Stationnary Convection Diffusion between two Co-Axial Cylinders.

Franck Plouraboué (1) , Charles Pierre (2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 LMAP - Laboratoire de Mathématiques appliquées de Pau

In this paper, the stationary heat transfer between a fluid flowing in a tube and a co-axial solid cylinder is examined. In this study of convection-diffusion in the fluid, longitudinal diffusion is considered to be negligible in comparison to convection; simultaneously pure diffusion is taking place in the solid coaxial cylinder. A family of analytical solutions based on eigenfunction expansion is proposed. Two families of real and imaginary eigenvalues are found to be associated respectively with a downstream convective relaxation and an upstream diffusive establishment. The asymptotic behavior of both families of eigenvalues in the limit of large Peclet number is studied and bring to the fore a single parameter dependence, previously mentioned in the literature from numerical investigations. The fully developed region is specifically studied thanks to the first eigenvalue dependence on the Peclet number, on the diffusion coefficients and on the diameter ratio of the cylinders. The effective transport between the fluid and the solid is investigated through the evaluation of the fully developed Nusselt number. The scaling of asymptotic behavior is discussed and compared with numerical computation. The results are also compared with available experimental measurements.

Mots clés: micro-systems; heat transfer; spectral analysis; asymptotic

Domaines: Analyse numérique [math.NA]; Thermique [physics.class-ph]; Thermique [physics.class-ph]

Franck Plouraboué, Charles Pierre. Stationnary Convection Diffusion between two Co-Axial Cylinders.. 2007. ⟨hal-00158250⟩