Simultaneous effect of rotation and natural convection on the flow about a liquid sphere (original) (raw)

Abstract

The problem of mixed convection around a liquid sphere that experiences a rotation about its axis parallel to the free stream is studied numerically using a finite-difference technique. The coupled boundary-layer energy and momentum equations are numerically solved over a wide range of Grashof number that represents the cases of aiding and opposing free convection and for wide range of the spin parameter Ta/Re 2 . The surface of the sphere also rotates as a result of the shear stress exerted from the external flow of air. The effect of both parameters on the velocity components as well as the temperature within the thermal boundary-layer is presented. Results show that increasing the aiding free convection and the spin parameter cause increases in the shear stress and the local heat transfer coefficient. Notation a sphere radius, m g gravitational acceleration, m/s 2 Gr Grashof number, Gr = 16gbqa 4 /kt 2 h local heat transfer coefficient, W/m 2°C k thermal conductivity of fluid, W/m°C m number of steps of the numerical mesh network in the x-direction n number of steps of the numerical mesh network in the z-direction Nu Nusselt number, 2ah k ¼ À2 @T @Z j o Pe Peclet number = Re à Pr Pr Prandtl number, m/a r radial coordinate measured from the sphere's center, m Re Reynolds number, 2U ¥ a/m t temperature,°C t w wall temperature,°C t ¥ free stream temperature,°C T dimensionless temperature, T = k(t w -t ¥ )/(aq) Ta Taylor number, Ta = 4W 2 a 4 /m 2 T w dimensionless wall temperature, T w = k(t w -t ¥ )/ (aq) u meridional (x-direction) component of velocity, m/s U dimensionless meridional component of velocity, u/U ¥ u à velocity component in x-direction for the potential flow outside the external boundary layer, -( ¶w/ ¶r)/ (r sin h) = U ¥ sin h [1 + a 3 /(2r 3 )], m/s U à dimensionless potential velocity component in the x-direction for external flow, u*/U ¥ U ¥ free stream velocity in the exterior flow, m/s v azimuthal velocity component, m/s v o circumferential velocity at the sphere's surface, v o = Wr o , m/s V dimensionless azimuthal velocity component, V = v/Wa V o dimensionless azimuthal velocity component at the sphere's surface, V o = r o /a w radial (z-direction) velocity component, m/s w à radial (z-direction) velocity component for potential flow outside the external boundary layer, ( ¶w/ ¶h)/(r 2 sin h) = -U ¥ cos h [1 -a 3 /r 3 ], m/s W dimensionless radial velocity component, w/U ¥

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References (22)

  1. Rajasekaran R, Palekar MG (1985) Mixed convection about a rotating sphere. Int J Heat Mass Transfer 28: 959-968
  2. Le Palec G, Daguenet M (1984) Analysis of free convection effects about a rotating sphere in forced flow. Int Comm Heat Mass Transfer 11: 409-416
  3. Le Palec G, Daguenet M (1987) Laminar three-dimensional mixed convection about a rotating sphere in a stream. Int J Heat Mass Transfer 30: 1511-1523
  4. Vasudevaiah M, Patturaj R (1992) Heat Convection from a spinning sphere, Int J Engineering Science 30(11): 1597-1605
  5. Tang L, Johnson AT (1990) Flow visualization of mixed convec- tion about a sphere. Int Comm Heat and Mass Transfer 17(1): 67-77
  6. Tieng M, Yan AC (1991) Holographic flow-visualization of heated spinning sphere. ASME Fluids Eng Divi (publication) FED. New-York, USA 128: 189-200
  7. Tieng MT, Yan AC (1993) Experimental investigation on con- vective heat transfer of heated spinning sphere. Int J Heat Mass Transfer 36(3): 599-610
  8. Ganapathy R, Purushothaman R (1990) Free convection in an infinite porous medium induced by a heated sphere. Int J Eng Sci 28(8): 751-759
  9. Ganapathy R (1997) Time-dependent free convection motion and heat transfer in an infinite porous medium induced by a heated sphere. Int J Heat Mass Transfer 40(7): 1551-1557
  10. Ferreira JM, Duarte Naia M, Chhabra RP (1998) Analytical study of the transient motion of a dense rigid sphere in an incom- pressible Newtonian fluid. Chem Eng Comm 168: 45-58
  11. Kleinstrueuer C, Wang T (1989) Mixed convection heat and mass transfer between power-law fluids and rotating permeable bodies. Chem Eng Sci 44(12): 2987-2994
  12. Wang T, Kleinstrueuer C (1989) Mixed convection over rotating bodies with blowing and suction. Int J Heat Mass Transfer 32(7): 1309-1319
  13. Hatzikonstantinou P (1990) Unsteady mixed convection about a porous rotating sphere. Int J Heat Mass Transfer 33(1): 19-27
  14. El-Shaarawi MA, I Ahmad NT, Kodah Z (1990) Mixed convection about a rotating sphere in an axial stream. Numer Heat Transfer Part A18: 71-93
  15. Ece MC (1996) Unsteady free convection over a spinning rotational symmetric body. Proc 3rd Biennial Joint Conf Eng Syst Design Analysis, ESDA, Part 6 (of 9), Montpellier, France
  16. Jia H, Gogos G (1996) Laminar natural convection heat transfer from isothermal spheres. Int J Heat Mass Transfer 39: 1603-1615
  17. Gogos G, Yang S (1997) Transient laminar natural convection heat transfer over an isothermal sphere: flow separation and associated wake vortex. Separated and complex flows ASME, Fluids Engineering Division FED 14: FEDSM97-3297
  18. Yan B, Pop I, Ingham DB (1997) Numerical study of unsteady free convection from a sphere in a porous medium. Int J Heat Mass Transfer 40(4): 893-903
  19. Hossain MA, Takhar HS (1976) Radiation-Conduction interaction in mixed convection along rotating bodies. Heat Mass Transfer 33(3): 210-218
  20. Hsu CH, Yang SA (1997) Mixed convection film condensation from downward flowing vapors onto a sphere with uniform wall heat flux. Heat Mass Transfer 32(5): 385-391
  21. Nguyen HD, Paik S, Douglass RW (1997) Legendre-spectral element method for flow and heat transfer about an accelerating droplet. J Scientific Comput 12(1): 75-97
  22. Antar MA, El-Shaarawi MAI (2002) Mixed convection around a liquid sphere in a gas stream. Heat Mass Transfer 38(4-5): 419-425