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Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis

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Abstract

The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic (MHD) micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied.

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Abbreviations

B :

applied magnetic field

T c :

characteristic temperature

C f :

skin-friction coefficient

t :

time

c p :

specific heat at constant pressure

U 0 :

characteristic velocity

e bλ :

Plank’s function

u, v :

velocities along the x- and y-axes

Re :

Reynolds number

r :

radiation parameter

Pr :

Prandtl number

T :

dimensional temperature

f :

dimensionless stream function

(x,y):

Cartesian coordinate

g :

gravitational acceleration

I :

dimensionless angular velocity

ζ:

ratio of the gyration vector component to the fluid shear at a solid boundary

j :

microinertia density

K :

material parameter

β :

thermal expansion coefficient

K λ :

absorption coefficient

κ :

thermal conductivity

L :

characteristic length

ν :

kinematic viscosity

M :

magnetic parameter

ρ :

fluid density

m w :

wall couple stress

γ 0 :

spin gradient viscosity

m 0 :

microrotation parameter

µ:

dynamic viscosity

N :

angular velocity

α :

thermal diffusivity

Nu :

Nusselt number

θ:

dimensionless temperature

q r :

thermal radiation flux

ψ :

stream function

k :

vortex viscosity

′:

differentiation with respect to η

w:

wall condition

∞:

free stream condition

References

  1. Hayat, T., Abbas, Z., and Javed, T. Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet. Physics Letters A, 372, 637–647 (2008)

    Article  MATH  Google Scholar 

  2. Ishak, A. Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica, 45, 367–373 (2010)

    Article  MATH  Google Scholar 

  3. Mahmoud, M. A. A. and Waheed, S. E. MHD flow and heat transfer of a micropolar fluid over a nonlinear stretching surface with variable surface heat flux and heat generation. Canadian Journal of Chemical Engineering, 89, 1408–1415 (2011)

    Article  Google Scholar 

  4. Eringen, A. Simple microfluids. International Journal of Engineering Science, 2, 205–217 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  5. Eringen, A. Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  6. Eringen, A. Theory of thermomicropolar fluids. Journal of Mathematical Analysis and Applications, 9, 480–496 (1972)

    Article  Google Scholar 

  7. Agarwal, R. S. and Dhanapal, C. Numerical solution of unsteady flow and heat transfer in a micropolar fluid past a porous flat plate. Indian Journal of Pure and Applied Mathematics, 20, 513–520 (1989)

    MATH  Google Scholar 

  8. Damesh, R. A., Al-Azab, T. A., Shannak, B. A., and Al-Husein, M. Unsteady natural convection heat transfer of micropolar fluid over a vertical surface with constant heat flux. Turkish Journal of Engineering and Environmental Sciences, 31, 225–233 (2007)

    Google Scholar 

  9. Nazar, R., Ishak, A., and Pop, I. Unsteady boundary layer flow over a stretching sheet in a micropolar fluid. International Journal of Engineering and Natural Sciences, 2, 161–165 (2008)

    Google Scholar 

  10. Nazar, R., Ishak, A., Darus, M., and Pop, I. Unsteady boundary layer flow and heat transfer over a stretching surface in a micropolar fluid. Proceedings of the 13th WSEAS International Conference on Applied Mathematics (Math’08), World Scientific and Engineering Academy and Society (WSEAS) Stevens Point, Wisconsin, 273–278 (2008)

    Google Scholar 

  11. Bachok, N., Ishak, A., and Nazar, R. Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid. Meccanica, 46, 935–942 (2011)

    Article  Google Scholar 

  12. Ibrahim, F. S. and Hamad, M. A. A. Group method analysis of mixed convection boundary-layer flow of a micropolar fluid near a stagnation point on a horizontal cylinder. Acta Mechanica, 181, 65–81 (2006)

    Article  MATH  Google Scholar 

  13. Abd-Elaziz, M. M. and Ahmed, S. E. Group solution for unsteady boundary layer flow of a micropolar fluid near the rear stagnation point of a plane surface in a porous medium. Latin American Applied Research, 38, 161–168 (2008)

    Google Scholar 

  14. Hassanien, I. A. and Hamad, M. A. Group theoretic method for unsteady free convection flow of a micropolar fluid along a vertical plate in a thermally stratified medium. Applied Mathematical Modelling, 32, 1099–1114 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Chamkha, A. J., Mohamed, R. A., and Ahmed, S. E. Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects. Meccanica, 46, 399–411 (2011)

    Article  MathSciNet  Google Scholar 

  16. Moran, M. J. and Gaggioli, R. A. A new systematic formalism for similarity analysis. Journal of Engineering Mathematics, 3, 151–162 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  17. El-Gendi, S. E. On Chebyshev solution of parabolic partial differential equations. Journal of the Institute of Mathematics and Its Applications, 16, 283–289 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hassanien, I. A., El-Hawary, H. M., and Salama, A. A. Chebyshev solution of axisymmetric stagnation flow on a cylinder. Energy Conversion and Management, 37, 67–76 (1996)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assuit University, Assuit, 71516, Egypt

    I. A. Hassanien & H. M. El-Hawary

  2. Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

    M. A. A. Mahmoud, R. G. Abdel-Rahman & A. S. Elfeshawey

Authors
  1. I. A. Hassanien
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  2. H. M. El-Hawary
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  3. M. A. A. Mahmoud
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  4. R. G. Abdel-Rahman
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  5. A. S. Elfeshawey
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Correspondence to A. S. Elfeshawey.

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Hassanien, I.A., El-Hawary, H.M., Mahmoud, M.A.A. et al. Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis. Appl. Math. Mech.-Engl. Ed. 34, 703–720 (2013). https://doi.org/10.1007/s10483-013-1701-6

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  • DOI: https://doi.org/10.1007/s10483-013-1701-6

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