STUDY OF HALL AND SORET EFFECT ON MHD FLOW WITH A RAMPED PLATE TEMPERATURE OF AN EXPONENTIALLY ACCELERATED VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM
DOI:
https://doi.org/10.4314/jfas.v11i1.25Keywords:
Soret effect; Hall current; Rotation; Radiation.Abstract
The present literature deals with the study of MHD flow of an incompressible viscous electrically conducting fluid along an exponentially accelerated infinite vertical plate in a rotating system. The effects of thermodiffusion, thermal radiation and Hall current, are analysed with ramped and isothermal plate conditions. The non-dimensional coupled partial differential equations of the model are solved analytically by using Laplace Transform method with the help of Heaviside step function; thus the expression for velocity field, temperature field, concentration field, skin friction coefficient, Nusselt number and Sherwood number are obtained. The influence of physical parameters such as m (Hall parameter), Sr (Soret number), K (Darcy permeability), λ (exponential parameter), Ω (rotation parameter) and R (radiation parameter) on these fields are discussed in detail through graphs.
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References
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[12] Ibrahim, A.A. (2009). Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, Dufour-Soret effect and Hall effect. Thermal science 13 (2), 183-197.
[13] Jaimala, Vikrant and K. Vivek (2013). Thermal convection in a Couple-Stress fluid in the presence of horizontal magnetic field with Hall currents. Application and applied Mathematics 8(1), 161-117.
[14] Kafoussias, N. G., and E.W. Williams (1995). Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity. International Journal of Engineering Science 33(9), 1369-1384.
[15] Kim, Y.J. (2004). Heat and mass transfer in MHD Micropolar flow over a vertical moving porous plate in a porous medium. Transport in Porous Media 56(1), 17–37.
[16] Makinde, O. D. (2011). MHD mixed convection with Soret and Dufour effects past a vertical plate embedded in a porous medium. Latin American Applied Research 41, 63-68.
[17] Makinde, O.D., and P.Y. Mhone (2005). Heat transfer to MHD oscillatory flow in a channel filled with porous medium. Romania Journal of Physics 50(9-10), 931–938.
[18] Mazumdar, B.S., A.S. Gupta, and N. datta (1976). Flow and heat transfer in hydrodynamic ekman layer on a porous plate with Hall effects. Int. J. heat mass Transfer 19, 523.
[19] Muthucumaraswamy, R., and K. M. A. Prema (2016). Hall effects on flow past an exponentially accelerated infinite isothermal vertical plate with mass diffusion. J. of App. Fluid Mech.9(2), 889-897.
[20] Muthucumaraswamy, R., N. Dhanasekar, and G. E. Prasad (2013). Rotation effects on unsteady flow past an accelerated isothermal vertical plate with variable mass transfer in the presence of chemical reaction of first order. Journal of Applied Fluid Mechanics 6 (4), 485 – 490.
[21] Muthucumaraswamy, R., P. Ganesan, and V.M. Soundalgeker (2001). Heat and mass transfer effect on flow past impulsively started vertical plate. Acta Mechanica 146 (1), 1-8.
[22] Osalusi, E., and P. Sibanda (2006). On variable laminar convection flow properties due to a porous rotating disk in a magnetic field. Romania Journal of Physics 51(9-10), 937 – 950.
[23] Owen, J. M., and R. H. Rogers (1989). Flow and heat transfer in rotating disc systems, Vol. I, Rotor - Stator Systems, John Wiley Sons, New York.
[24] Platten, J.K.( 2006). The Soret effect: A review of recent experimental results. Journal of applied mechanics 73, 5-15.
[25] 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 Dufour effects. Int. J. Heat & Mas Transfer 47, 1467-1472.
[26] Postelnicu, A. (2007). Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat Mass Transfer 43, 595-602.
[27] Prasad, V.R., N.B. Reddy, and R. Muthucumaraswamy (2007). Radiation and mass transfer effects on two-dimensional flow past an impulsively started infinite vertical plate. International Journal of Thermal Sciences 46, 1251-1258.
[28] Rajput, U.S., and Shareef, M.(2017). Unsteady MHD flow along exponentially accelerated vertical flat surface through porous medium with variable temperature and Hall current in a rotating system. Journal of Fundamental and Applied Sciences 9(2), 1050-1062.
[29] Raptis, A. (1998). Radiation and free convection flow through a porous medium. Int. Comm. Heat Mass Transfer 25, 289-295.
[30] Raptis, A., and C.V. Massalas (1998). Magnetohydrodynamic flow past a plate by the presence of radiation. Heat and Mass Transfer 34, 107-109.
[31] Raptis, N., and N.G. Kafousias (1982). Magnetohydrodynamic free convection flow and mass transfer through porous medium bounded by an infinite vertical porous plate with constant heat flux. Can. J. Physics 60(12), 1725-1729.
[32] Sattar, M. A. (1993). Unsteady hydromagnetic free convection flow with Hall current, mass transfer and variable suction through a porous medium near an infinite vertical porous plate with constant heat flux. Int. J. Energy Research 17, 1-5.
[33] Soong, C. Y. (2001). Thermal buoyancy effects in rotating non-isothermal flows, Int. J. Rotating Machinery 7(6), 435-446.
[34] Soong, C. Y., and H. L. Ma (1995). Unsteady analysis of non-isothermal flow and heat transfer between rotating co-axial disks, Int. J. of Heat and Mass Transfer 38(10), 1865-1878.
[35] Soundalgekar, V. M. (1979). Effects of Mass Transfer and free-convection currents on the flow past an impulsively started vertical plate. J. Appl. Mech 46(4), 757-760.
[36] Takhar, H.S., A.J. Chamkha, and G. Nath (2001).Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces. International Journal of Heat and Mass Transfer 37, 397-402.
[37] Takhar, H.S., R.S.R. Gorla, and V.M. Soundalgekar (1996). Radiative effects on MHD free convection flow of a gas past a semi-infinite vertical plate. International Journal of Numerical Heat Fluid Flow 2(2), 77-83.
[2] Alam, M.S., and M.M. Rahman (2006). Dufour and Soret effects on mixed convection flow past a vertical porous flat plate with variable suction. Nonlinear Analysis: Modelling and Control 11(1), 3-12.
[3] Anghel, M., H. S. Takhar, I. Pop (2000). Dufour and Soret effects on free convection boundary-layer over a vertical surface embedded in a porous medium. Studia Universitatis Babes-Bolyai. Mathematica XLV (4), 11-21.
[4] Beg, O.A., T. A. Beg, A.Y. Bakier, and V.R. Prasad (2009). Chemically-reacting mixed convective heat and mass transfer along inclined and vertical plates with Soret and Dufour effects: Numerical solutions. Int. J. Applied Mathematics and Mechanics 5(2), 39-57.
[5] Bhargava, R., R. Sharma and O. A. Beg (2009). Oscillatory chemically-reacting MHD free convection heat and mass transfer in a porous medium with Soret and Dufour effects: finite element modelling. Int. J. Applied Mathematics and Mechanics 5(6), 15-37.
[6] Branover, H. (1978). Magnetohydrodynamic Flow in Ducts. John Wiley and Sons, New York.
[7] Chamkha, A. J. (2000). Thermal radiation and buoyancy effects on hydromagnetic flow over an accelerating permeable surface with heat source or sink. International Journal of Engineering Sciences 38, 1699 -1712.
[8] Cowling, T.G. (1957). Magnetohydrodynamics. Interscience, New York.
[9] Ganesan, P., and P. Laganathan (2002). Radiation and mass transfer effects on flow of an incompressible viscous fluid past a moving cylinder. Int. J. of Heat and Mass Transfer 45, 4281-4288.
[10] Greenspan, H. P. (1968). The Theory of Rotating Fluids, Cambridge University Press, London.
[11] Hossain, M.A. and H.S. Takhar (1996). Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat and Mass Transfer 31, 243-248.
[12] Ibrahim, A.A. (2009). Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, Dufour-Soret effect and Hall effect. Thermal science 13 (2), 183-197.
[13] Jaimala, Vikrant and K. Vivek (2013). Thermal convection in a Couple-Stress fluid in the presence of horizontal magnetic field with Hall currents. Application and applied Mathematics 8(1), 161-117.
[14] Kafoussias, N. G., and E.W. Williams (1995). Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity. International Journal of Engineering Science 33(9), 1369-1384.
[15] Kim, Y.J. (2004). Heat and mass transfer in MHD Micropolar flow over a vertical moving porous plate in a porous medium. Transport in Porous Media 56(1), 17–37.
[16] Makinde, O. D. (2011). MHD mixed convection with Soret and Dufour effects past a vertical plate embedded in a porous medium. Latin American Applied Research 41, 63-68.
[17] Makinde, O.D., and P.Y. Mhone (2005). Heat transfer to MHD oscillatory flow in a channel filled with porous medium. Romania Journal of Physics 50(9-10), 931–938.
[18] Mazumdar, B.S., A.S. Gupta, and N. datta (1976). Flow and heat transfer in hydrodynamic ekman layer on a porous plate with Hall effects. Int. J. heat mass Transfer 19, 523.
[19] Muthucumaraswamy, R., and K. M. A. Prema (2016). Hall effects on flow past an exponentially accelerated infinite isothermal vertical plate with mass diffusion. J. of App. Fluid Mech.9(2), 889-897.
[20] Muthucumaraswamy, R., N. Dhanasekar, and G. E. Prasad (2013). Rotation effects on unsteady flow past an accelerated isothermal vertical plate with variable mass transfer in the presence of chemical reaction of first order. Journal of Applied Fluid Mechanics 6 (4), 485 – 490.
[21] Muthucumaraswamy, R., P. Ganesan, and V.M. Soundalgeker (2001). Heat and mass transfer effect on flow past impulsively started vertical plate. Acta Mechanica 146 (1), 1-8.
[22] Osalusi, E., and P. Sibanda (2006). On variable laminar convection flow properties due to a porous rotating disk in a magnetic field. Romania Journal of Physics 51(9-10), 937 – 950.
[23] Owen, J. M., and R. H. Rogers (1989). Flow and heat transfer in rotating disc systems, Vol. I, Rotor - Stator Systems, John Wiley Sons, New York.
[24] Platten, J.K.( 2006). The Soret effect: A review of recent experimental results. Journal of applied mechanics 73, 5-15.
[25] 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 Dufour effects. Int. J. Heat & Mas Transfer 47, 1467-1472.
[26] Postelnicu, A. (2007). Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat Mass Transfer 43, 595-602.
[27] Prasad, V.R., N.B. Reddy, and R. Muthucumaraswamy (2007). Radiation and mass transfer effects on two-dimensional flow past an impulsively started infinite vertical plate. International Journal of Thermal Sciences 46, 1251-1258.
[28] Rajput, U.S., and Shareef, M.(2017). Unsteady MHD flow along exponentially accelerated vertical flat surface through porous medium with variable temperature and Hall current in a rotating system. Journal of Fundamental and Applied Sciences 9(2), 1050-1062.
[29] Raptis, A. (1998). Radiation and free convection flow through a porous medium. Int. Comm. Heat Mass Transfer 25, 289-295.
[30] Raptis, A., and C.V. Massalas (1998). Magnetohydrodynamic flow past a plate by the presence of radiation. Heat and Mass Transfer 34, 107-109.
[31] Raptis, N., and N.G. Kafousias (1982). Magnetohydrodynamic free convection flow and mass transfer through porous medium bounded by an infinite vertical porous plate with constant heat flux. Can. J. Physics 60(12), 1725-1729.
[32] Sattar, M. A. (1993). Unsteady hydromagnetic free convection flow with Hall current, mass transfer and variable suction through a porous medium near an infinite vertical porous plate with constant heat flux. Int. J. Energy Research 17, 1-5.
[33] Soong, C. Y. (2001). Thermal buoyancy effects in rotating non-isothermal flows, Int. J. Rotating Machinery 7(6), 435-446.
[34] Soong, C. Y., and H. L. Ma (1995). Unsteady analysis of non-isothermal flow and heat transfer between rotating co-axial disks, Int. J. of Heat and Mass Transfer 38(10), 1865-1878.
[35] Soundalgekar, V. M. (1979). Effects of Mass Transfer and free-convection currents on the flow past an impulsively started vertical plate. J. Appl. Mech 46(4), 757-760.
[36] Takhar, H.S., A.J. Chamkha, and G. Nath (2001).Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces. International Journal of Heat and Mass Transfer 37, 397-402.
[37] Takhar, H.S., R.S.R. Gorla, and V.M. Soundalgekar (1996). Radiative effects on MHD free convection flow of a gas past a semi-infinite vertical plate. International Journal of Numerical Heat Fluid Flow 2(2), 77-83.
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Published
2018-12-21
How to Cite
RAJPUT, U. S.; SHAREEF, M. STUDY OF HALL AND SORET EFFECT ON MHD FLOW WITH A RAMPED PLATE TEMPERATURE OF AN EXPONENTIALLY ACCELERATED VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM. Journal of Fundamental and Applied Sciences, [S. l.], v. 11, n. 1, p. 385–411, 2018. DOI: 10.4314/jfas.v11i1.25. Disponível em: https://jfas.info/index.php/JFAS/article/view/103. Acesso em: 29 jan. 2025.
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