Physical Model Most foods have low thermal conductivity and relatively large thickness and geometric dimensions. Therefore, thermal conductivity and surface heat transfer and mass transfer must be considered in foods. In order to simplify the calculation, the following assumptions are made: (1) The physical parameters of the food in the cooling process are constant and constant; (2) The surface and the environment of the food only have mass transfer heat transfer, ignoring convection heat transfer, heat conduction and radiation heat transfer; (3) The internal water mass diffusion is neglected; (4) The food material is isotropic.
The basic formula of heat conduction is Fourier's law. It has cTt=2Tr2 for the three most basic shapes of ordinary properties (infinite slab-R≤r≤R, infinite-long cylinder 0≤r≤R, and sphere 0≤r≤R). -1) Trr (1) Product initial temperature T = Tin (0 ≤ r ≤ Rt ≥ 0) (2) Boundary conditions at r = 0 Tr = 0 (r = 0t ≥ 0) (3) Surface boundary conditions of foods (r=R) The expression is (Tr)r=R=mwL(t>0) (4) Mass diffusion rate of water under any condition according to Stephen's law integral expression mw=DpRwTllnp-pawp-pM(5) The value is D = D0p0pT03/2 (6) The partial pressure of water vapor in the surface layer of food is the product of water vapor pressure and water activity pM = awpw (7) According to formula (5-7), formula (4) can be changed to Trr =R=D0p0RwTlT03/2lnp-pawp-awpw(8) The main factors affecting equation (8) are the partial pressure of water vapor in the environment, food surface temperature and water activity, especially the food water activity coefficient aw and the moisture content of the food surface. Relevantly, the moisture content itself is closely related to the movement (diffusion or capillary action) of moisture on the surface of the food, the state, and the rate of evaporation of the epidermis and the water, so that the pressure of water vapor on the food surface follows Surface temperature varies nonlinearly. To accurately solve the equations (1) to (8), it is necessary to establish a real-time model for paw and aw, and obtain the dynamic values ​​of the characteristic parameters of the food. However, in practical applications, the advantage of accurately simulating heat and mass transfer can theoretically be difficult to achieve. Therefore, as long as the error is not too large, approximate solutions can be used to solve equations (1) to (8).
In addition, the water activity coefficients of different foods vary greatly, and the moisture content on the surface and inside of the same food also differs greatly. Under natural conditions, foods generally have a skin layer that protects moisture, and the internal tissues are not in direct contact with the air. If the cortex is directly exposed to air, the water activity coefficient of the food is relatively large, close to 1. For skinned foods, The cortex is considered part of the mass transfer resistance layer while ignoring cortical water storage.
The mathematical model uses the difference method to solve the equations (1) to (8). The grid is first divided, and the food center point is taken as the first node, and m=0, the largest node M, which is located on the surface of the food. Except for the outermost and innermost elements, because the thickness is only r/2, the node is set on one side of the element, and the other nodes of each volume element are located between the two faces of the element.
The temperature drop curve is a comparison of the simulated surface temperature changes of the potato slices with actual measured values. It can be seen from the above that the theoretical temperature drop curve of the food analogy is basically similar to the shape of the actually measured curve, but the theoretically simulated curve is steeper than the actual one, but there is always some deviation between the two in the cooling period.
The cooling time is 10 mm from the surface of the potato chips, and the time required for the temperature of the thermocouple to drop from 20°C to 2°C for the temperature drop curve is taken as an example. The experimental test result is 900 s. According to the theoretical simulation time 804 s, the actual cooling ratio is larger than the theory. When the time is 96s, the error is about 10.7%. If the radiation heat transfer of the food is considered in the theoretical calculation, the cooling time of the food is increased to 852s, and the error is 5.3%.
The water loss rate was determined according to the formula, and the mass average temperature of the potato chips was obtained. According to the enthalpy difference between the initial temperature of the food and the final mass average temperature, the water loss of the product was 1.53 g, and the water loss rate was 3.50%. The mass flow rate of surface water diffusivity in the product was calculated as 1.72 g of water loss and 3.93% of water loss. The actual mass of the product after the experiment was 42.10 g, and the rate of water loss was 3.77%. The water loss rate was calculated based on the mass flow rate. The error between the experimental results and the experimental results was 4.24%, while the error between the water loss rate and the actual value calculated by the mass average temperature was close to 7.16%.
Analysis and conclusions When the radiation heat transfer is not considered, the theoretical simulation results are quite different from the experimental ones. This shows that the radiation cannot be neglected for the single experiment in the experimental device. However, for industrial applications or multi-body experiments, radiation is negligible. For this model, the error between theoretical simulation and experimental results is still about 5%. The main reasons are: first, the water vapor content in the environment changes with the continuous evaporation of food moisture; secondly, many assumptions are made in theoretical calculations, such as the assumption of the physical properties of the physical parameters of food, and in the actual process, The parameters such as density, thermal conductivity, specific heat capacity, and quality of foods are constantly changing. Finally, there are certain errors in the placement of thermocouples in experiments, and the thickness of foods cannot be absolutely uniform.
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