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Journal of Applied Mechanics | Volume 76 | Issue 1 | Technical Brief
Technical Briefs

Unsteady Free-Convection Flow on a Vertical Oscillating Porous Plate With Constant Heating

[+] Author and Article Information
C. J. Toki

Department of Ecology and Environment, Technological Educational Institute of Ionian Islands, Square of Kalvou, 29100, Zakynthos, Greecechristina_toki@yahoo.com

1

Corresponding author. Permanent address: Pediou Volis 32, Stavraki, 453 22, Ioannina, Greece.

J. Appl. Mech 76(1), 014503 (Oct 31, 2008) (4 pages) doi:10.1115/1.2998758 History: Received November 23, 2007; Revised July 16, 2008; Published October 31, 2008
Article
References
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Citing Articles

In this paper, we consider the unsteady free-convection flows of a viscous and incompressible fluid near an oscillating porous infinite vertical plate (or wall) during the heating of the plate. The governing equations are solved in closed form by the Laplace transform technique, when the Prandtl number (Pr) of the fluid is arbitrary and the suction (or injection) is constant. This solution is applied for a special case of the constant heating effects from the harmonically oscillating plate. The resulting velocity and temperature are shown graphically and are also discussed for the case of air (Pr=0.71) or water (Pr=7.0) flows.
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References

1
Gebhart, B., Jaluria, Y., Mahajan, R. L., and Sammakia, B., 1988, "Buoyancy-Induced Flows and Transport", Hemisphere, New York, Chap. 10.
2
Lighthill, M. J., 1954, “The Response of Laminar Skin Friction and Head Transfer to Fluctuations in the Stream Velocity,” Proc. R. Soc. London, Ser. A, 224 , pp. 1–23.
3
Debnath, L., 1975, “Exact Solutions of the Unsteady Hydrodynamic and Hydromagnetic Boundary Layer Equations in a Rotating Fluid System,” Z. Angew. Math. Mech., 55 , pp. 431–438.
4
Soundalgekar, V. M., 1973, “Free Convection Effects on the Oscillatory Flow Past an Infinite, Vertical, Porous Plate With Constant Suction (I),” Proc. R. Soc. London, Ser. A, 333 , pp. 25–36.
5
Soundalgekar, V. M., 1979, “Free Convection Effects on the Flow Past an Infinite Vertical Oscillating Plate,” Astrophys. Space Sci., 64 , pp. 165–171.
6
Nanousis, N. D., and Tokis, J. N., 1984, “MHD Free-Convection Flow Near a Vertical Oscillator Plate,” Astrophys. Space Sci., 98 , pp. 397–403.
7
Mansour, M. A., 1990, “Radiative and Free Convection Effects on the Oscillatory Flow Past a Vertical Plate,” Astrophys. Space Sci., 166 , pp. 269–275.
8
Soundalgekar, V. M., Pohanerkar, S. G., Lahurikar, R. M., and Birajdar, N. S., 1995, “Mass Transfer Effects on Flow Past a Vertical Oscillating Plate With Variable Temperature,” Heat Mass Transfer, 30 (5), pp. 309–312.
9
Soundalgekar, V. M., Das, U. N., and Deka, R. K., 1997, “Free Convection Effects on MHD Flow Past an Infinite Vertical Oscillating Plate With Constant Heat Flux,” Indian J. Math., 39 (3), pp. 195–202.
10
Turbatu, S., Bühler, K., and Zierep, J., 1998, “New Solutions of the II Stokes Problem for an Oscillating Flat Plate,” Acta Mech., 129 , pp. 25–30.
11
Revankar, S. T., 2000, “Free Convection Effect on Flow Past an Impulsively Started or Oscillating Infinite Vertical Plate,” Mech. Res. Commun., 27 , pp. 241–246.
12
Gupta, A. S., Misra, J. C., Reza, M., and Soundalgekar, V. M., 2003, “Flow in the Ekman Layer on an Oscillating Porous Plate,” Acta Mech., 165 , pp. 1–16.
13
Hossain, M. A., Pop, I., and Ress, D. A. S., 2000, “The Effect of Time-Periodic Surface Temperature Oscillations on Free Convection From a Vertical Surface in a Porous Medium,” Transp. Porous Media, 39 , pp. 119–130.
14
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.
15
Chaudhary, R. C., and Jain, A., 2007, “Combined Head and Mass Transfer Effects on MHD Free Convection Flow Past an Oscillating Plate Embedded in Porous Medium,” Rom. J. Physiol., 52 , pp. 505–524.
16
Kythe, P. K., and Puri, P., 1988, “Unsteady MHD Free-Convection Flows on a Porous Plate With Time-Dependent Heating in a Rotating Medium,” Astrophys. Space Sci.  [CrossRef], 143 , pp. 51–62.
17
Toki, C. J., and Tokis, J. N., 2007, “Exact Solutions for the Unsteady Free Convection Flows on a Porous Plate With Time-Dependent Heating,” Z. Angew. Math. Mech.  [CrossRef], 87 (1), pp. 4–13.
18
Toki, C. J., 2008, “Free Convection and Mass Transfer Flow Near a Moving Vertical Porous Plate: An Analytical Solution,” ASME J. Appl. Mech.  [CrossRef], 75 (1), p. 011014.

Figures

Grahic Jump Location
+Velocity profiles of the flow near the single cooling (G>0) porous vertical oscillating plate for varying Prandtl numbers (Pr)
View Large  |  Save Figure  |  Download Slide (.ppt)
Velocity profiles of the flow near the single cooling (G>0) porous vertical oscillating plate for varying Prandtl numbers (Pr)
Figure 3

Velocity profiles of the flow near the single cooling (G>0) porous vertical oscillating plate for varying Prandtl numbers (Pr)

Grahic Jump Location
+Temperature profiles for the case of the air flows (Pr=0.71) and water flows (Pr=7) near the single heating porous vertical plate, which oscillates harmonically
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature profiles for the case of the air flows (Pr=0.71) and water flows (Pr=7) near the single heating porous vertical plate, which oscillates harmonically
Figure 2

Temperature profiles for the case of the air flows (Pr=0.71) and water flows (Pr=7) near the single heating porous vertical plate, which oscillates harmonically

Grahic Jump Location
+Velocity profiles for the case of the air flows near the single heating (G<0) or cooling (G>0) porous vertical plate, which oscillates harmonically
View Large  |  Save Figure  |  Download Slide (.ppt)
Velocity profiles for the case of the air flows near the single heating (G<0) or cooling (G>0) porous vertical plate, which oscillates harmonically
Figure 1

Velocity profiles for the case of the air flows near the single heating (G<0) or cooling (G>0) porous vertical plate, which oscillates harmonically

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