A mathematical model for a class of frying processes

We present a mathematical model for deep frying in absence of mechanical deformation and in one-dimensional geometry. In the generic stage of the process the inner zone is saturated with liquid water below the boiling point at atmospheric pressure. When the boiling point is reached partial vaporization occurs and a zone of water-vapor thermodynamical equilibrium is formed, followed by a region of pure vapor. The interface between mixed and vapor region can be either a zero saturation surface or a level set of pressure when the latter reaches an imposed constraint. The outmost layer is crust. In each region the governing equations are written for temperature and pressure and the conditions at the interfaces comes out as the corresponding Rankine-Hugoniot relations. Boundary conditions at the crust-oil interface are discussed. Rescaling leads to only moderate simplifications and we are left with a considerably difficult free boundary problem for a parabolic system.