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Journal Articles International Journal of Thermal Sciences Year : 2019

A 2D1/2 model for natural convection and solidification in a narrow enclosure


Efficient numerical models are derived for problems of natural convection and material solidification in a horizontal differentially heated slender cavity. These 2D 1/2 models are obtained by averaging the equations momentum, heat, and mass conservation along the transverse direction assuming both a constant temperature and a well defined velocity profile in this direction. Based on our former works, the transverse velocity profile is assumed to be either a Poiseuille profile (2D 1/2 P model), or Hartmann-type profiles featuring two boundary layers on the sides of a uniform bulk (2D 1/2 H model). For this 2D 1/2 H model, however, a parameter δ (giving the boundary layer thickness) has to be adjusted: optimal values have been found in a large range of the control parameters and expressed as a reliable fitted function of Gr. The ability of the model to reproduce 3D results in a 2D framework is investigated in a large range of the control parameters (Prandtl number P r and Grashof number Gr); the validity domain of the model in this parameter space is also clarified and rigorously defined. A good precision is obtained for natural convection problems (intensity of the flow, temperature field) as well as for solid-liquid phase change problems (shape, position , and evolution of the front). Yet, a comparison with unpublished experimental data of solidification of pure tin is particularly presented. For this, boundary conditions for the simulation are defined after a post-treatment of time-dependent experimental data. This ensures the implemented boundary conditions to be representative of the experimental process despite a significant and time dependent thermal resistance between the walls of the crucible and the liquid. A very good agreement is observed between the 2D 1/2 H model and the experimental measurements for this pure tin solidification experiment in the AFRODITE setup .
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hal-02106220 , version 1 (22-04-2019)



I. Hamzaoui, S. Millet, Valéry Botton, A. Benzaoui, D. Henry, et al.. A 2D1/2 model for natural convection and solidification in a narrow enclosure. International Journal of Thermal Sciences, 2019, 140, pp.167-183. ⟨10.1016/j.ijthermalsci.2019.02.028⟩. ⟨hal-02106220⟩
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