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Magnetohydrodynamic Free Convective Flow of Nanofluids Past an Oscillating Porous Flat Plate in A Rotating System with Thermal Radiation and Hall Effects

Published online by Cambridge University Press:  15 July 2015

S. Das ,
R.N. Jana  and
O.D. Makinde
S. Das*
Affiliation:
Department of Mathematics, University of Gour Banga, Malda, India
R.N. Jana
Affiliation:
Department of Applied Mathematics, Vidyasagar University, Midnapore, India
O.D. Makinde
Affiliation:
Faculty of Military Science, Stellenbosch University, Saldanha, South Africa
*
*Corresponding author ([email protected])
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Abstract

The unsteady magnetohydrodynamic free convective flow due to an oscillating porous flat plate in a rotating frame of reference are studied when thermal radiation and Hall currents are taken into consideration. The entire system rotates with a uniform angular velocity about an axis normal to the plate. A uniform magnetic field is applied along the normal to the plate directed into the fluid region. Copper, alumina and titania water nanofluids are considered. The governing equations are solved analytically by employing the small perturbation approximation. The numerical results for fluid velocity and temperature are presented graphically for the pertinent parameters and discussed in details.

Keywords

MagnetohydrodynamicNanofluidHall currentsOscillating porous plate
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 2 , April 2016 , pp. 197 - 210
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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References

REFERENCES

1.Choi, S.U.S., “Enhancing Thermal Conductivity of Fluids with Nanoparticles, Developments and Applications of Non-Newtonian Flows,” The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, 66, pp. 99–105 (1995).Google Scholar
2.Das, S.K., Choi, S.U.S., Yu, W. and Pradeep, T., Nanofluids: Science and Technology, Wiley-Interscience, New Jersey (2007).CrossRefGoogle Scholar
3.Wang, X.Q. and Mujumdar, A.S., “Heat transfer characteristics of nanofluids: A review,” Internaltional Journal of Thermal Science, 46, pp.1–19 (2007).CrossRefGoogle Scholar
4.Abu-Nada, E. and Oztop, H.F., “Effect of Inclination Angle on Natural Convection in Enclosures Filled with Cu-Water Nanofluid,” Internaltional Journal of Heat Fluid Flow, 30, pp. 669–678 (2009).CrossRefGoogle Scholar
5.Liron, N. and Wilhelm, H.E., “Integration of the Magneto-Hydrodynamic Boundary Layer Equations by Meksyn’s Method,” Journal of Appilled Mathematics and Mechanics, 54, pp. 27–37 (1974).Google Scholar
6.Katagiri, T., “The Effect of Hall Currents on the Magnetohydrodynamic Boundary Layer Flow Past a Semi-Infinite Flat Plate,” Journal of the Physical Society of Japan, 27, pp.1051–1059 (1969).CrossRefGoogle Scholar
7.Pop, I., “Effects of Hall Currents on Hydromagnetic Flow Near a Porous Plate,” Acta Mechanica, 20, pp. 316–318 (1974).CrossRefGoogle Scholar
8.Gupta, A.S., “Hydromagnetic Flow Past a Porous Flat Plate with Hall Effects,” Acta Mechanica, 22, pp. 281–267 (1975).CrossRefGoogle Scholar
9.Deka, R.K., Gupta, A.S., Takhar, H.S. and Soundalgekar, V.M., “Flow Past an Accelerated Horizontal Plate in a Rotating System,” Acta Mechanica, 165, pp. 13–19 (1999).CrossRefGoogle Scholar
10.Takhar, H.S., Chamkha, A.J. and Nath, G., “MHD Flow over a Moving Plate in a Rotating Fluid with Magnetic Field, Hall Currents and Free-Stream Velocity,” Internaltional Journal of Enggineering Science, 40, pp. 1511–1527 (2002).CrossRefGoogle Scholar
11.Gupta, A.S., Misra, J.C., Reza, M. and Soundalgekar, V.M., “Flow in the Ekman Layer on an Oscillating Porous Plate,” Acta Mechanica, 165, pp. 1–16 (2003).CrossRefGoogle Scholar
12.Guria, M. and Jana, R.N., “Hydromagnetic Flow in the Ekman Layer on an Oscillating Porous Plate,” Magnetohydrodynamics, 43, pp. 3–11 (2007).Google Scholar
13.Maji, S.L., Kanch, A.K., Guria, M. and Jana, R.N., “Hall Effects on Hydromagnetic Flow on an Oscillating Porous Plate,” Applied Mathematics and Mechanics, 30, pp. 503–512 (2009).CrossRefGoogle Scholar
14.Das, S., Guria, M. and Jana, R.N., “Unsteady Hy-drodynamic Flow Induced by a Porous Plate in a Rotating System,” Internaltional Journal of Fluid Mechanics Research, 36, pp. 289–299 (2009).Google Scholar
15.Jana, M., Maji, S.L., Das, S. and Jana, R.N., “Unsteady Flowof Viscous Fluid Through a Porous Medium Bounded by a Porous Plate in a Rotating System,” Journal of Porous Media, 13, pp. 645–653 (2010).CrossRefGoogle Scholar
16.Guria, M., Manna, G. and Jana, R.N., “Flow and Heat Transfer Along an Infinite Horizontal Porous Plate Through a Porous Medium in a Rotating System,” Journal of Porous Media, 13, pp. 387–393 (2010).CrossRefGoogle Scholar
17.Guria, M., Kanch, A.K., Das, S. and Jana, R.N., “Effects of Hall Current and Slip Condition on Unsteady Flow of a Viscous Fluid Due to Non-Coaxial Rotation of a Porous Disk and a Fluid at Infinity,” Meccanica, 45, pp. 23–32 (2010).CrossRefGoogle Scholar
18.Gupta, A.S., Guria, M. and Jana, R.N., “Hall Effects on the Magnetohydrodynamic Shear Flow Past an Infinite Porous Flat Plate Subjected to Uniform Suction or Blowing,” Internaltional Journal of NonLinear Mechanics, 46, pp. 1057–1064 (2011).CrossRefGoogle Scholar
19.Ghara, N., Guria, M. and Jana, R.N., “Hall Effects on Oscillating Flow Due to Eccentrically Rotating Porous Disk and a Fluid at Infinity,” Meccanica, 47, pp. 557–571 (2012).CrossRefGoogle Scholar
20.Jana, M., Das, S. and Jana, R.N. “Unsteady MHD Appllications Flow Induced by a Porous Flat Plate in a Rotating System,” Internaltional Journal of Engineering Research and Appllications, 2, pp. 2360–2367 (2012).Google Scholar
21.Das, K., “Flow and Heat Transfer Characteristics of Nanofluids in a Rotating Frame,” Alexandria Engineering Journal, http://dx.doi.org/10.1016/j.aej.2014.04.003 (2014).CrossRefGoogle Scholar
22.Mutuku-Njane, W.N. and Makinde, O.D., “On Hy-dromagnetic Boundary Layer Flow of Nanofluids over a Permeable Moving Surface with Newtonian Heating,” Latin American Applied Research, 44, pp. 57–62 (2014).CrossRefGoogle Scholar
23.Soundalgekar, V.M. and Takhar, H.S., “MHD Oscillatory Flow Past a Semi-Infinite Plate,” AIAA Journal, 15, pp. 457–458 (1977).CrossRefGoogle Scholar
24.Soundalgekar, V.M., Patil, M.R. and Takhar, H.S., “MHD Flow Past a Vertical Oscillating Plate,” Nuclear Engineering and Design, 64, pp. 43–48 (1981).CrossRefGoogle Scholar
25.Ram, P.C. and Takhar, H.S., “Unsteady MHD Flow with a Suspension of Spherical Particles Through a Channel,” Internaltional Journal of Non-Linear Mechanics, 29, pp. 775–780 (1994).CrossRefGoogle Scholar
26.Takhar, H.S. and Ram, P.C., “Free Convection in Hydromagnetic Flows of a Viscous Heat-Generating Fluid with Wall Temperature Oscillation and Hall Currents,” Astrophysics and Space Science, 183, pp. 193–198 (1991).CrossRefGoogle Scholar
27.Kinyanjui, M., Kwanza, J.K. and Uppal, S.M., “Magnetohydrodynamic Free Convection Heat and Mass Transfer of a Heat Generating Fluid Past an Impulsively Started Infinite Vertical Porous Plate with Hall Current and Radiation Absorption,” Energy Conversion and Management, 42, pp. 917–931 (2001).CrossRefGoogle Scholar
28.Aboeldahab, E.M. and Elbarbary, E.M.E., “Hall Current Effect on Magnetohydrodynamic Free-Convection Flow Past a Semiinfinite Vertical Plate with Mass Transfer,” Internaltional Journal of Engineering Science, 39, pp. 1641–1652 (2001).CrossRefGoogle Scholar
29.Abo-Eldahab, E.M. and El Aziz, M.A., “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 Modelling, 29, pp. 579–595 (2005).CrossRefGoogle Scholar
30.Chaudhary, R.C. and Jain, P., “Hall Effect on MHD Mixed Convection Flow of a Viscous Elastic Fluid Past an Infinite Vertical Porous Plate with Mass Transfer And Radiation,” European Journal of Physics, 52, pp. 110–127 (2007).Google Scholar
31.Ahmed, N. and Goswami, J.K., “Hall Effect on MHD Forced Convection From an Infinite Porous Plate with Dissipative Heat in a Rotating System,” Turkish Journal of Physics, 35, p. 293 (2011).Google Scholar
32.Aurangzaib, and Shafie, S., “Effects of Soret and Dufour on Unsteady MHD Flow by Mixed Convection over a Vertical Surface in Porous Media with Internal Heat Generation, Chemical Reaction and Hall Current,” Canadian Journal Science Enggi-neering Mathematics, 2, pp. 153–162 (2011).Google Scholar
33.Jain, N.C. and Singh, H., “Hall and Thermal Radiation Effects on an Unsteady Rotating Free Convection Slip Flow along a Porous Vertical Moving Plate,” International Journal of Applied Mechanics and Engineering, 17, pp. 53–70 (2012).Google Scholar
34.Dash, K., Alam, M. and Wahiduzzaman, M., “MHD Free Convection and Mass Transfer Flow From a Vertical Plate in the Presence of Hall and Ion-Slip Currents,” Advances Mechanics Engineering, 2012, Article ID 851957, pp. 1–20 (2012).Google Scholar
35.Makinde, O.D. and Onyejekwe, O.O., “A Numerical Study of MHD Generalized Couette Flow and Heat Transfer with Variable Viscosity and Electrical Conductivity,” Journal of Magnetism and Magnetic Materials, 323, pp. 2757–2763 (2011).CrossRefGoogle Scholar
36.Motsumi, T.G. and Makinde, O.D., “Effects of Thermal Radiation and Viscous Dissipation on Boundary Layer Flow of Nanofluids over a Permeable Moving Flat Plate,” Physical Scripta, 86, p. 045003 (2012).CrossRefGoogle Scholar
37.Chaudhary, D., Singh, H. and Jain, N.C., “Effects of Hall Current and Thermal Radiation on an Unsteady Free Convection Slip Flow along a Vertical Plate Embedded in a Porous Medium with Constant Heat and Mass Flux,” Applied Mathematics and Physics, 1, pp. 11–26 (2013).Google Scholar
38.Venkateswarlu, B. and Satya Narayana, P.V., “Chemical Reaction and Radiation Absorption Effects on the Flow and Heat Transfer of a Nanofluid in a Rotating System,” Applied Nanoscience, doi: 10.1007/s13204-014-0324-3.CrossRefGoogle Scholar
39.Makinde, O.D. and Mutuku, W.N., “Hydromag-netic Thermal Boundary Layer of Nanofluids over a Convectively Heated Flat Plate with Viscous Dissipation and Ohmic Heating,” UPB Scientific Bulletin, Series A, 76, pp.181–192 (2014).Google Scholar
40.Kakac, S. and Pramuanjaroenkij, A., “Review of Convective Heat Transfer Enhancement with Nanofluids,” International of Journal Heat Mass Transfer, 52, pp. 3187–96 (2009).CrossRefGoogle Scholar
41.Oztop, H.F. and Abu-Nada, E., “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International of Journal Heat Fluid Flow, 29, pp. 1326–1336 (2008).CrossRefGoogle Scholar
42.Cowling, T.G., Magnetohydrodynamics, Interscience Publisher, Inc, New York (1957).Google Scholar
43.Rosseland, S., Astrophysik und atom-theoretische Grundlagen, Springer-Verlag, Berlin (1931).CrossRefGoogle Scholar