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On propose dans cette étude une solution analytique, valable pour des nombres de Reynolds intermédiaires, de perturbations faibles de l'écoulement de Poiseuille dans un canal. La méthode considérée est basée sur la résolution d'une forme linéarisée des équations aux perturbations. La solution obtenue permet de déterminer les deux bases de fonctions propres symétriques et antisymétriques de ces perturbations. Par la suite, ces bases sont orthonormalisées et utilisées pour établir la solution complète de l'écoulement lorsqu'un profil de vitesses, introduisant ce genre de perturbations, est imposé à l'entrée du canal. Pour citer cet article : A.

A numerical investigation of the heat transfer enhancement through fins using the Ansys Mechanical solver is presented. Results are given for a uniform fin with elliptical cross-sections and uniform heat flux applied on its base while heat is dissipated to its surroundings by convection from both its lateral surface and tip. The peak temperature at the base of the fin is used to evaluate the thermal performance. Ansys Mechanical solver is automated using Python scripting to run 792 simulations for various materials, fin lengths, and ratios between the minor and major axes of the elliptical cross-sectional shape for both cases of natural and forced convection. The use of the original automated numerical procedure significantly decreases the computational time and the user intervention. It was found that the thermal performance is improved by increasing the length of the fin, using a material with higher thermal conductivity, or having a ratio between the minor and major axes of the ellipse that is farther from unity. Forced convection gives better thermal performance compared to natural convection.

In this work, we present a temporal linear stability analysis of developing channel flow. For the main flow, the considered solution is analytic. It is based on the hypothesis of small disturbances from fully developed flow and it is valid for intermediate Reynolds numbers. The disturbances are separated into symmetric and anti-symmetric eigenmodes of the velocity. We deal subsequently with the linear stability of this main flow, taking into account the nearly parallel flow assumption. The stability problem formulation leads to the Orr–Sommerfeld equation. This equation is then resolved using the Chebyshev spectral collocation method. The stability results depend essentially on the shape and amplitude of the velocity profiles imposed at the channel entry.