On the numerical solution of a rising sphere in a Newtonian fluid with temperature-dependent viscosity

• Zambrano, Marcos ^[1]
  1. [1] Dpto. Académico de Ciencias Básicas, Universidad Nacional de Barranca - UNAB, Lima-Perú
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 6, Nº. 2, 2019 (Ejemplar dedicado a: Agosto-Diciembre), págs. 140-147
• Idioma: inglés
• DOI: 10.17268/sel.mat.2019.02.1
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this work, we present some numerical results about the problem of a rising hot solid sphere immersed in a Newtonian fluid which viscosity depends on the temperature. The model formulated to solve the problem considers two dimensionless parameters: The Peclet number, Pe and a parameter related with the viscosity, e. Small and large variations on e lead to interesting results segregated into two regimes which exhibit an asymptotic structure.To carry out the computations to solve the proposed model, the element finite method was used along with a non-slip boundary condition for the contact surface between the sphere and the fluid and the results obtained were compared to those shown recently in papers related wherein contact surface has a slip-boundary condition prescribed.

• Referencias bibliográficas
  • Ribe, N. M. Diapirism in the Earth’s Mantle: Experiments on the motion of a hot sphere in a fluid with temperature-dependent visocity, Journal...
  • Marsh, B. D. On the cooling of ascending andesitic magma, Philos. Trans. R. Soc. London; 1978; 288:611-625.
  • Hadamard, J. Mouvement permanent lent d’une sphere liquide et visqueuse dans un liquid visqueus, C.R. Acad. Sci. 1911; 152:1735-1738.
  • Rybczynski, W. Über die fortschreitende ewegung einer flüssigen Kugel in einen zähen Medium, Bull Acad. Sci. 1911; 1:40-46.
  • Acrivos, A. and Goddard J. D. Asymptotic expansions for laminar forced convection heat and mass transfer. Part 1. Low speed flows, J. Fluid...
  • Acrivos, A. and Taylor T. D. Heat and Mass transfer from single spheres in Stokes flow, Phys, Fluids. 1962; 5:387-394.
  • Batchelor, G. K. An Introduction to Fluid Dynamics, Cambridge University Press, 1967.
  • Ansari, M. and Morris S. The effects of a strongly temperature-dependent viscosity on Stokes’ draw law: experiments and theory, Journal of...
  • Vynnycky, M. and O’Brien, M. A. The slow, steady ascent of a hot solid sphere in a Newtonian fluid with strongly temperature-dependent viscosity,...
  • Zhang, L. et al. Numerical Simulation of a bubble rising in shear-thinning fluids. J. Non-Newtonian Fluid Mech. 2010; 165:555-567.
  • Weinberg, R. and Podladchikov Y. Diapiric ascent of magmas through power law crust and mantle, J. Geophys. Res. 1994; B5:9543-9559.