An enhanced mathematical model for phase change problems with natural convection. (English) Zbl 1376.80005

Belhamadia, Youssef; Kane, Abdoulaye S.; Fortin, André

Int. J. Numer. Anal. Model., Ser. B 3, No. 2, 192-206 (2012).

Summary: The enthalpy-porosity technique is commonly used for modeling phase change problems with natural convection. In most applications however, this technique is restricted to equal thermophysical properties of solid and liquid phases. In this paper, an enhanced formulation based on the enthalpy-porosity method is proposed where the different thermophysical properties between the two phases can be easily taken into account. Accurate temporal and spatial discretizations are also presented for solving the proposed formulation. Numerical simulations on pure gallium melting and a comparison between experimental and numerical results for water solidification are presented to illustrate the performance of the proposed model and numerical methodology.

MSC:

80A22	Stefan problems, phase changes, etc.
80A20	Heat and mass transfer, heat flow (MSC2010)
80M10	Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids
76R10	Free convection

Keywords:

phase change problems with natural convection; mixed finite element formulation; interface liquid-solid; gallium melting; water solidification