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Homann Flow and Heat Transfer of a Newtonian Fluid Over a Translating Plate with Viscous Dissipation and Heat Generation

Published online by Cambridge University Press:  13 May 2016

M. Ş. Demir  and
S. Barış
M. Ş. Demir*
Affiliation:
Faculty of EngineeringDepartment of Mechanical EngineeringIstanbul UniversityIstanbul, Turkey
S. Barış
Affiliation:
Faculty of EngineeringDepartment of Mechanical EngineeringIstanbul UniversityIstanbul, Turkey
*
*Corresponding author (demirms@istanbul.edu.tr)
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Abstract

A theoretical study is presented for the problem of orthogonal axisymmetric stagnation flow towards an infinite horizontal plate with a constant velocity in the presence of viscous dissipation and heat generation. The governing equations are reduced to a system of nonlinear ordinary differential equations by means of appropriate transformations for the velocity components and temperature. The similarity equations are solved numerically using the Matlab routine bvp4c. The results are compared with those known from the literature and an excellent agreement is found. The effects of involved parameters on the x-wise velocity component, temperature, skin friction, heat transfer and entropy generation rate are presented in graphical and tabular forms. It was found that the Eckert number Ec, the Prandtl number Pr and the heat generation parameter α play a significant role on the temperature, heat transfer and entropy generation rate.

Keywords

Homann flowSimilarity transformationViscous dissipationEntropy generation
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 6 , December 2016 , pp. 759 - 766
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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References

1. Blasius, H., “Grenzschichten in Flüssigkeiten Mit Kleiner Reibung,” Zeitschrift für angewandte Mathematik und Physik, 56, pp. 1–37 (1908).Google Scholar
2. Hiemenz, K., “Die Grenzschicht an Einem in Den Gleichformigen Flussigkeitsstrom Eingetauchten Geraden Kreiszylinder,” Dinglers Polytechnisches Journal, 326, pp. 321–324 (1911).Google Scholar
3. Goldstein, S., Modern Development in Fluid Dynamics, Oxford University Press, London (1938).Google Scholar
4. Homann, F., “Der Einfluss Grosser Zahigkeit Bei Der Strömung Um Den Zylinder Und Um Die Kugel,” Zeitschrift für angewandte Mathematik und Mechanik, 16, pp. 153–164 (1936).Google Scholar
5. Sibulkin, M., “Heat Transfer Near the Forward Stagnation Point of a Body of Revolution,” Journal of the Aeronautical Sciences, 19, pp. 570–571 (1952).Google Scholar
6. Howarth, L., “The Boundary Layer in Three-Dimensional Flow, Part II: The Flow Near a Stagnation Point,” Philosophical Magazine, 42, pp. 1433–1440 (1951).Google Scholar
7. Davey, A., “Boundary Layer Flow at a Saddle Point of Attachment,” Journal of Fluid Mechanics, 10, pp. 593–610 (1961).Google Scholar
8. Libby, P. A., “Heat and Mass Transfer at a General Three-Dimensional Stagnation Point,” American Institute of Aeronautics and Astronautics, 5, pp. 507–517 (1967).Google Scholar
9. Wang, C. Y., “Similarity Stagnation Point Solutions of the Navier-Stokes Equations-Review and Extension,” European Journal of Mechanics-B/Fluids, 27, pp. 678–683 (2008).Google Scholar
10. Tamada, K., “Two-Dimensional Stagnation Point Flow Impinging Obliquely on a Plane Wall,” Journal of the Physical Society of Japan, 46, pp. 310–311 (1979).Google Scholar
11. Dorrepaal, J. M., “An Exact Solution of the Navier-Stokes Equation Which Describes Non-Orthogonal Stagnation-Point Flow in Two Dimensions,” Journal of Fluid Mechanics, 163, pp. 141–147 (1986).Google Scholar
12. Yang, K. T., “Unsteady Laminar Boundary Layers in an Incompressible Stagnation Flow,” Journal of Applied Mechanics, 25, pp. 421–427 (1958).CrossRefGoogle Scholar
13. Williams, J. C., “Nonsteady Stagnation Point Flow,” American Institute of Aeronautics and Astronautics, 6, pp. 2417–2419 (1968).Google Scholar
14. Cheng, E. H. W., Ozisik, M. N. and Williams, J. C., “Nonsteady Three-Dimensional Stagnation Point Flow,” Journal of Applied Mechanics, 38, pp. 282–287 (1971).Google Scholar
15. Wang, C. Y., “The Unsteady Oblique Stagnation Point Flow,” Physics of Fluids, 28, pp. 2046–2049 (1985).CrossRefGoogle Scholar
16. Rott, N., “Unsteady Viscous Flow in the Vicinity of a Stagnation Point,” Quarterly of Applied Mathematics, 13, pp. 444–451 (1956).Google Scholar
17. Glauert, M. B., “The Laminar Boundary Layer on Oscillating Plates and Cylinders,” Journal of Fluid Mechanics, 1, pp. 97–110 (1956).Google Scholar
18. Wang, C. Y., “Axisymmetric Stagnation Flow Towards a Moving Plate,” AIChE Journal, 19, pp. 1080–1081 (1973).Google Scholar
19. Libby, P. A., “Wall Shear at a Three-Dimensional Stagnation Point with a Moving Wall,” American Institute of Aeronautics and Astronautics, 12, pp. 408–409 (1974).Google Scholar
20. Wang, C. Y., “Shear Flow Over a Rotating Plate,” Applied Scientific Research, 46, pp. 89–96 (1989).Google Scholar
21. Weidman, P. D. and Mahalingam, S., “Axisymmetric Stagnation Point Flow Impinging on a Transversely Oscillating Plate with Suction,” Journal of Engineering Mathematics, 31, pp. 305–318 (1997).Google Scholar
22. Labropulu, F. and Chinichian, M., “Unsteady Oscillatory Stagnation Point Flow of a Viscoelastic Fluid,” International Journal of Engineering Science, 42, pp. 625–633 (2004).CrossRefGoogle Scholar
23. Wang, C. Y., “Stagnation Slip Flow and Heat Transfer on a Moving Plate,” Chemical Engineering Science, 61, pp. 7668–7672 (2006).Google Scholar
24. Javed, T., Abbas, Z., Hayat, T. and Asghar, S., “Homotopy Analysis for Stagnation Slip Flow and Heat Transfer on a Moving Plate,” Journal of Heat Transfer, 131, pp. 094506-1–094506-5 (2009).Google Scholar
25. Weidman, P. D. and Sprague, M. A., “Flows Induced by a Plate Moving Normal to Stagnation-Point Flow,” Acta Mechanica, 219, pp. 219–229 (2011).Google Scholar
26. Ja’fari, M. and Rahimi, A. B., “Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Plate with Time-Dependent Axial Velocity and Uniform Transpiration,” Scientia Iranica, 20, pp. 152–161 (2013).Google Scholar
27. Rashidi, M. M., Shamekhi, L. and Kumar, S., “Parametric Analysis of Entropy Generation in Offcentered Stagnation Flow Towards a Rotating Disc,” Nonlinear Engineering, 3, pp. 27–41 (2014).Google Scholar
28. Bejan, A., Entropy Generation Minimization, CRC Press, New York (1996).Google Scholar
29. Shampine, L. F., Gladwell, I. and Thompson, S., Solving ODEs with Matlab, Cambridge University Press, Cambridge (2003).Google Scholar
30. Demir, M. Ş. and Barış, S., “MHD Stagnation Flow of a Newtonian Fluid Towards a Uniformly Heated and Moving Vertical Plate,” Journal of Applied Fluid Mechanics (in press).Google Scholar
31. Toki, C. J., “An Analytical Solution for Boundary Layer Flows Over a Moving-Flat Porous Plate with Viscous Dissipation,” Journal of Fluids Engineering, 136, pp. 024501-1–024501-5 (2014).Google Scholar
32. Crepeau, J. C. and Clarksean, R., “Similarity Solutions of Natural Convection with Internal Heat Generation,” Journal of Heat Transfer, 119, pp. 183–185 (1997).Google Scholar