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Mixed Convection Flow of a Micropolar Fluid Past a Vertical Stretching Surface in a Thermally Stratified Porous Medium with Thermal Radiation

Published online by Cambridge University Press:  01 May 2013

Mostafa A.A. Mahmoud  and
Shimaa E. Waheed
Mostafa A.A. Mahmoud
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Egypt
Shimaa E. Waheed*
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Benha Taif Univesity, Taif, KSA
*
*Corresponding author ([email protected])
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Abstract

This paper is concerned with the effect of thermally stratification on the steady, two-dimensional mixed convection flow of a micropolar fluid past a vertical stretching permeable surface saturated in porous medium taking into account the effect of thermal radiation. The governing system of partial differential equations describing the problem are converted into a system of non-linear ordinary differential equations using similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Chebyshev spectral method. The numerical results for the velocity, the micro-rotation and the temperature are displayed graphically showing the effects of various parameters like the buoyancy parameter, the radiation parameter, the stratification parameter, the permeability parameter and the suction/injection parameter. Moreover, the numerical values of the local skinfriction coefficient, the wall couple stress and the local Nusselt number for these parameters are also tabulated and discussed.

Keywords

Micropolar fluidMixed convectionStretching plateThermally stratified porous mediumThermal radiation
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 3 , September 2013 , pp. 461 - 470
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

REFERENCES

1.Nield, D. A. and Bejan, A., Convection in Porous Media, 3rd Edition, Springer, New York (2006).Google Scholar
2.Ingham, D. B. and Pop, I. Des., Transport Phenomena in Porous Media, vol. II 2002, Pergamon, Oxford (1998).Google Scholar
3.Ingham, D. B. and Pop, I. Des., Transport Phenomena in Porous Media, 1, III, Elsevier, Oxford (2005).Google Scholar
4.Vafai, K. Ed., Handbook of Porous Media, Marcel Dekker, New York (2000).Google Scholar
5.Vafai, K. Ed., Handbook of Porous Media, 2nd Edition, Taylor & Francis, New York (2005).CrossRefGoogle Scholar
6.Pop, I. and Ingham, D. B., Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Pergamon Pr., Oxford (2001).Google Scholar
7.Ingham, D. B., Bejan, A., Mamut, E. and Pop, I. Eds., Emerging Technologies and Techniques in Porous Media, Kluwer Academic Publishers, Dordecht, The Netherlands (2004).CrossRefGoogle Scholar
8.Bejan, A., Dincer, I., Lorente, S., Miguel, A.F. and Reis, A.H., Porous and Complex Flow Structures in Modern Technologies, Springer-Verlag, New York (2004).Google Scholar
9.Eringen, A. C., “Theory of Micropolar Fluids,” Journal of Mathematics and Mechanics, 16, pp. 1–18 (1966).Google Scholar
10.Eringen, A. C., “Theory of Thermomicropolar Fluids,” Journal of Mathematical Applications, 38, pp. 480–495 (1972).Google Scholar
11.Armin, T., Turk, M. A. and Sylvester, N. D., “Microcontinuum Fluid Mechanics a Review,” International Journal of Engineering Science, 11, pp. 905–915 (1973).CrossRefGoogle Scholar
12.Armin, T., Turk, M. A. and Sylvester, N. D., “Application of Microcontinuum Fluid Mechanics,” International Journal of Engineering Science, 12, pp. 273–279 (1974).CrossRefGoogle Scholar
13.Lukaszewicz, G., Micropolar Fluids: Theory and Application, Birkhäuser, Basel (1999).Google Scholar
14.Eringen, A. C., Microcontinuum Field Theories, II: Fluent Media, Springer, New York (2001).Google Scholar
15.Bhargava, R., Kumar, L. and Takhar, H. S., “Mixed Convection from a Continuous Surface in a Parallel Moving Stream of a Micropolar Fluid,” Heat and Mass Transfer, 39, pp. 407–413 (2003).CrossRefGoogle Scholar
16.Rahman, M. M. and Sattar, M. A., “Transient Convective Flow of Micropolar Fluid Past a Continuously Moving Vertical Porous Plate in the Presence of Radiation,” International Journal of Applied Mechanics and Engineering, 12, pp. 497–513 (2007).Google Scholar
17.Rahman, M. M. and Sattar, M. A., “Magnetohydrodynamic Convective Flow of a Micropolar Fluid Past a Continuously Moving Vertical Porous Plate in the Presence of Heat Generation/Absorption,” Journal of Heat Transfer, ASME, 128, pp. 142–152 (2006).Google Scholar
18.Ishak, A., Nazar, R. and Pop, I., “Mixed Convection Stagnation Point Flow of a Micropolar Fluid Towards a Stretching Sheet,” Meccanica, 43, pp. 411–418 (2008).Google Scholar
19.Hayat, T., Abbas, Z. and Javed, T., “Mixed Convection Flow of a Micropolar Fluid over a Non-Linearly Stretching Sheet,” Physics Letters A, 372, pp. 637–647 (2008).CrossRefGoogle Scholar
20.Gupta, U. and Sharma, R. S., “Thermal Convection in Micropolar Fluids in Porous Medium,” International Journal of Engineering Science, 33, pp. 1887–1892 (1995).Google Scholar
21.Raptis, A., “Boundary Layer Flow of a Micorpolar Fluid Through a Porous Medium,” Journal of Porous Media, 3, pp. 95–96 (2000).Google Scholar
22.Cheesewright, R., “Natural Convection from a Plane Vertical Surface in Non-Isothermal Surroundings,” International Journal Heat and Mass Transfer, 10, pp. 1847–1859 (1967).Google Scholar
23.Chen, C. C. and Eichhorn, R., “Natural Convection from a Vertical Surface to a Thermally Stratified Fluid,” Journal of Heat Transfer, ASME, 98, pp. 446–451 (1976).Google Scholar
24.Venkatachala, B. J. and Nath, G., “Non-Similar Laminar Natural Convection in a Thermally Stratified Fluid,” International Journal Heat and Mass Transfer, 24, pp. 1848–1859 (1981).Google Scholar
25.Kulkarni, A. K., Jacob, H. R. and Hwang, J. J., “Similarity Solution for Natural Convection Flow over an Isothermal Vertical Wall Immersed in a Thermally Stratified Medium,” International Journal Heat and Mass Transfer, 30, pp. 691–698 (1987).Google Scholar
26.Angirasa, D. and Srinivasan, J., “Natural Convection Flows Due to the Combined Buoyancy of Heat and Mass Transfer in a Thermally Stratified Medium,” Journal of Heat Transfer, ASME, 111, pp. 657–663 (1989).CrossRefGoogle Scholar
27.Takhar, H. S., Chamkha, A. J. and Nath, G., “Natural Convection Flow from a Continuously Moving Vertical Surface Immersed in a Thermally Stratified Medium,” Heat and Mass Transfer, 38, pp. 17–24 (2001).Google Scholar
28.Ishak, A., Nazar, R. and Pop, I., “Mixed Convection Boundary Layer Flow Adjacent to a Vertical Surface Embedded in a Stable Stratified Medium,” International Journal Heat and Mass Transfer, 51, pp. 3693–3695 (2008).Google Scholar
29.Bejan, A., Convection Heat Transfer, John Wiley & Sons, New York (1984).Google Scholar
30.Chang, C.-L. and Lee, Z.-Y., “Free Convection on a Vertical Plate with Uniform and Constant Heat Flux in a Thermally Stratified Micropolar Fluid,” Mechanics Research Communications, 35, pp. 421–427 (2008).Google Scholar
31.Perdikis, C. and Raptis, A., “Heat Transfer of a Micropolar Fluid by the Presence of Radiation,” Heat and Mass Transfer, 31, pp. 381–382 (1996).Google Scholar
32.Kim, Y. I. and Fedorov, A. G., “Transient Mixed Radiation Convection Flow of a Micorpolar Fluid Past a Moving, Semi-Infinite Vertical Porous Plate,” International Journal Heat and Mass Transfer, 46, pp. 1751–1758 (2003).Google Scholar
33.Raptis, A., “Flow of a Micropolar Fluid Past a Continuously Moving Plate by the Presence of Radiation,” International Journal Heat and Mass Transfer, 41, pp. 2865–2866 (1998).Google Scholar
34.Mahmoud, M. A. A., Mahmoud, A. E. M., Waheed, S. E., “Hydromagnetic Boundary Layer Micropolar Fluid Flow over a Stretching Surface Embedded in a Non-Darcian Porous Medium in the Presence of Radiation,” Mathematical Problems in Engineering, pp. 1–10 (2006).Google Scholar
35.Raptis, A., “Radiation and Free Convection Flow Through a Porous Medium,” International Communications Heat and Mass Transfer, 25, pp. 289–295 (1998).Google Scholar
36.Ahmadi, G., “Self-Similar Solution of Incompressible Micropolar Boundary Layer Flow over a Semi-Infinite Plate,” International Journal of Engineering Science, 14, pp. 639–646 (1976).CrossRefGoogle Scholar
37.Kline, K. A., “A Spin Vorticity Relation for Unidirectional Plane Flows of Micropolar Fluids,” International Journal of Engineering Science, 15, pp. 131–134 (1977).Google Scholar
38.Jena, S. K. and Mathur, M. N., “Similarity Solution for Laminar Free Convection Flow of Thermo-Micropolar Fluid Past a Non-Isothermal Vertical Flat Plate,” International Journal of Engineering Science, 19, pp. 1431–1439 (1981).CrossRefGoogle Scholar
39.Peddieson, J. and Mcnitt, R. P., “Boundary Layer Theory for a Micropolar Fluid,” Recent Advances in Engineering Science, 5, PP. 405–426 (1970).Google Scholar
40.Raptis, A., “Radiation and viscoelastic flow,” International Communications Heat and Mass Transfer, 26, pp. 889–895 (1999).Google Scholar
41.El-Gendi, S. E., “Chebyshev Solution of Differential, Integral and Integro-Differential Equations,” Computer Journal, 12, pp. 282–287 (1969).Google Scholar
42.Morchoisne, Y., “Pseudo-Spectral Space-Time Calculations of Incompressible Viscous Flows,” AIAA Journal, 19, pp. 81–82 (1981).Google Scholar
43.Ishak, A., Nazar, R. and Pop, I., “Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet,” Heat and Mass Transfer, 44, pp. 921–927 (2008).CrossRefGoogle Scholar
44.Ali, F. M., Nazar, R., Arifin, N. M. and Pop, I., “Effect of Hall Current on MHD Mixed Convection Boundary Layer Flow over a Stretched Vertical Flat Plate,” Meccanica, 46, pp. 1103–1112 (2011).CrossRefGoogle Scholar
45.Prandtl, L., Essentials of Fluid Dynamics, Blackie, London (1952).Google Scholar
46.Jaluria, Y. and Himasekhar, K., “Buoyancy Induced Two Dimensional Vertical Flows in a Thermally Stratified Environment,” Computer and Fluids, 11, pp. 39–49 (1983).Google Scholar