Buradasınız

Hall Effect on Unsteady MHD Free Convection Flow Past an Impulsively Started Porous Plate with Viscous and Joule’s Dissipation

Journal Name:

Publication Year:

Abstract (2. Language): 
An investigation on the nonlinear problem of the effect of Hall current on the unsteady free convection flow of viscous, incompressible, electrically conducting fluid past an impulsively started infinite vertical porous plate is carried out, when a uniform magnetic field is applied transverse to the plate, while the viscous and Joule’s dissipations are taken into account. The solutions of the coupled nonlinear partial differential equations have been obtained by using finite difference methods. Hall current effect on primary and secondary velocity, skin friction and rate of heat transfer are analyzed in detail for heating and cooling of the plate by convection currents. Physical interpretations and justifications are rendered for various results obtained.
64-71

REFERENCES

References: 

[1] V.J. Rossow, NACATN 3971, 1957.
[2] R.H. Levy, and H.E. Petschek, LAS Paper, , Los Angeles, California,
June 1962, pp 62-100.
[3] V.M. Soundalgekhar, S.K. Gupta, and R.N. Aranake, “Free convection
currents on MHD Stokes problem for a vertical plate,” Journal of
Nuclear Engineering Design, vol. 51, pp. 403-407, 1979.
[4] N.D. Nanousis, G.A. Georgantopoulos, and A.I. Papaioannou,
“Hydromagnetic free convection flow in the stokes problem for a porous
vertical limiting surface with constant suction”, Astrophysics and Space
Science, vol.70, pp. 377-383, 1980.
[5] A.K. Singh, “MHD free-convection flow in the Stoke’s problem for a
porous vertical plate by finite difference method,” Astrophysics and
Space Science, vol.90, Number 1, pp. 67 – 74, 1983a.
[6] A.K. Singh, “Finite difference analysis of MHD free-convection flow
past an accelerated vertical porous plate,” Astrophysics and Space
Science, vol. 94, pp.395-400, 1983b.
[7] Th. I. Lekas, and G.A. Georgantopoulos, “Influence of viscous
dissipation on a hydromagnetic field,” Astrophysics and Space Science,
vol. 191, pp. 299-305, 1992.
[8] N.C. Sacheti, N.C., P. Chandran, and A.K. Singh, “An exact solution
for the unsteady MHD flow,” Int. comm. Heat Mass Transfer, vol. 21,
pp. 131-142, 1994.
[9] N. Chaturvedi, “On MHD flow past an infinite porous plate with
variable suction,” Journal of Energy Conversion Management, vol. 37,
pp. 623-627, 1996.
[10] M.A. Hossain, S.K. Das, and I. Pop, “Heat transfer response of MHD
free convection flow along a vertical plate to surface temperature
oscillations,” International Journal of Non-linear Mechanics, vol.33,
pp.541-553, 1998.
[11] E.M.A. Elbashbeshy, “Free convection flow with variable viscosity and
thermal diffusivity along a vertical plate in the presences of the magnetic
field,” International journal of Engineering Science, vol. 38, pp. 207-213, 2000.
[12] P.C.Ram, “Recent developments of heat and mass transfer in
hydromagnetic flows,” International Journal of Energy Research, vol.
15, pp. 691-713, 1991.
[13] M.A. Hossain, “Effect of Hall current on unsteady hydromagnetic free
convection flow near an infinite vertical porous plate,” J. Phys. Soc.
Jpn., vol. 55, pp. 2183-2190, 1986.
[14] I. Pop, and T. Watanabe, “Hall effect on magnetohydrodynamic free
convection about a semi-infinite vertical flat plate,” Int. J. Engg. Sci.,
vol. 32, pp. 1903-1911, 1994.
[15] T. Watanabe, and I.Pop, “Hall effects on magnetohydrodynamic
boundary layer flow over a continuous moving flat plate,” Acta
Mechanica, vol.108, pp. 35-47, 1995.
[16] E.M.Aboeldahab and E.M.E.Elbarbary, “Hall current effect on
magnetohydrodynamic free convection flow past a semi-infinite vertical
plate with mass transfer”, Int. J. Engg. Science, vol. 39, pp. 1641-1652,
2001.
[17] K. Shailendhra, Studies on unsteady and enhanced heat transfer in
MHD flows, Ph.D. Thesis, Bharathiar University, Coimbatore- 641046,
India, 2002.
[18] N.G. Kafousis, N.D. Nanousis, and G.A. Georgantopoulos, “Free
convection effects on the stokes problem for an infinite vertical limiting
surface with constant suction,” Astrophysics and Space Science, vol. 64,
pp. 391-399, 1979.
[19] H. Schlichting and K.Gersten, Boundary Layer Theory, 8
th
edition,
Springer-Verlag : Berlin Heidelberg, 2000.
[20] E.R.G. Eckert, and R.M. M. Drake Jr., Heat and Mass Transfer, 2
nd
Edition, McGraw Hill Book Company, Inc.: New York, 1959.
[21] B. Gebhart, “Effects of viscous dissipation in natural convection,”
Journal of Fluid Mechanics, vol. 14, pp. 225-232, 1962.
[22] W.G. Sutton, and A. Sherman, Engineering Magnetohydrodynamics,
McGraw- Hill Book Company: New York, 1965.
[23] K. R. Cramer, and S.I. Pai, Magnetofluid Dynamics for Engineers
and Applied Physicists, Scripta Publishing Company: Washington
D.C., 1973.
[24] E.M. Blums, A.Yu, and R. Ozols., Heat and Mass Transfer in MHD
Flows, World Scientific Publishing Co. Pte. Ltd.: Singapore, 1987.
[25] A.K. Singh, .K.S. Ajay, and N.P. Singh, “Hydromagnetic free
convection and mass transfer flow with Joule heating, thermal
diffusion,” Heat Source and Hall current, Bull. of Inst. Math. Acad.
Sinica, vol. 33 (3), pp 291-310, 2005 .
[26] E. M. Aboeldahab, M.A.E. Aziz, “ Viscous dissipation and Joule heating
effects on MHD free convection from a vertical plate with power-law
variation in surface temperature in the presence of Hall and ion-slip
currents,” Applied Mathematical Modeling, vol. 29(6), pp 579-595,
2005.
[27] E. Osalusi, J. Side, R. Harris, B. Johnston, “ On the effectiveness of
viscous dissipation and Joule heating on steady MHD and slip flow of a
Bingham fluid over a porous rotating disk in the presence of Hall and
ion-slip currents,” Romanian Reports in Physics, vol. 61(1), pp 71-93,
2009.
[28] A.K. Singh and R.S.R. Gorla, “Free convection heat and mass transfer
with Hall current, Joule heating and thermal diffusion,” Heat and Mass
Transfer, vol.45(11), pp 1341-1349, 2009.
[29] B.O. Anwar, Z.Joaquin, H.S.Takhar, “Unsteady magnetohydrodynamic
Hartmann-Couette flow and heat transfer in a Darcian channel with Hall
current, ion-slip, viscous and Joule heating effects : Network numerical
solutions,” Communications in Nonlinear Science and Numerical
Simulation, vol.14(4), pp.1082-1097, 2009.
[30] S. P. Anjali Devi and B.Ganga, “ Effect of viscous and Joule’s
dissipation on MHD flow, heat and mass transfer past a stretching
porous surface embedded in a porous medium,” Nonlinear Analysis :
Modelling and Control, vol.14 (3), pp. 303-314, 2009.
[31] N. Ahmed, H. Kalita, D.P.Barua, “Unsteady MHD free convective flow
past a vertical porous plate immersed in a porous medium with Hall
current, thermal diffusion and heat source,” International Journal of
Science, Engineering and Technology, Vol.2, No.6, pp.59-74, 2010.
[32] S.P. Anjali Devi, K. Shailendhra, and P.T. Hemamalini, “Pulsated
convective MHD flow with Hall current, heat source and viscous
dissipation along a vertical porous plate,” International Journal of
Applied Mathematics and Computation Vol. 3(2), pp.141-150, 2011.
[33] H.F. Oztop and K.A.Salem, “Effects of Joule Heating on MHD Natural
convection in non-isothermally heated enclosure,” Journal of Thermal
Science and Technology, vol. 32(1), pp 81-90, 2012.
[34] I.A. Hassanien, H.M. El-Hawary, R.G.A.Rahman, A.S.Elfeshawey,
“Corrigendum of Similarity analysis in magnetohydrodynamics : Hall
effects on free convection flow and mass transfer past a semi-infinite
vertical plate,” International Journal of Nonlinear Mechanics, vol.47(6),
pp. 719-725, 2012.
[35] Youn J. Kim, “Unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction,”
International Journal of Engineering Science, vol.38, pp. 833-845, 2000.
[36] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford
University Press: Oxford, 1961.
[37] G. Poots, “Laminar natural convection flow in magnetohydrodynamics,”
International Journal of Heat Mass Transfer, vol.3, pp.1-25, 1961.
[38] G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge
University Press: Cambridge, 1997.

Thank you for copying data from http://www.arastirmax.com