Generalized numerical modelling of unsteady heat transfer during cooling and freezing using an improved enthalpy method and quasi-one-dimensional formulation

A numerical solution of a generalized Stefan problem is presented. It covers a great variety of unsteady heat conduction cases accompanied by phase transformations. A mathematical model is developed for determination of the unsteady-state temperature and enthalpy fields (as well as the space-time evolution of the phase content) and of the cooling and freezing (heating and thawing) times of food materials and other bodies of various configuration (representing multicomponent two-phase systems having one freezable component). An improved enthalpy method is proposed by which all non-linearities, caused by the temperature dependence of the thermophysical coefficients, are introduced in a functional relationship between the volumetric specific enthalpy and the Kirchhoff function. Thus the non-linearities are eliminated as a factor making the solution difficult. The applied approach possesses great adaptivity and flexibility in solving complicated moving boundary problems: it is suitable for both isothermal and non-isothermal phase change, reaches a high degree of correspondence between the real physical phenomenon and its mathematical formalization, uses uniform and easy fixed-grid computational techniques, makes it possible to avoid complications and to eliminate possible errors caused by 'jumping' of the equivalent specific heat capacity peak at the maximum of the latent heat effect, etc. Efficient procedures and algorithms for computer simulation of complex refrigerating technological processes are created. Experimental verification demonstrating the applicability and accuracy of the model is carried out.