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Journal of Applied Mechanics | Volume 72 | Issue 4 | TECHNICAL PAPERS
TECHNICAL PAPERS

Nonclassical Thermal Effects in Stokes’ Second Problem for Micropolar Fluids

[+] Author and Article Information
F. S. Ibrahem1

 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egyptfibrahim@acc.aun.edu.eg

I. A. Hassanien

 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

A. A. Bakr

 Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt

1

To whom correspondence should be addressed.

J. Appl. Mech 72(4), 468-474 (Aug 16, 2004) (7 pages) doi:10.1115/1.1875412 History: Received January 24, 2004; Revised August 16, 2004
Article
References
Figures
Tables
Citing Articles

The MCF model is used to study the nonclassical heat conduction effects in Stokes’ second problem of a micropolar fluid. The effects of the thermal relaxation time and the structure wave on angular velocity, velocity field, and temperature are investigated. The skin friction, the displacement thickness, and the rate of the heat transfer at the plate are determined.
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Copyright © 2005 by American Society of Mechanical Engineers
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References

1
Maxwell, J. C., 1867, “On the Dynamical Theory of Gases,” Philos. Trans. R. Soc. London, 157 , pp. 49–88.
2
Ackerman, C. C., Bertman, B., Fairbank, H. A., and Guyer, R. A., 1966, “Second Solid Helium,” Phys. Rev. Lett.  [CrossRef], 16 , pp. 789–791.
3
Puri, P., and Kythe, P. K., 1998, “Stokes’ First and Second Problems for Rivlin—Ericksen Fluids With Nonclassical Heat Conduction,” ASME J. Heat Transfer, 120 , pp. 44–50.
4
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.
5
Puri, P., and Kythe, P. K., 1995, “Nonclassical Thermal Effects in Stokes’ Second Problem,” Acta Mech.  [CrossRef], 112 , pp. 1–9.
6
Puri, P., and Jordan, P. M., 2002, “Some Recent Developments in the Unsteady Flow of Dipolar Fluids,” "Developments in Theoretical and Applied Mechanics", XXI , pp. 499–508.
7
McTaggart, C. L., and Lindsay, K. A., 1985, “Nonclassical Effects in the Benard Problem,” SIAM J. Appl. Math.  [CrossRef], 45 , pp. 70–92.
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Joseph, D. D., and Preziosi, L., 1989, “Heat Waves,” Rev. Mod. Phys.  [CrossRef], 61 , pp. 41–73.
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Joseph, D. D., and Preziosi, L., 1990, “Addendum to the Paper Heat Waves,” Rev. Mod. Phys.  [CrossRef]62 , pp 375–391.
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Puri, P., 1973, “Plane waves in Generalized Thermoelasticity,” Int. J. Eng. Sci.  [CrossRef], 11 , pp. 735–744.
11
Puri, P., and Jordan, P. M., 1999, “Stokes First Problem for a Dipolar With Nonclassical Heat Conduction,” J. Eng. Math.  [CrossRef], 36 , pp. 219–240.
12
Eringen, A. C. J., 1966, “Theory of Micropolar Fluids,“ J. Math. Mech., 16 , pp. 1–18.
13
Peddieson, J., and McNitt, R. P., 1970, “Boundary Layer Theory for Micropolar Fluid,” Recent Adv. Engng. Sci., 5 , pp 405–426.
14
Willson, A., 1970, “Boundary Layers in Micropolar Fluid,” Proc. Cambridge Philos. Soc., 67 , pp. 469–481.
15
Soundalgekar, V. M., and, Takhar, H. S., 1977, “MHD Forced and Free Convective Flow Past a Semi-Infinite Plate,” AIAA J., 15 , pp 457–485.
16
Lukaszewicz, G., 1999, "Micropolar Fluids-Theory and Applications", Birkhauser, Boston.
17
Kim, Y. J., and Fedorov, A. G., 2003, “Transient Mixed Radiative Convection Flow of a Micropolar Fluid Past a Moving, Semi-Infinite Vertical Porous Plate,” Int. J. Heat Mass Transfer  [CrossRef], 46 , pp. 1751–1758.
18
Kim, Y. J., 2001, “Unsteady MHD Micropolar Flow and Heat Transfer Over a Vertical Porous Moving Plate With Variable Suction,” "Proceedings 2nd International Conference on Computational Heat and Mass Transfer", COPPA/UFRJ- Federal University of Rio de Janerio, Brazil, October, 22–26.
19
Puri, P., and Jordan, P. M., 1999, “Wave Structure in Stokes’ Second Problem for a Dipolar Fluid With Nonclasical Heat Conduction,” Acta Mech.  [CrossRef], 133 , pp. 145–160.
20
Müller, I., and Ruggeri, T., 1993, “Extended Thermodynamics,” "Springer Tracts in Natural Philosophy", Vol. 37 , C.Truesdell, ed., Springer-Verlag, New York, p. 230.
21
Ahmadi, G., 1976, “Self-Similar Solution of Incompressible Micropolar Boundary Layer Flow Over a Semi-Infinite Plate,” Int. J. Eng. Sci.  [CrossRef], 14 , pp. 639–646.

Figures

Grahic Jump Location
+Behavior of ∣N∣ versus z for p=1, ω=10, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ∣N∣ versus z for p=1, ω=10, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 10

Behavior of ∣N∣ versus z for p=1, ω=10, t=0.1, λ=0.005, β=0.2, and G=±5

Grahic Jump Location
+Behavior of Reu versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5.0 and β=0, 5, 13.5 and 50
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of Reu versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5.0 and β=0, 5, 13.5 and 50
Figure 1

Behavior of Reu versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5.0 and β=0, 5, 13.5 and 50

Grahic Jump Location
+Behavior of ∣u∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5.0 and β=0.5, 5, and 50
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ∣u∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5.0 and β=0.5, 5, and 50
Figure 2

Behavior of ∣u∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5.0 and β=0.5, 5, and 50

Grahic Jump Location
+Behavior of Reu versus z for p=1.0, ω=10.0, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of Reu versus z for p=1.0, ω=10.0, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 3

Behavior of Reu versus z for p=1.0, ω=10.0, t=0.1, λ=0.005, β=0.2, and G=±5

Grahic Jump Location
+Behavior of ∣u∣ versus z for p=1, ω=10.0, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ∣u∣ versus z for p=1, ω=10.0, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 4

Behavior of ∣u∣ versus z for p=1, ω=10.0, t=0.1, λ=0.005, β=0.2, and G=±5

Grahic Jump Location
+Behavior of Reu versus zforp=1.0, ω=1000.0, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of Reu versus zforp=1.0, ω=1000.0, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 5

Behavior of Reu versus zforp=1.0, ω=1000.0, t=0.1, λ=0.005, β=0.2, and G=±5

Grahic Jump Location
+Behavior of ∣u∣ versus z for p=1, ω=1000, t=0.10, λ=0.005, β=0.2 and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ∣u∣ versus z for p=1, ω=1000, t=0.10, λ=0.005, β=0.2 and G=±5
Figure 6

Behavior of ∣u∣ versus z for p=1, ω=1000, t=0.10, λ=0.005, β=0.2 and G=±5

Grahic Jump Location
+Behavior of ReN versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5 and β=2.5, 5, 13.5, and 50
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ReN versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5 and β=2.5, 5, 13.5, and 50
Figure 7

Behavior of ReN versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5 and β=2.5, 5, 13.5, and 50

Grahic Jump Location
+Behavior of ∣N∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5 and β=2.5, 5, 13.5, and 50
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ∣N∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5 and β=2.5, 5, 13.5, and 50
Figure 8

Behavior of ∣N∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, G=5 and β=2.5, 5, 13.5, and 50

Grahic Jump Location
+Behavior of ReN versus z for p=1, ω=10, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ReN versus z for p=1, ω=10, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 9

Behavior of ReN versus z for p=1, ω=10, t=0.1, λ=0.005, β=0.2, and G=±5

Grahic Jump Location
+Behavior of ReN versus z for p=1, ω=1000, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ReN versus z for p=1, ω=1000, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 11

Behavior of ReN versus z for p=1, ω=1000, t=0.1, λ=0.005, β=0.2, and G=±5

Grahic Jump Location
+Behavior of ∣N∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, β=0.2, and G=±5
View Large  |  Save Figure  |  Download Slide (.ppt)
Behavior of ∣N∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, β=0.2, and G=±5
Figure 12

Behavior of ∣N∣ versus z for p=1, ω=1000, t=0.1, λ=0.005, β=0.2, and G=±5

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