875–887 (2016).
[12] K. Srihari, Combined effects of Hall current and magnetic field on unsteady flow past a semi-infinite vertical plate with thermal radiation and heat source, Physical Science International Journal 7(2), 73–89 (2015).
[13] M.Thamizhsudar,J.Pandurangan,Combinedeffectsofradi- ation and Hall current on MHD flow past an exponentially accelerated vertical plate in the presence of rotation, Inter- national Journal of Innovative Research in Computer and Communication Engineering 2(12) (2014).
[14] B.Vasu,V.R.Prasad,N.B.Reddy,Radiationandmasstrans- fer effects on transient free convection flow of a dissipative fluid past semi-infinite vertical plate with uniform heat and mass flux, Journal of Applied Fluid Mechanics 4(1), 15–26 (2011).
[15] P. Vyas, N. Srivastava, Radiative MHD flow over a non- isothermal stretching sheet in a porous medium, Applied Mathematical Sciences 4(49-52), 2475–2484 (2010).
[16] H.E. Wilhem, S.H. Choi, Magneto hydrodynamic diffusion flow across homogeneous magnetic field, The Physics of Flu- ids 21, 1717 (1978).
The present study deals with an analysis of the effects of radiation and porosity of the medium on unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively started inclined plate under the influence of transversely applied uniform magnetic field and Hall current. The medium of the flow is taken as porous. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The results obtained are discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof Number, Prandtl number, Hall current, radiation, permeability, magnetic field parameter and Schmidt number. The numerical values obtained for skin-friction and Nusselt number have been tabulated. The objective of this study is to analyze radiation and the porosity of the medium in the MHD flow model. In the study we found that the velocity in the boundary layer increases with the values of radiation and porosity of the medium. It is also observed that radiation and porosity of the medium increases the skin-friction at the wall surface. The results of the study are found to be in agreement with the actual flow. The importance of the problem can be seen in cooling of electronic components of a nuclear reactor, bed thermal storage and heat sink in the turbine blades.
Key words:
Hall current, mass diffusion, MHD flow, porous medium, radiation effect
References:
[1] A.N. Armstrong, R. Muthucumaraswamy, MHD flow past a parabolic started vertical plate with variable temperature and mass diffusion, Journal of Mechanical Engineering and Sciences, 7, 1251–1260 (2014).
[2] I.G. Baoku, C.I. Cookey, B.I. Olajuwon, Influence of thermal radiation on a transient MHD Couette flow through a porous medium, Journal of Applied Fluid Mechanics 5(1), 81–87 (2012).
[3] D. Deka, R.K. Deka, Radiation effects on MHD flow past an infinite vertical plate with variable temperature and uniform mass diffusion, JP Journal of Mathematical Sciences, 1(1), 15–29. (2011).
[4] S.K. Guchhait, S. Das, R.N. Jana, Combined effects of Hall current and radiation on MHD free convective flow in a ver- tical channel with an oscillatory wall temperature, Open Journal of Fluid Dynamics 3, 9–22 (2013).
[5] M.A. Hossain, M.A. Alim, D.A.S. Rees, The effect of radi- ation in free convection from a porous vertical plate, Int J Heat and Mass transfer, 42(1), 181–191 (1999).
[6] D. Pal, H. Mondal, Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity, Meccanica, 44 133–144 (2009).
[7] A. Raptis, Radiation and free convection flow through a porous medium, Int Comm. Heat Mass Transfer 25(2), 289– 295 (1998).
[8] A.Raptis,C.Perdikis,Unsteadyflowthroughahighlyporous medium in the presence of radiation, Transport Porous Media 57, 171–179 (2004).
[9] U.S. Rajput, P.K. Sahu, Radiation effects on steady hydro- magnetic flow of a viscous fluid through a vertical channel in a porous medium with heat generation or absorption, Int J of Math Archive 2(10), 1–7 (2011).
[10] U.S.Rajput,G.Kumar,Chemicalreactioneffectonunsteady MHD flow past an impulsively Started oscillating inclined plate with variable temperature and mass diffusion in the presence of Hall current, Applied Research Journal 2(5), 244–253 (2016).
[11] C.S.K.Raju,N.Sandeep,S.Saleem,Effectsofinducedmag- netic field and homogeneous–heterogeneous reactions on stagnation flow of a Casson fluid, Engineering Science and Technology, an International Journal 19, 875–887 (2016).
[12] K. Srihari, Combined effects of Hall current and magnetic field on unsteady flow past a semi-infinite vertical plate with thermal radiation and heat source, Physical Science International Journal 7(2), 73–89 (2015).
[13] M.Thamizhsudar,J.Pandurangan,Combinedeffectsofradi- ation and Hall current on MHD flow past an exponentially accelerated vertical plate in the presence of rotation, Inter- national Journal of Innovative Research in Computer and Communication Engineering 2(12) (2014).
[14] B.Vasu,V.R.Prasad,N.B.Reddy,Radiationandmasstrans- fer effects on transient free convection flow of a dissipative fluid past semi-infinite vertical plate with uniform heat and mass flux, Journal of Applied Fluid Mechanics 4(1), 15–26 (2011).
[15] P. Vyas, N. Srivastava, Radiative MHD flow over a non- isothermal stretching sheet in a porous medium, Applied Mathematical Sciences 4(49-52), 2475–2484 (2010).
[16] H.E. Wilhem, S.H. Choi, Magneto hydrodynamic diffusion flow across homogeneous magnetic field, The Physics of Flu- ids 21, 1717 (1978).
