FDM for the freezing process of a slab using integral average properties.

The finite difference method (FDM) was used to calculate the temperature profile of the slab T (x,t) and freezing time (t calc). The methodology is based on the integral average property (P av) for each property P(T) (k, ρ , and Cp ap), which is the integral of P(T) from the initial slab temperature (T 0) up to a reference temperature (T ref), divided by the temperature range (T ref – T 0). The objective is to obtain an adequate (T ref) and a set of appropriate P(T) for a given set of experimental data. Simulations were performed to test several (T ref), obtaining (t calc), which was compared with 337 data from the slab freezing process. The principal findings were used to obtain the following parameters: minimum error E min = -6.71 %, overall mean error E mean = -0.27 %, maximum error E max = 5.84 %, and standard deviation σ n-1 = 1.69 %. When the Biot number is large, Bi f → ∞, T ref = T arith or T ref = T(i) is generally adequate to calculate (t calc), (T arith) being the average arithmetic temperature and T(i) temperature at a point (i), respectively. If Bi f → 0, T ref = T cf generally produces good results for (t calc), (T cf) being the final temperature in the center of the slab. If the traditional Biot number Bi → 0, the average temperature (T av) → (T c), obtained from the analytical solution with the convective boundary condition for a slab, (T c) being the center temperature. If Bi → ∞, (T av) → (T a) + (2/π)(T c - T a), (T a) being the ambient temperature. [ABSTRACT FROM AUTHOR]