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Journal of Fluids Engineering | Volume 130 | Issue 10 | Research Paper
Research Papers: Fundamental Issues and Canonical Flows

Effect of Slip on the Entropy Generation From a Single Rotating Disk

[+] Author and Article Information
Aytac Arikoglu

Faculty of Aeronautics and Astronautics, Aeronautical Engineering Department, Istanbul Technical University, Maslak, TR-34469 Istanbul, Turkey

Guven Komurgoz

Faculty of Electric and Electronics, Istanbul Technical University, Maslak, TR-34469, Istanbul, Turkey

Ibrahim Ozkol1

Faculty of Aeronautics and Astronautics, Aeronautical Engineering Department, Istanbul Technical University, Maslak, TR-34469 Istanbul, Turkeyozkol@itu.edu.tr

1

Corresponding author.

J. Fluids Eng 130(10), 101202 (Sep 02, 2008) (9 pages) doi:10.1115/1.2953301 History: Received November 13, 2007; Revised May 15, 2008; Published September 02, 2008
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In this study, it is the first time that the effect of slip on the entropy generation is investigated for the flow over a rotating single free disk. The problem is considered for steady and axially symmetrical case in a Newtonian ambient fluid. The classical approach introduced by Von Karman is followed to reduce nonlinear flow and heat field equations to ordinary differential equations. Then these equations are solved by using differential transform method. Entropy generation equation for this system is then derived and nondimensionalized. This equation, which has never been introduced for such a geometry and boundary conditions before in open literature, is interpreted for various physical cases by using nondimensional parameters of fluid and heat fields. It is observed that the effects of slip are to reduce the magnitude of entropy generation and to reduce the total energy in the system by reducing velocities and velocity gradients. Also, while entropy generation reduces, Bejan number converges to 1 with increasing slip factor.
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References

1
Owen, J. M., 1989, "Flow and Heat Transfer in Rotating-Disc Systems", Research Studies Press, Taunton.
2
Bejan, A., 1980, “Second Law Analysis in Heat Transfer,” Energy  [CrossRef], 5 , pp. 721–732.
3
Ozkol, I., Komurgoz, G., and Arikoglu, A., 2007, “Entropy Generation in the Laminar Natural Convection From a Constant Temperature Vertical Plate in an Infinite Fluid,” Proc. Inst. Mech. Eng., Part A, 221 (A5), pp. 609–616.
4
Baytas, A. C., 1997, “Optimisation in an Inclined Enclosure for Minimum Entropy Generation in Natural Convection,” J. Non-Equil. Thermodyn., 22 (2), pp. 145–155.
5
Ogulata, R. T., Doba, F., and Yilmaz, T., 1997, “Second-Law and Experimental Analysis of a Cross-flow Heat Exchanger,” Heat Transfer Eng., 20 (2), pp. 20–27.
6
Erbay, L. B., Ercan, M. S., Sulus, B., and Yalcin, M. M., 2003, “Entropy Generation During Fluid Flow Between Two Parallel Plates With Moving Bottom Plate,” Entropy, 5 (5), pp. 506–518.
7
Mahmud, S., and Fraser, R. A., 2002, “The Second Law Analysis in Fundamental Convective Heat Transfer Problems,” Int. J. Therm. Sci., 42 (2), pp. 177–186.
8
Yilbas, B. S., 2001, “Entropy Analysis of Concentric Annuli With Rotating Outer Cylinder,” Exergy Int. J., 1 (1), pp. 60–66.
9
Abu-Hijleh, B. A. K., and Heilen, W. N., 1999, “Entropy Generation Due to Laminar Natural Convection Over a Heated Rotating Cylinder,” Int. J. Heat Mass Transfer  [CrossRef], 42 (22), pp. 4225–4233.
10
Arikoglu, A., and Ozkol, I., 2005, “Analysis for Slip Flow Over a Single Free Disk With Heat Transfer,” ASME J. Fluids Eng.  [CrossRef], 127 (3), pp. 624–627.
11
Arikoglu, A., and Ozkol, I., 2006, “On the MHD and Slip Flow Over a Rotating Disk With Heat Transfer,” Int. J. Numer. Methods Heat Fluid Flow, 16 (2), pp. 172–184.
12
Arikoglu, A., and Ozkol, I., 2005, “Solution of Boundary Value Problems for Integro-differential Equations by Using Differential Transform Method,” Appl. Math. Comput., 168 (2), pp. 1145–1158.
13
Arikoglu, A., and Ozkol, I., 2006, “Solution of Difference Equations by Using Differential Transform Method,” Appl. Math. Comput., 174 (2), pp. 1216–1228.
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Gad-el-Hak, M., 1999, “The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture,” ASME J. Fluids Eng.  [CrossRef], 121 (1), pp. 5–33.
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Karniadakis, G. E., and Beskok, A., "Micro-Flows: Fundamentals and Simulation", Springer-Verlag, New York, 2002.
16
Attia, H. A., 2008, “Rotating Disk Flow and Heat Transfer Through a Porous Medium of a Non-Newtonian Fluid With Suction and Injection,” Commun. Nonlinear Sci. Numer. Simul., 13 (8), pp. 1571–1580.
17
Benton, E. R., 1966, “On the Flow Due to a Rotating Disc,” J. Fluid Mech.  [CrossRef], 24  pp. 781–800.

Figures

Grahic Jump Location
+The change of Beav with respect to γ and Re for Ψ=10−10
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The change of Beav with respect to γ and Re for Ψ=10−10
Figure 1

The change of Beav with respect to γ and Re for Ψ=10−10

Grahic Jump Location
+The change of NG,av with respect to γ and Re for Ψ=10−10
View Large  |  Save Figure  |  Download Slide (.ppt)
The change of NG,av with respect to γ and Re for Ψ=10−10
Figure 2

The change of NG,av with respect to γ and Re for Ψ=10−10

Grahic Jump Location
+The change of Beav with respect to γ and Ψ for Re=60,000
View Large  |  Save Figure  |  Download Slide (.ppt)
The change of Beav with respect to γ and Ψ for Re=60,000
Figure 3

The change of Beav with respect to γ and Ψ for Re=60,000

Grahic Jump Location
+The change of NG,av with respect to γ and Ψ for Re=60,000
View Large  |  Save Figure  |  Download Slide (.ppt)
The change of NG,av with respect to γ and Ψ for Re=60,000
Figure 4

The change of NG,av with respect to γ and Ψ for Re=60,000

Grahic Jump Location
+The change of NG at ζ=0 with respect to r¯ and Ψ for Re=60,000 and γ=0.5
View Large  |  Save Figure  |  Download Slide (.ppt)
The change of NG at ζ=0 with respect to r¯ and Ψ for Re=60,000 and γ=0.5
Figure 5

The change of NG at ζ=0 with respect to r¯ and Ψ for Re=60,000 and γ=0.5

Grahic Jump Location
+The change of NG at ζ=0 with respect to r¯ and Re for Ψ=10−10 and γ=0.5
View Large  |  Save Figure  |  Download Slide (.ppt)
The change of NG at ζ=0 with respect to r¯ and Re for Ψ=10−10 and γ=0.5
Figure 6

The change of NG at ζ=0 with respect to r¯ and Re for Ψ=10−10 and γ=0.5

Grahic Jump Location
+The change of Δ with respect to γ and Re for Ψ=5×10−10
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The change of Δ with respect to γ and Re for Ψ=5×10−10
Figure 7

The change of Δ with respect to γ and Re for Ψ=5×10−10

Grahic Jump Location
+The change of Δ with respect to γ and Ψ for Re=60,000
View Large  |  Save Figure  |  Download Slide (.ppt)
The change of Δ with respect to γ and Ψ for Re=60,000
Figure 8

The change of Δ with respect to γ and Ψ for Re=60,000

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