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Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

Published online by Cambridge University Press:  09 May 2013

G. C. Shit ,
R. Haldar  and
A. Sinha
G. C. Shit*
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata, India
R. Haldar
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata, India
A. Sinha
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata, India
*
*Corresponding author (gcs@math.jdvu.ac.in)
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Abstract

A non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

Keywords

Thermal radiationMicro-polar fluidMHDHeat transferPorous medium
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 3 , September 2013 , pp. 559 - 568
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

REFERENCES

1.Eringen, A. C., “Theory of Micropolar Fluids,” Journal of Mathematics and Mechanics, 16, pp. 1–18 (1966).Google Scholar
2.Bhargava, R. and Takhar, H. S., “Numerical Study of Heat Transfer Characteristics of the Micropolar Boundary Layer Near a Stagnation Point on a Moving Wall,” International Journal of Engineering Science, 38, pp. 383–394 (2000).Google Scholar
3.Eringen, A. C., “Theory of Thermomicrofluids,” Journal of Mathematical Analysis and Applications, 38, pp. 480–496 (1972).Google Scholar
4.Gorla, R. S. R. and Nakamura, S., “Mixed Convection from a Rotating Cone to Micropolar Fluids,” International Journal of Heat and Fluid Flow, 16, pp. 69–73 (1975).Google Scholar
5.Khonsari, M. M. and Brewe, D. E., “Effects of Viscous Dissipation on the Lubrication Characteristics of Micropolar Fluids,” Acta Mechanica, 105, pp. 57–68 (1994).Google Scholar
6.Bachok, N., Ishak, A. and Pop, I., “MHD Flow and Heat Transfer Near the Stagnation Point on a Stretching/Shrinking Sheet in a Micropolar Fluid,” Magnetohydrodynamics, 47, pp. 237–248 (2011).Google Scholar
7.Shit, G. C., Roy, M. and Ng, E. Y. K., “Effect of Induced Magnetic Field on Peristaltic Flow of a Micro-Polar Fluid in an Asymmetric Channel,” International Journal of Numerical Methods in Biomedical Engineering, 26, pp. 1380–1403 (2010).Google Scholar
8.Shit, G. C. and Roy, M., “Pulsatile Flow and Heat Transfer of a Magneto-Micro-Polar Fluid Through a Stenosed Artery Under the Influence of Body Acceleration,” Journal of Mechanics in Medicine and Biology, 11, pp. 643–611 (2011).CrossRefGoogle Scholar
9.Choi, J. J., Rusak, Z. and Tichy, J. A., “Maxwell Fluid Suction Flow in a Channel,” Journal of Non-Newtonian Fluid Mechanics, 85, pp. 165–187 (1999).Google Scholar
10.Tripathi, D., “Peristaltic Flow of Couple-Stress Conducting Fluids Through a Porous Channel: Applications to Blood Flow in the Microcirculatory System,” Journal of Biological Systems, 19, pp. 461–477 (2011).Google Scholar
11.Kaviany, M., “Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates,” International Journal of Heat and Mass Transfer, 28, pp. 851–858 (1985).Google Scholar
12.Sparrow, E. M. and Cess, R. D., “Magnetohydrody-namic Flow and Heat Transfer About a Rotating Disk,” Journal of Applied Mechanics, ASME, 29, pp. 181–197 (1962).Google Scholar
13.Katukani, T., “Hydromagnetic Flow Due to a Rotating Disk,” Journal of the Physical Society of Japan, 17, pp. 1496–1506 (1962).Google Scholar
14.Misra, J. C. and Shit, G. C., “Flow and Heat Transfer of a MHD Viscoelastic Fluid in a Channel with Stretching Walls: Some Applications on Hemodynamics,” Computers & Fluids, 37, pp. 1–11 (2008).Google Scholar
15.Siddheshwar, P. G. and Pranesh, S., “Magnetocon-vection in a Micropolar Fluid,” International Journal of Engineering Science, 36, pp. 1173–1181 (1998).Google Scholar
16.Pavlov, K. B., “Magnetohydrodynamic Flow of an Incompressible Viscous Fluid Caused by Deformation of Plane Surface,” Magnitnaya Gidro-dinamika, 4, pp. 146–147 (1974).Google Scholar
17.Andersson, H. I., “MHD Flow of a Visco-Elastic Fluid Past a Stretching Surface,” Acta Mechanica, 95, pp. 227–230 (1992).Google Scholar
18.Char, M. I., “Heat Transfer in a Hydromagnetic Flow Over a Stretching Sheet,” Heat and Mass Transfer, 29, pp. 495–500 (1994).Google Scholar
19.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).Google Scholar
20.Jena, S. K. and Mathur, M. N., “Free-Convection in the Laminar Boundary Layer Flow of Thermomi-cropolar Fluid Past a Non-Isothermal Vertical Flat Plate with Suction/Injection,” Acta Mechanica, 42, pp. 227–238 (1982).Google Scholar
21.Rahman, M. M., Eltayeb, I. A. and Mujibur Rahman, S. M., “Thermo-Micropolar Fluid Flow Along a Vertical Permeable Plate with Uniform Surface Heat Flux in the Presence of Heat Generation,” Thermal Science, 13, pp. 23–36 (2009).Google Scholar
22.Rahman, M. M., “Convective Flows of Micropolar Fluids from Radiate Isothermal Porous Surfaces with Viscous Dissipation and Joule Heating,” Communications in Non-linear Science and Numerical Simulation, 14, pp. 3018–3030 (2009).Google Scholar
23.Rahman, M. M. and Sattar, M. A., “MHD Convec-tive 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
24.Chamkha, A. J., Grosan, T. and Pop, I., “Fully Developed Free Convection of a Micropolar Fluid in a Vertical Channel,” International Communications in Heat and Mass Transfer, 29, pp. 1021?196 (2002).Google Scholar
25.Soundalgekar, V. M. and Patti, M. R., “Stokes Problem for a Vertical Plate with Constant Heat Flux,” Astrophysics Space Science, 70, pp. 179–182 (1980).Google Scholar
26.Ibrahim, F. S., Elaiw, A. M. and Bakr, A. A., “Effect of the Chemical Reaction and Radiation Absorption on the Unsteady MHD Free Convection Flow Past a Semi Infinite Vertical Permeable Moving Plate with Heat Source and Suction,” Communications in Nonlinear Science and Numerical Simulation, 13, pp. 1056–1066 (2008).Google Scholar
27.Damseh, R. A., AL-Odat, M. Q., Chamkha, A. J. and Benbella Shannak, A., “Combined Effect of Heat Generation or Absorption and First Order Chemical Reaction on Micropolar Fluid Flows Over a Uniform Stretched Permeable Surface,” International Journal of Thermal Science, 48, pp. 1658–1663 (2009).Google Scholar
28.Bakr, A. A., “Effects of Chemical Reaction on MHD Free Convection and Mass Transfer Flow of a Micropolar Fluid with Oscillatory Plate Velocity and Constant Heat Source in a Rotating Frame of Reference,” Communications in Nonlinear Science and Numerical Simulation, 16, pp. 698–710 (2011).Google Scholar
29.Abdus Sattar, M. D. and Hamid, Kalim MD., “Unsteady Free-Convection Interaction with Thermal Radiation in a Boundary Layer Flow Past a Vertical Porous Plate,” Journal of Mathematical and Physical Sciences, 30, pp. 25–37 (1996).Google Scholar
30.Vajravelu, K., “Flow and Heat Transfer in a Saturated Porous Medium,” Journal of Applied Mathe mattes and Mechanics (ZAMM), 74, pp. 605–614 (1994).Google Scholar
31.Hossain, v and Takhar, H. S., “Radiation Effect on Mixed Convection Along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, 31, pp. 243–248 (1996).Google Scholar
32.Raptis, A., “Radiation and Free Convection Flow Through a Porous Medium,” International Communications in Heat and Mass Transfer, 25, pp. 289–295 (1998).Google Scholar
33.Chamkha, A. J., “MHD Flow of a Uniformly Stretched Vertical Permeable Surface in the Presence of Heat Generation/Absorption and a Chemical Reaction,” International Communications in Heat and Mass Transfer, 30, pp. 413–422 (2003).Google Scholar
34.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).Google Scholar
35.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
36.Yucel, A., “Mixed Convection in Micropolar Fluid Over a Horizontal Plate with Surface Mass Transfer,” International Journal of Engineering Science, 27, pp. 1593–1608 (1989).Google Scholar
37.Jena, S. K. and Mathur, M. N., “Self-Similarity Solution of Incompressible Microplar Boundary Layer Flow Over a Semi-Infinite Plate,” International Journal of Engineering Science, 14, pp. 639–646 (1976).Google Scholar
38.Ahmadi, G., “Similarity Solution for Laminar Free Convection Flow of Thermo-Micropolar Fluid Past a Non-Isothermal Vertical Flat Plat,” International Journal of Engineering Science, 19, pp. 1431–1439 (1981).Google Scholar
39.Cebeci, T. and Cousteix, J., Modelling and Computation of Boundary-Layer Flows, Springer-Verlag (1999).Google Scholar
40.Crane, L. J., “Flow Past a Stretching Sheet,” Journal of Applied Mathematics and Physics (ZAMP), 21, pp. 645–647 (1970).Google Scholar