Stationary convection–diffusion between two co-axial cylinders

In this note, we examine the high Péclet number limit of the stationary extended Graetz problem for which two families of real and imaginary eigenvalues are associated, respectively, with a downstream convective relaxation and the upstream diffusive establishment. The asymptotic behavior of both families of eigenvalues is studied, in the limit of large Péclet number and thin wall, which bring to the fore a single parameter dependence, previously mentioned in the literature from numerical investigations [M.A. Cotton, J.D. Jackson, in: R.W. Lewis, K. Morgan (Eds.), Numerical Methods in Thermal Problems, vol. IV, Pineridge Press, Swansea, 1985, pp. 504–515]. The fully developed region is specifically studied thanks to the first eigenvalue dependence on the Péclet number, on the thermal conductivity 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 and experimental measurements.