{"references": ["Bedaux D., Albano A. M., Mazur P., Boundary conditions and non equilibrium thermodynamics, Physica 82A, 1996, pp. 438-462.", "Bilicki Z., Michaelides E. E., Thermodynamic of bubbly none equilibrium in liquid-vapor flows, Valter Degruyer, 1997.", "Boure J. A., 1978, Two-phase flows and Heat transfer with application to Nuclear reactor Design problem, Hemisphere Pub Corp. Washington, 1978.", "Danho E., Non linear distributions theory for jump conditions in two-phase flows instabilities, In journal of Africa Mathematical Union, 1993.", "Drew D. A. and Segal L. A., Averaged equations for two-phase flow, Studies in Appl. Math. L, 1971, pp. 205-231.", "Drumheller, D. S. and Bedford, A., A theory of liquids with vapor bubbles. J. Acoust. Soc. Am. 667, 1971, pp. 186-200.", "Gatignol R., Dynamics of multiphase flows across Interfaces, edited by Annie Steichen, Springer-Verlag, 1996.", "Hewitt G. H., Two phase flows and heat transfer with application to nuclear reactor design problems, pp. 1-15.", "Hsieh D. Y., On dynamics of bubbly liquids, Advances in applied mechanics 26, 63-13, Academic Press, 1988. [10] Lombard B, Piraux J., Numerical treatment of two-dimensional interfaces for acoustic and elastic waves, Journal of computational physics, 195-1, 2004, pp. 90-116. [11] Properriti, A., Boundary conditions at liquid-vapor Interfaces, Meccanica 19, 1979 p p. 123-136. [12] Roger P. and Thomas D. T., Computational Methods for Fluids Flows, Springer-Verlag New York, Heidelberg Berlin, 1983. [13] William G. and Kevin O., ''On the general Equations for Flow in Porous media and their Reduction to Darcy's Law'' Water Ressources Research, Vol. 12. ,n\u252c\u25912, April 1976 pp. 148-154."]}

A satured liquid is warmed until boiling in a parallelepipedic boiler. The heat is supplied in a liquid through the horizontal bottom of the boiler, the other walls being adiabatic. During the process of boiling, the liquid evaporates through its free surface by deforming it. This surface which subdivides the boiler into two regions occupied on both sides by the boiled liquid (broth) and its vapor which surmounts it. The broth occupying the region and its vapor the superior region. A two- fluids model is used to describe the dynamics of the broth, its vapor and their interface. In this model, the broth is treated as a monophasic fluid (homogeneous model) and form with its vapor adiphasic pseudo fluid (two-fluid model). Furthermore, the interface is treated as a zone of mixture characterized by superficial void fraction noted α* . The aim of this article is to describe the dynamics of the interface between the boiled fluid and its vapor within a boiler. The resolution of the problem allowed us to show the evolution of the broth and the level of the liquid.