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Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

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Abstract.

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.

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References

  1. Siekann I (1962) The calculation of the thermal boundary layer on a rotating sphere. Z Angew Math Phys 13: 468–482

    Google Scholar 

  2. Chao BT; Grief R (1974) Laminar forced convection over rotating bodies. J Heat Transfer 96: 463–466

    Google Scholar 

  3. Lee MH; Jeng DR; De Witt KJ (1978) Laminar boundary layer transfer over rotating bodies in forced flow. J Heat Transfer 100: 496–502

    Google Scholar 

  4. Kumari M; Nath G (1982) Nonsimilar incompressible boundary layer flow over a rotating sphere. Arch Mech 34: 147–164

    Google Scholar 

  5. Kumari M; Nath G (1982) Unsteady incompressible boundary layer flow over a rotating sphere. J Appl Mech 49: 234–236

    Google Scholar 

  6. Takhar HS; Nath G (2000) Self-similar solution of the unsteady flow in the stagnation point region of a rotating sphere with a magnetic field. Heat Mass transfer 36: 89–96

    Article  Google Scholar 

  7. Takhar HS; Slaouti A; Kumari M; Nath G (1998) Unsteady free convection flow in the stagnation point region of a rotating sphere. Int J Non-Linear Mech 33: 857–865

    Google Scholar 

  8. Gebhart B; Jaluria Y; Mahajan RL; Sammakia B (1988) Buoyancy – induced flows and transport. Hemisphere, New York

  9. Bejan A (1995) Convection heat transfer. Wiley, New York

  10. Chen TS; Mucoglu A (1977) Analysis of mixed forced and free convection about a sphere. Int J Heat Mass Transfer 20: 867–875

    Article  Google Scholar 

  11. Mucoglu A; Chen TS (1978) Mixed convection about a sphere with uniform surface heat flux. J Heat Transfer 100: 542

    Google Scholar 

  12. Amin N; Riley N (1995) Mixed convection at a stagnation point. Quart J Mech Appl Math 48: 111–121

    Google Scholar 

  13. Seshadri R; Sreeshylan N; Nath G (2002) Unsteady mixed convection flow in the stagnation region of heated vertical plate due to impulsive motion. Int J Heat Mass Transfer 45: 1345–1352

    Google Scholar 

  14. Merkin JH; Pop I (2002) Mixed convection along a vertical surface: similarity solutions for uniform flow. Fluid Dyn Res 30: 233–250

    Article  Google Scholar 

  15. Ma PKH; Hui WH (1990) Similarity solutions of the two-dimensional unsteady boundary layer equation. J Fluid Mech 216: 537–559

    Google Scholar 

  16. Inouye K; Tate A (1974) Finite difference version quasilinearization applied to boundary layer equations. AIAAJ 12: 558–560

    Google Scholar 

  17. Varga RS (2000) Matrix iterative analysis. Prentice Hall, New Jersey

  18. Ingham DB (1984) Unsteady separation. J Comp Phys 53: 90–99

    Google Scholar 

  19. Smith FT (1986) Steady and unsteady boundary layer separation. Ann Rev Fluid Mech 18: 197–220

    Article  Google Scholar 

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Acknowledgements.

The authors thank Professor G. Nath, Department of Mathematics, Indian Institute of Science, Bangalore, India, for useful discussions.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

    D. Anilkumar & S. Roy

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  1. D. Anilkumar
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  2. S. Roy
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Correspondence to D. Anilkumar.

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Anilkumar, D., Roy, S. Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere. Heat and Mass Transfer 40, 487–493 (2004). https://doi.org/10.1007/s00231-003-0447-7

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