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 (T₀) up to a reference temperature (T_ref), divided by the temperature range (T_ref – T₀). 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.

使用有限差分法（FDM）计算板坯的温度曲线T（x，t）和凝固时间（t _calc）。该方法基于每个属性P（T）（k，ρ和Cp _ap）的积分平均属性（P _av），它是从初始板坯温度（T ₀）到初始板坯温度（T ₀）到P（T）的积分。参考温度（T _ref）除以温度范围（T _ref – T ₀）。的目的是获得一个适当的（Ť_ref）和一组给定实验数据的适当P（T）。进行模拟以测试多个（T _ref），获得（t _calc），并将其与板坯冻结过程中的337数据进行比较。主要发现用于获得以下参数：最小误差E _min  = -6.71％，总体平均误差E _mean  = -0.27％，最大误差E _max  = 5.84％，标准偏差σn _-1  = 1.69％。当比奥数大时，Bi _f  →∞，T _ref  =  T _arith或T _ref  =  T（i）通常足以计算（t _calc），（T _arith）分别是点（i）的平均算术温度和T（i）温度。如果Bi _f  →0，则对于（t _calc）（T _cf）是板坯中心的最终温度，T _ref  =  T _cf通常会产生良好的结果。如果传统的毕奥数Bi  →0，则平均温度（T _av）→（T _c）是从平板的对流边界条件（T _c为中心温度）的分析溶液中获得的。如果毕 →∞，（Ť _AV）→（Ť_一）+（2 /π）（Ť _Ç - Ť_一），（Ť_一个）是环境温度。