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Heat Transfer Analysis on Axisymmetric Mhd Flow of a Micropolar Fluid Between the Radially Stretching Sheets

Published online by Cambridge University Press:  07 December 2011

T. Hayat ,
M. Nawaz  and
A. A. Hendi
T. Hayat
Affiliation:
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
M. Nawaz*
Affiliation:
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
A. A. Hendi
Affiliation:
Department of Physics, Faculty of Science, King Saud University, Riyadh 11321, Saudi Arabia
*
**Corresponding author
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Abstract

The effect of heat transfer on the axisymmetric flow of MHD micropolar fluid between two radially stretching sheets is described. The governing partial differential equations are reduced into the ordinary differential equations by using transformations. The resulting problems are solved by homotopy analysis method (HAM). Dimensionless velocities and temperature are plotted for the variation of influential parameters. The local skin friction coefficient, local couple stress coefficient and Nusselt number are tabulated with respect to the influence of several physical parameters.

Keywords

Heat transferRadial stretchingAxisymmetric flowSkin friction coefficientCouple stress coefficientNusselt number.
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 4 , December 2011 , pp. 607 - 617
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

REFERENCES

1.Eringen, A. C., “Theory of Micropolar Fluids,” Journal of Mathematical Mechanics, 16, pp. 1–18 (1966).Google Scholar
2.Ezzat, M. A., Othman, M. I. and Helmy, K. A., “A Problem of Micropolar Magnetohydrodynamic Boundary Layer Flow,” Canadian Journal of Physics, 77, pp. 813–827 (1999).CrossRefGoogle Scholar
3.Guram, G. S. and Smith, A. C., “Stagnation Flows of Micropolar Fluids with Strong and Weak Interactions,” Computers & Mathematics with Applications, 6, pp. 213–233 (1980).CrossRefGoogle Scholar
4.Ahmadi, G., “Self Similar Solution of Incompressible Micropolar Boundary Layer Flow over Semi-Infinite Flat Plate,” International Journal of Engineering Science, 14, pp. 639–646 (1976).CrossRefGoogle Scholar
5.Nazar, R., Amin, N., Filip, D. and Pop, I., “Stagnation Point Flow of a Micropolar Fluid Towards a Stretching Sheet,” International Journal of Non-Linear Mechanics, 39, pp. 1227–1235 (2004).CrossRefGoogle Scholar
6.Helmy, K. A., Idriss, H. F. and Kassem, S. E., “MHD Free Convection Flow of a Micropolar Fluid Past a Vertical Porous Plate,” Canadian Journal of Physics, 80, pp. 1661–1673 (2002).CrossRefGoogle Scholar
7.Rees, D. A. S. and Pop, I., “Free Convection Boundary Layer Flow of a Micropolar Fluid from a Vertical Flat Plate,” IMA, Journal of Applied Mechanics, 61, pp. 179–197 (1998).Google Scholar
8.Takhar, H. S., Bhargava, R., Agrawal, R. S. and Balaji, A. V. S., “Finite Element Solution of a Micropolar Fluid Flow and Heat Transfer Between Two Porous Discs,” International Journal of Engineering Science, 38, pp. 1907–1922 (2000).CrossRefGoogle Scholar
9.Jena, S. K. and Mathur, M. N., “Similarity Solution for Laminar Free Convection Flow of Thermo-Micropolar Fluid Past a Noniosthermal Flat Plate,” International Journal of Engineering, 19, pp. 1431–1439 (1981).Google Scholar
10.Abo-Eldahab, E. M. and El-Aziz, M. A., “Flow of and Heat Transfer in Micropolar Fluid Past a Stretching Surface Embedded in a Non-Darcian Porous Medium with Uniform Free Stream,” Applied Mathematics and Computation, 162, pp. 881–899 (2005).CrossRefGoogle Scholar
11.Chang, C. L., “Numerical Simulation of Micropolar Fluid Along a Flat Plate with Wall Conduction and Buoyancy Effects,” Journal of Physics D: Applied Physics, 39, pp. 1132–1140 (2006).CrossRefGoogle Scholar
12.Ibrahem, F. S., Hassanein, I. A. and Bakr, A. A., “Thermal Effects in Stokes' Second Problem for Unsteady Micropolar Fluid Flow,” Applied Mathematics and Computation, 173, pp. 916–937 (2005).CrossRefGoogle Scholar
13.Ariel, P. D., “Axisymmetric Flow of a Second Grade Fluid Past a Stretching Sheet,” International Journal of Engineering Science, 39, pp. 529–553 (2001).CrossRefGoogle Scholar
14.Ariel, P. D., “Axisymmetric Flow Due to a Stretching Sheet with Partial Slip,” Computers & Mathematics with Applications, 54, pp. 1169–1183 (2007).CrossRefGoogle Scholar
15.Ishak, A., Nazar, R. and Pop, I., “Magnetohydrodynamic (MHD) Flow and Heat Transfer Due to a Stretching Cylinder,” Energy Conversion and Management, 49, pp. 3265–3269 (2008).CrossRefGoogle Scholar
16.Hayat, T. and Sajid, M., “Analytic Solution for Axisymmetric Flow and Heat Transfer of a Second Grade Fluid Past a Stretching Sheet,” International Journal of Heat and Mass Transfer, 50, pp. 75–84 (2007).CrossRefGoogle Scholar
17.Ahmad, I., Sajid, M., Hayat, T. and Ayub, M., “Unsteady Axisymmetric Flow of a Second-Grade Fluid over a Radially Stretching Sheet,” Computers & Mathematics with Applications, 56, pp. 1351–1357 (2008).CrossRefGoogle Scholar
18.Ahmad, I., Sajid, M. and Hayat, T., “Heat Transfer in Unsteady Axisymmetric Second Grade Fluid,” Applied Mathematics and Computation, 215, pp. 1685–1695 (2009).CrossRefGoogle Scholar
19.Mirgolbabaei, H., Ganji, D. D., Etghani, M. M. and Sobati, A., “Adapted Variational Iteration Method and Axisymmetric Flow over a Stretching Sheet,” World Journal of Modelling and Simulation, 5, pp. 307–314 (2009).Google Scholar
20.Sahoo, B., “Effects of Partial Slip on Axisymmetric Flow of an Electrically Conducting Viscoelastic Fluid Past a Stretching Sheet,” Central European Journal of Physics, 8, pp. 498–508 (2010).Google Scholar
21.Hayat, T. and Nawaz, M., “Effects of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets,” Zeitschrift für Naturforschung A, 65, pp. 1–8 (2010).Google Scholar
22.Liao, S. J., Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall, CRC Press, Boca Raton (2003).CrossRefGoogle Scholar
23.Liao, S. J., “A New Branch of Solutions of Unsteady Boundary Layer Flows over an Impermeable Stretched Plate,” International Journal of Heat and Mass Transfer, 48, pp. 2529–2539 (2005).CrossRefGoogle Scholar
24.Chen, J. and Liao, S. J., “Series Solutions of Nano-Boundary Layer Flows by Means of the Homotopy Analysis Method,” Journal of Mathematical Analytical Applied, 343, pp. 233–245 (2008).CrossRefGoogle Scholar
25.Abbasbandy, S. and Parkes, E. J., “Solitary Smooth Hump Solutions of the Camassa-Holm Equation by Means of Homotopy Analysis Method,” Chaos, Soliton and Fractals, 36, pp. 581–591 (2008).CrossRefGoogle Scholar
26.Abbasbandy, S., “Approximate Solution of the Nonlinear Model of Diffusion and Reaction Catalysts by Means of the Homotopy Analysis Method,” Chemical Engineering Journal, 136, pp. 144–150 (2008).CrossRefGoogle Scholar
27.Abbasbandy, S. and Zakaria, F. S., “Soliton Solution for the Fifth-Order Kdv Equation with the Homotopy Analysis Method,” Non-Linear Dynamics, 51, pp. 83–87 (2008).CrossRefGoogle Scholar
28.Hayat, T., Qasim, M. and Abbas, Z., “Radiation and Mass Transfer Effects on the Magnetohydrodynamic Unsteady Flow Induced by a Stretching Sheet,” Zeitschrift für Naturforschung A, 65, pp. 231–239 (2010).CrossRefGoogle Scholar
29.Hayat, T., Qasim, M. and Abbas, Z., “Homotopy Solution for the Unsteady Three-Dimensional MHD Flow and Mass Transfer in a Porous Space,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 2375–2387 (2010).CrossRefGoogle Scholar
30.Hayat, T. and Nawaz, M., “Magnetohydrodynamic Three-Dimensional Flow of a Second-Grade Fluid with Heat Transfer,” Zeitschrift für Naturforschung A, 65, pp. 683–691 (2010).CrossRefGoogle Scholar
31.Hayat, T. and Nawaz, M., “Hall and Ion-Slip Effects on Three-Dimensional Flow of a Second Grade Fluid,” International Journal for Numerical Methods in Fluids, DOI:10.1002/f ld.2251.CrossRefGoogle Scholar
32.Hayat, T. and Awais, M., “Three-Dimensional Flow of an Upper-Convected Maxwell (UCM) Fluid,” International Journal for Numerical Methods in Fluids, DOI: 10.1002/f ld.2289.CrossRefGoogle Scholar