MHD Free Convective Flow of Water near 4℃ past a Vertical Moving Plate with Constant Suction

Affiliation(s)

Department of Mathematics, University of Ioannina, Ioannina, Greece.

Instituto de Matemática, Estatística e Computa??o Científica, Universidade Estadual de Campinas, Campinas, Brasil.

Department of Mathematics, University of Ioannina, Ioannina, Greece.

Instituto de Matemática, Estatística e Computa??o Científica, Universidade Estadual de Campinas, Campinas, Brasil.

ABSTRACT

The aim of this work is the study of the magnetohydrodynamic (MHD) unsteady free convective flow of water near 4℃ past an infinitely vertical plate moving with constant velocity. The influence of constant uniform suction was also considered. The partial differential equations (PDEs) and their initial and boundary conditions, describing the problem under consideration, are dimensionalized and the numerical solution is obtained by using the finite volume discretization methodology which is suitable for Fluid Mechanics applications. The numerical results for the velocity and temperature fields are shown in figures for different dimensionless parameters entering in the problem under consideration, such as the magnetic parameter,*M* and the Grashof number, *Gr*. This study predicts the effects of a constant magnetic field and uniform suction on the free convective flow of water near 4℃, when the water is electrically conductive. Analysis of the results showed that the velocity and temperature profiles are noticeably influenced by these parameters.

The aim of this work is the study of the magnetohydrodynamic (MHD) unsteady free convective flow of water near 4℃ past an infinitely vertical plate moving with constant velocity. The influence of constant uniform suction was also considered. The partial differential equations (PDEs) and their initial and boundary conditions, describing the problem under consideration, are dimensionalized and the numerical solution is obtained by using the finite volume discretization methodology which is suitable for Fluid Mechanics applications. The numerical results for the velocity and temperature fields are shown in figures for different dimensionless parameters entering in the problem under consideration, such as the magnetic parameter,

Cite this paper

M. Xenos, S. Dimas and A. Raptis, "MHD Free Convective Flow of Water near 4℃ past a Vertical Moving Plate with Constant Suction,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 52-57. doi: 10.4236/am.2013.41010.

M. Xenos, S. Dimas and A. Raptis, "MHD Free Convective Flow of Water near 4℃ past a Vertical Moving Plate with Constant Suction,"

References

[1] S. Goren, “On Free Convection in Water at 4℃,” Chemical Engineering Science, Vol. 21, No. 6-7, 1966, pp. 515-518. doi:10.1016/0009-2509(66)85065-0

[2] T. Govindarajulu, “Free Convection Flow of Water at 4℃ on Vertical and Horizontal Plates,” Chemical Engineering Science, Vol. 25, No. 11, 1970, pp. 1827-1828. doi:10.1016/0009-2509(70)80076-8

[3] V. Soundalgekar, “Free Convection Effects on the Oscillatory Flow of Water at 4℃ past an Infinite Vertical, Porous Plate with Constant Suction,” Heat and Mass Transfer, Vol. 9, 1976, pp. 111-115.

[4] I. Pop and A. Raptis, “A Note on Transient Free Convection of Water at 4℃ over a Doubly Infinite Vertical Porous Plate,” Journal of Heat Transfer-Transactions of the ASME, Vol. 104, 1982, pp. 800-802. doi:10.1115/1.3245206

[5] A. Raptis and I. Pop, “Combined Convection Flow of Water at 4℃ through a Porous Medium Bounded by a Vertical Surface,” Letters in Heat and Mass Transfer, Vol. 9, 1982, pp. 309-318. doi:10.1016/0094-4548(82)90039-X

[6] A. Raptis and C. Perdikis, “Free Convection Flow of Water at 4?C past an Infinite Porous Plate with Constant Suction and Free Stream Velocity,” Bulletin de la Classe des Sciences Academie Royale de Belgique, 5th Series—Tome LXVIII, 1982-1984, pp. 259-266.

[7] A. Singh and A. Raptis, “Free-Convection Flow of Water at 4℃ past an Infinite Vertical Porous Plate with Constant Heat Flux,” Astrophysics and Space Science, Vol. 104, 1984, pp. 399-404. doi:10.1007/BF00650312

[8] S. Ling, R. Nazar and I. Pop, “Steady Mixed Convection Boundary Layer Flow over a Vertical Flat Plate in a Porous Medium Filled with Water at 4℃: Case of Variable Wall Temperature,” Transport in Porous Media, Vol. 69, No. 3, 2007, pp. 359-372. doi:10.1007/s11242-006-9077-0

[9] S. Ling, R. Nazar and J. Merkin, “Steady Mixed Convection Boundary-Layer Flow over a Vertical Flat Surface in a Porous Medium Filled with Water at 4℃: Variable Surface Heat Flux,” Transport in Porous Media, Vol. 70, No. 3, 2007, pp. 307-321. doi:10.1007/s11242-007-9101-z

[10] H. Oztop, Y. Varol and I. Pop, “Investigation of Natural Convection in Triangular Enclosure Filled with Porous Media Saturated with Water near 4℃,” Energy Conversion and Management, Vol. 50, No. 6, 2009, pp. 1473-1480. doi:10.1016/j.enconman.2009.02.023

[11] J. Merkin and V. Kumaran, “Free Convection Stagnation-Point Boundary-Layer Flow in a Porous Medium with a Density Maximum,” International Journal of Thermal Sciences, Vol. 50, No. 11, 2011, pp. 2176-2183. doi:10.1016/j.ijthermalsci.2011.05.012

[12] W. Khan and R. Gorla, “Mixed Convection of Water at 4℃ along a Wedge with Variable Surface Temperature in a Porous Medium,” International Journal of Thermophysics, Vol. 32, No. 10, 2011, pp. 2079-2091. doi:10.1007/s10765-011-1069-9

[13] W. Khan and R. Gorla, “Nonsimilar Solutions for Mixed Convection of Water at 4℃ over a Vertical Surface with Prescribed Surface Heat Flux in a Porous Medium,” Journal of Porous Media, Vol. 13, 2010, pp. 1025-1032. doi:10.1615/JPorMedia.v13.i11.90

[14] G. Georgantopoulos, N. Nanousis and C. Douskos, “Hydromagnetic Free Convection Effects on the Oscillatory Flow of Water at 4℃ past an Infinite Porous Plate,” Revue Roumaine de Physique, Vol. 26, 1982, pp. 39-58.

[15] C. Perdikis and H. Takhar, “MHD Free Convective Flow of Water at 4?C past a Semi-Infinite Porous Plate,” Bulletin De la Classe des Sciences, 6th serie—Tome V, 1994, pp. 67-70.

[16] M. Guedda, E. Aly and A. Quahsine, “Analytical and ChPDM Analysis of MHD Mixed Convection over a Vertical Flat Plate Embedded in a Porous Medium Filled with Water at 4℃,” Applied Mathematical Modelling, Vol. 35, No. 10, 2011, pp. 5182-5197. doi:10.1016/j.apm.2011.04.014

[17] M. Xenos, S. Dimas and A. Raptis, “MHD and Thermal Radiation of an Optically Thin Gray Fluid in the Presence of an Induced Magnetic Field,” Advances and Applications in Fluid Mechanics, Vol. 11, No. 2, 2012, pp. 73-85.

[18] Wolfram-Reasearch, Inc., “Mathematica Edition: Version 8.0,” Wolfram Research, Inc., Champaign, 2010.

[19] S. Patankar, “Numerical Heat Transfer and Fluid Flow,” McGraw-Hill, New York, 1980.

[20] A. Raptis and C. Perdikis, “Free Convection Flow of Water near 4℃ past a Moving Plate,” Forschung im Ingenieurwesen, Vol. 67, 2002, pp. 206-208. doi:10.1007/s10010-002-0093-0

[1] S. Goren, “On Free Convection in Water at 4℃,” Chemical Engineering Science, Vol. 21, No. 6-7, 1966, pp. 515-518. doi:10.1016/0009-2509(66)85065-0

[2] T. Govindarajulu, “Free Convection Flow of Water at 4℃ on Vertical and Horizontal Plates,” Chemical Engineering Science, Vol. 25, No. 11, 1970, pp. 1827-1828. doi:10.1016/0009-2509(70)80076-8

[3] V. Soundalgekar, “Free Convection Effects on the Oscillatory Flow of Water at 4℃ past an Infinite Vertical, Porous Plate with Constant Suction,” Heat and Mass Transfer, Vol. 9, 1976, pp. 111-115.

[4] I. Pop and A. Raptis, “A Note on Transient Free Convection of Water at 4℃ over a Doubly Infinite Vertical Porous Plate,” Journal of Heat Transfer-Transactions of the ASME, Vol. 104, 1982, pp. 800-802. doi:10.1115/1.3245206

[5] A. Raptis and I. Pop, “Combined Convection Flow of Water at 4℃ through a Porous Medium Bounded by a Vertical Surface,” Letters in Heat and Mass Transfer, Vol. 9, 1982, pp. 309-318. doi:10.1016/0094-4548(82)90039-X

[6] A. Raptis and C. Perdikis, “Free Convection Flow of Water at 4?C past an Infinite Porous Plate with Constant Suction and Free Stream Velocity,” Bulletin de la Classe des Sciences Academie Royale de Belgique, 5th Series—Tome LXVIII, 1982-1984, pp. 259-266.

[7] A. Singh and A. Raptis, “Free-Convection Flow of Water at 4℃ past an Infinite Vertical Porous Plate with Constant Heat Flux,” Astrophysics and Space Science, Vol. 104, 1984, pp. 399-404. doi:10.1007/BF00650312

[8] S. Ling, R. Nazar and I. Pop, “Steady Mixed Convection Boundary Layer Flow over a Vertical Flat Plate in a Porous Medium Filled with Water at 4℃: Case of Variable Wall Temperature,” Transport in Porous Media, Vol. 69, No. 3, 2007, pp. 359-372. doi:10.1007/s11242-006-9077-0

[9] S. Ling, R. Nazar and J. Merkin, “Steady Mixed Convection Boundary-Layer Flow over a Vertical Flat Surface in a Porous Medium Filled with Water at 4℃: Variable Surface Heat Flux,” Transport in Porous Media, Vol. 70, No. 3, 2007, pp. 307-321. doi:10.1007/s11242-007-9101-z

[10] H. Oztop, Y. Varol and I. Pop, “Investigation of Natural Convection in Triangular Enclosure Filled with Porous Media Saturated with Water near 4℃,” Energy Conversion and Management, Vol. 50, No. 6, 2009, pp. 1473-1480. doi:10.1016/j.enconman.2009.02.023

[11] J. Merkin and V. Kumaran, “Free Convection Stagnation-Point Boundary-Layer Flow in a Porous Medium with a Density Maximum,” International Journal of Thermal Sciences, Vol. 50, No. 11, 2011, pp. 2176-2183. doi:10.1016/j.ijthermalsci.2011.05.012

[12] W. Khan and R. Gorla, “Mixed Convection of Water at 4℃ along a Wedge with Variable Surface Temperature in a Porous Medium,” International Journal of Thermophysics, Vol. 32, No. 10, 2011, pp. 2079-2091. doi:10.1007/s10765-011-1069-9

[13] W. Khan and R. Gorla, “Nonsimilar Solutions for Mixed Convection of Water at 4℃ over a Vertical Surface with Prescribed Surface Heat Flux in a Porous Medium,” Journal of Porous Media, Vol. 13, 2010, pp. 1025-1032. doi:10.1615/JPorMedia.v13.i11.90

[14] G. Georgantopoulos, N. Nanousis and C. Douskos, “Hydromagnetic Free Convection Effects on the Oscillatory Flow of Water at 4℃ past an Infinite Porous Plate,” Revue Roumaine de Physique, Vol. 26, 1982, pp. 39-58.

[15] C. Perdikis and H. Takhar, “MHD Free Convective Flow of Water at 4?C past a Semi-Infinite Porous Plate,” Bulletin De la Classe des Sciences, 6th serie—Tome V, 1994, pp. 67-70.

[16] M. Guedda, E. Aly and A. Quahsine, “Analytical and ChPDM Analysis of MHD Mixed Convection over a Vertical Flat Plate Embedded in a Porous Medium Filled with Water at 4℃,” Applied Mathematical Modelling, Vol. 35, No. 10, 2011, pp. 5182-5197. doi:10.1016/j.apm.2011.04.014

[17] M. Xenos, S. Dimas and A. Raptis, “MHD and Thermal Radiation of an Optically Thin Gray Fluid in the Presence of an Induced Magnetic Field,” Advances and Applications in Fluid Mechanics, Vol. 11, No. 2, 2012, pp. 73-85.

[18] Wolfram-Reasearch, Inc., “Mathematica Edition: Version 8.0,” Wolfram Research, Inc., Champaign, 2010.

[19] S. Patankar, “Numerical Heat Transfer and Fluid Flow,” McGraw-Hill, New York, 1980.

[20] A. Raptis and C. Perdikis, “Free Convection Flow of Water near 4℃ past a Moving Plate,” Forschung im Ingenieurwesen, Vol. 67, 2002, pp. 206-208. doi:10.1007/s10010-002-0093-0