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International Journal of Fluid Mechanics Research
ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimer: 2152-5102
ISSN En ligne: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v38.i1.10
pages 1-12

Exact Solution for the Oscillating Creeping Flow between Concentric Spheres

Sokrates Tsangaris
Lab. of Biofluid-Mechnics and Biomedical Engineering of National Technical University of Athens
D. Kondaxakis
School of Mechanical Engineering, Fluids Section, National Technical University of Athens Athens
N. W. Vlachakis
School of Mechanical Engineering, Fluids Section, National Technical University of Athens Athens

RÉSUMÉ

The Navier-Stokes equations are solved to obtain an analytical solution of the developed unsteady oscillating flow within the gap formed between two concentric spheres. This flow field spatially evolves between the north and the south poles of the geometrical configuration. The present paper contributes to the mathematical as well as to the mechanical characterization of the flow in spherical gaps and provides exact solutions for unsteady cases when convection effects are neglected. The results are mainly illustrated by representing the velocity as a function of two non-dimensional parameters: the gap spacing parameter and the reduced frequency parameter (Womersley number).

RÉFÉRENCES

  1. Bird, R. B., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena.

  2. Buehler, K. and Zierep, J., Die Stroemung im Spalt Zwischen Zwei Rotierenden Kugeln mit Durchflus.

  3. Landau, L. D. and Lifshitz, E. M., Fluid Mechanics.

  4. Sexl, Th., On the Annular Effect Discovered by Richardson, E. G.

  5. Tsangaris, S. and Vlachakis, N. W., Exact Solution for the Pulsating Finite Gap Dean Flow.

  6. Tsangaris, S., Kondaxakis, D., and Vlachakis, N. W., Exact Solution of the Navier-Stokes Equations for the Pulsating Dean Flow in a Channel with Porous Walls.

  7. Vatistas, G. H. and Ghaly, W., On the Pure Polar Flow within Two Concentric Spheres.


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