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Research Papers

Unsteady Hydromagnetic Natural Convection Flow of a Dusty Fluid Past an Impulsively Moving Vertical Plate With Ramped Temperature in the Presence of Thermal Radiation

[+] Author and Article Information
R. Nandkeolyar

School of Mathematics, Statistics and
Computer Science,
University of Kwazulu-Natal,
Private Bag X01, Scottsville 3209,
Pietermaritzburg, South Africa
e-mail: rajnandkeolyar@gmail.com

G. S. Seth

Department of Applied Mathematics,
Indian School of Mines,
Dhanbad 86004, India
e-mail: gsseth_ism@yahoo.com

O. D. Makinde

Institute for Advance Researchin Mathematical Modelling and Computations,
Cape Peninsula University of Technology,
P.O. Box 1906, Bellville 7535, South Africa
e-mail: makinded@cput.ac.za

P. Sibanda

School of Mathematics, Statistics and
Computer Science,
University of Kwazulu-Natal,
Private Bag X01, Scottsville 3209,
Pietermaritzburg, South Africa
e-mail: sibandap@ukzn.ac.za

Md. S. Ansari

School of Petroleum Technology,
Pandit Deendayal Petroleum University,
Gandhinagar 382007, India
e-mail: shariffuddin@gmail.com

1Corresponding author.

Manuscript received April 21, 2012; final manuscript received March 1, 2013; accepted manuscript posted March 16, 2013; published online August 19, 2013. Assoc. Editor: Nesreen Ghaddar.

J. Appl. Mech 80(6), 061003 (Aug 19, 2013) (9 pages) Paper No: JAM-12-1162; doi: 10.1115/1.4023959 History: Received April 21, 2012; Revised March 01, 2013; Accepted March 16, 2013

Unsteady hydromagnetic natural convection boundary layer flow of a viscous, incompressible, and electrically conducting dusty fluid past an impulsively moving vertical plate with ramped temperature in the presence of thermal radiation and transverse magnetic field is studied. Exact solutions of the governing equations for fluid and particle velocities and fluid and particle temperatures are obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of an isothermal plate, exact solutions of the governing equations are also obtained for an isothermal plate. The expressions for the skin friction and Nusselt number are also derived for both ramped temperature and isothermal plates. Numerical values of fluid and particle velocities and fluid and particle temperatures are displayed graphically for various values of pertinent flow parameters for both ramped temperature and isothermal plates, whereas numerical values of skin friction and Nusselt number for both ramped temperature and isothermal plates are presented in tabular form for pertinent flow parameters.

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References

Gupta, A. S., 1960, “Steady and Transient Free Convection of an Electrically Conducting Fluid From a Vertical Plate in the Presence of a Magnetic Field,” Appl. Sci. Res., A9, pp. 319–333. [CrossRef]
Gupta, A. S., 1962, “Laminar Free Convection Flow of an Electrically Conducting Fluid From a Vertical Plate With Uniform Surface Heat Flux and Variable Wall Temperature in the Presence of Magnetic Field,” ZAMP, 13, pp. 324–333. [CrossRef]
Cramer, K. R., 1963, “Several Magnetohydrodynamic Free Convection Solutions,” J. Heat Transfer, 85, pp. 35–40. [CrossRef]
Pop, I., 1969, “On the Unsteady Hydromagnetic Free Convection Flow Past a Vertical Infinite Flat Plate,” Indian J. Phys., 43, pp. 196–200.
Kuiken, H. K., 1970, “Magnetohydrodynamic Free Convection in a Strong Cross Field,” J. Fluid Mech., 40, pp. 1–15. [CrossRef]
Graham, W., 1976, “Magnetohydrodynamic Free Convection About a Semi-Infinite Vertical Plate in a Strong Cross Field,” ZAMP, 27, pp. 621–631. [CrossRef]
Hossain, M. A., 1986, “Effect of Hall Current on Unsteady Hydromagnetic Free Convection Flow Near an Infinite Vertical Porous Plate,” J. Phys. Soc. Jpn., 55, pp. 2183–2190. [CrossRef]
Aldoss, T. K., Al-Nimr, M. A., Jarrah, M. A., and Al-Shaer, B. J., 1995, “Magnetohydrodynamic Mixed Convection From a Vertical Plate Embedded in a Porous Medium,” Numer. Heat Transfer, 28, pp. 635–645. [CrossRef]
Helmy, K. A., 1998, “MHD Unsteady Free Convection Flow Past a Vertical Porous Plate,” ZAMM, 78, pp. 255–270. [CrossRef]
Kim, Y. J., 2000, “Unsteady MHD Convective Heat Transfer Past a Semi-Infinite Vertical Porous Moving Plate With Variable Suction,” Int. J. Eng. Sci., 38, pp. 833–845. [CrossRef]
Takhar, H. S., Roy, S., and Nath, G., 2003, “Unsteady Free Convection Flow of an Infinite Vertical Porous Plate Due to the Combined Effects of Thermal and Mass Diffusion, Magnetic Field and Hall Currents,” Heat Mass Transfer, 39, pp. 825–834. [CrossRef]
Ahmed, N., Sarmah, H. K., and Kalita, D., 2011, “Thermal Diffusion Effect on a Three-Dimensional MHD Free Convection With Mass Transfer Flow From a Porous Vertical Plate,” Latin Am. Appl. Res., 41, pp. 165–176.
Hossain, M. A., and Takhar, H. S., 1996, “Radiation Effect on Mixed Convection Along a Vertical Plate With Uniform Surface Temperature,” Heat Mass Transfer, 31, pp. 243–248. [CrossRef]
Bakier, A. Y., and Gorla, R. S. R., 1996, “Thermal Radiation Effect on Mixed Convection From Horizontal Surfaces in Saturated Porous Media,” Transp. Porous Media, 23, pp. 357–363. [CrossRef]
Takhar, H. S., Gorla, R. S. R., and Soundalgekar, V. M., 1996, “Radiation Effects on MHD Free Convection Flow of a Gas Past a Semi-Infinite Vertical Plate,” Int. J. Numer. Methods Heat Fluid Flow, 6, pp. 77–83. [CrossRef]
Chamkha, A. J., 2000, “Thermal Radiation and Buoyancy Effects on Hydromagnetic Flow Over an Accelerating Permeable Surface With Heat Source or Sink,” Int. J. Eng. Sci., 38, pp. 1699–1712. [CrossRef]
Azzam, G. E. A., 2002, “Radiation Effects on the MHD Mixed Free-Forced Convective Flow Past a Semi-Infinite Moving Vertical Plate for High Temperature Differences,” Phys. Scr., 66, pp. 71–76. [CrossRef]
Israel-Cookey, C., Ogulu, A., and Omubo-Pepple, V. B., 2003, “Influence of Viscous Dissipation and Radiation on Unsteady MHD Free-Convection Flow Past an Infinite Heated Vertical Plate in a Porous Medium With Time-Dependent Suction,” Int. J. Heat Mass Transfer, 46, pp. 2305–2311. [CrossRef]
Mostafa, A. A. M., 2009, “Thermal Radiation Effect on Unsteady MHD Free Convection Flow Past a Vertical Plate With Temperature Dependent Viscosity,” Can. J. Chem. Eng., 87, pp. 47–52. [CrossRef]
Bestman, A. R., and Adjepong, S. K., 1988, “Unsteady Hydromagnetic Free-Convection Flow With Radiative Heat Transfer in a Rotating Fluid,” Astrophys. Space Sci., 143, pp. 73–80. [CrossRef]
Mbeledogu, I. U., and Ogulu, A., 2007, “Heat and Mass Transfer of an Unsteady MHD Natural Convection Flow of a Rotating Fluid Past a Vertical Porous Flat Plate in the Presence of Radiative Heat Transfer,” Heat Mass Transfer, 50, pp. 1902–1908. [CrossRef]
Saffman, P. G., 1962, “On the Stability of Laminar Flow of a Dusty Gas,” J. Fluid Mech., 13, pp. 120–134. [CrossRef]
Liu, J. T. C., 1966, “Flow Induced by an Oscillating Infinite Flat Plate in a Dusty Gas,” Phys. Fluids, 9, pp. 1716–1720. [CrossRef]
Michael, D. H., and Miller, D. A., 1966, “Plane Parallel Flow of Dusty Gas,” Mathematika, 13, pp. 97–109. [CrossRef]
Ghosh, S., and Ghosh, A. K., 2005, “On Hydromagnetic Flow of a Two-Phase Fluid Near a Pulsating Plate,” Indian J. Pure Appl. Math., 36, p. 529.
Ghosh, A. K., and Debnath, L., 1986, “Hydromagnetic Stokes Flow in a Rotating Fluid With Suspended Small Particles,” Appl. Sci. Res, 43, pp. 165–192. [CrossRef]
Ghosh, A. K., and Debnath, L., 1995, “On Hydrodynamic Rotating Flow of Two-Phase Fluid,” ZAMM, 75, pp. 156–159. [CrossRef]
Ghosh, S., and Ghosh, A. K., 2008, “On Hydromagnetic Rotating Flow of a Dusty Fluid Near a Pulsating Plate,” Comput. Appl. Math., 27(1), pp. 1–30.
Chamkha, A. J., 2000, “Unsteady Laminar Hydromagnetic Fluid-Particle Flow and Heat Transfer in Channels and Circular Pipes,” Int. J. Heat Fluid Flow, 21, pp. 740–746. [CrossRef]
Attia, H. A., 2005, “Hall Effect on Couette Flow With Heat Transfer of a Dusty Conducting Fluid in the Presence of Uniform Suction and Injection,” African J. Math. Phys., 2, pp. 97–110.
Makinde, O. D., and Chinyoka, T., 2010, “MHD Transient Flows and Heat Transfer of Dusty Fluid in a Channel With Variable Physical Properties and Navier Slip Condition,” Comp. Math. Appl., 60, pp. 660–669. [CrossRef]
Hayday, A. A., Bowlus, D. A., and McGraw, R. A., 1967, “Free Convection From a Vertical Plate With Step Discontinuities in Surface Temperature,” ASME J. Heat Transfer, 89, pp. 244–250. [CrossRef]
Kelleher, M., 1971, “Free Convection From a Vertical Plate With Discontinuous Wall Temperature,” ASME J. Heat Transfer, 93, pp. 349–356. [CrossRef]
Kao, T. T., 1975, “Laminar Free Convective Heat Transfer Response Along a Vertical Flat Plate With Step Jump in Surface Temperature,” Lett. Heat Mass Transfer, 2, pp. 419–428. [CrossRef]
Lee, S., and Yovanovich, M. M., 1991, “Laminar Natural Convection From a Vertical Plate With a Step Change in Wall Temperature,” ASME J. Heat Transfer, 113, pp. 501–504. [CrossRef]
Chandran, P., Sacheti, N. C., and Singh, A. K., 2005, “Natural Convection Near a Vertical Plate With Ramped Wall Temperature,” Heat Mass Transfer, 41, pp. 459–464. [CrossRef]
Seth, G. S., Ansari, M. S., and Nandkeolyar, R., 2011, “MHD Natural Convection Flow With Radiative Heat Transfer Past an Impulsively Moving Plate With Ramped Wall Temperature,” Heat Mass Transfer, 47, pp. 551–561. [CrossRef]
Cramer, K. R., and Pai, S. I., 1973, Magnetofluiddynamics for Engineers and Applied Physicists, McGraw-Hill, New York.
Meyer, R. C., 1958, “On Reducing Aerodynamic Heat-Transfer Rates by Magnetohydrodynamic Techniques,” J. Aero. Sci., 25, pp. 561–572. [CrossRef]
Brewster, M. Q., 1992, Thermal Radiative Transfer and Properties, John Wiley and Sons, New York.

Figures

Grahic Jump Location
Fig. 1

Physical model of the problem

Grahic Jump Location
Fig. 2

Fluid velocity when N = 1, R = 0.2, and t = 0.7

Grahic Jump Location
Fig. 3

Fluid velocity when M = 6, R = 0.2, and t = 0.7

Grahic Jump Location
Fig. 4

Fluid velocity when M = 6, N = 1, and t = 0.7

Grahic Jump Location
Fig. 5

Particle velocity when N = 1, R = 0.2, and t = 0.7

Grahic Jump Location
Fig. 6

Particle velocity when M = 6, R = 0.2, and t = 0.7

Grahic Jump Location
Fig. 7

Particle velocity when M = 6, N = 1, and t = 0.7

Grahic Jump Location
Fig. 8

Fluid temperature when R = 0.2 and t = 0.7

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Fig. 9

Fluid temperature when N = 1 and t = 0.7

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Fig. 10

Particle temperature when R = 0.2 and t = 1.5

Grahic Jump Location
Fig. 11

Particle temperature when N = 1 and t = 1.5

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Fig. 12

Fluid velocity when Gr = 2, M = 6, and R = 0.2

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Fig. 13

Fluid temperature when R = 0.2 and Pr = 0.71

Grahic Jump Location
Fig. 14

Slip between fluid and dust particles when Gr = 2, M = 6, R = 0.2, and t = 0.7

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