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FST 151 FOOD FREEZING FOOD SCIENCE AND TECHNOLOGY 151 Food Freezing - Basic concepts (cont’d) Lecture Notes Prof. Vinod K. Jindal (Formerly Professor, Asian Institute of Technology) Visiting Professor Chemical Engineering Department Mahidol University Salaya, Nakornpathom Thailand.
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FST 151 FOOD FREEZING FOOD SCIENCE AND TECHNOLOGY 151 Food Freezing - Basic concepts (cont’d) Lecture Notes Prof. Vinod K. Jindal (Formerly Professor, Asian Institute of Technology) Visiting Professor Chemical Engineering Department Mahidol University Salaya, Nakornpathom Thailand Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Frozen-Food Properties • Depend on thermal properties of the food product • Phase change: Liquid (water) change to solid, the density, thermal conductivity, heat content (enthalpy), specific heat of the product change as temperature decreases below the initial freezing point for water in the food. • 1. Density • The density of solid water is less than that of liquid water • The density of a frozen food is less than the unfrozen product Intensive properties • The magnitude of change in density is proportional to the moisture content of the product • 2. Thermal conductivity • The thermal conductivity of ice is about four times larger than that of liquid water. • Same influence in the thermal conductivity of a frozen food Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Frozen-Food Properties • 3. Enthalpy (heat content) • Important parameter for refrigeration requirement • The heat content normally zero at -40 oC and increases with increasing temperature • Significant changes in enthalpy occur in 10 oC below the initial freezing temperature. • 4. Apparent specific heat • Depend on function of temperature and phase changes for water in the product • The specific heat of a frozen food at a temperature greater than 20 below the initial point (-2.61 oC) • 5. Apparent thermal diffusivity • The apparent thermal diffusivity increases as the temperature decreases below the initial freezing point • Frozen product shows larger magnitude than unfrozen product Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Freezing Time Calculations Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Freezing Time Calculation • In freezing time calculations, the imprecise control of freezing conditions and uncertainty in thermal properties data of foods are mainly responsible for not so accurate predictions. • The overall accuracy of prediction is governed more by the uncertainty in thermal properties data rather than the calculation procedure. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
There are three alternatives for obtaining the thermal properties data of foods: • 1) Use data from literature • 2) Direct measurement • 3) Using prediction equations based on the composition information Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
PLANK’S EQUATION • Plank’s equation is an approximate analytical • solution for a simplified phase-change model. • Plank assumed that the freezing process: • (a) commences with all of the food unfrozen • but at its freezing temperature. • (b) occurs sufficiently slowly for heat transfer • in the frozen layer to take place under steady-state conditions. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Plank’s equation considers only phase change period during freezing process. However, Plank’s approximate solution is sufficient for many practical purposes. • This method when applied to calculate the time taken to freeze to the centre of a slab (Fig. 1) whose length and breadth are large compared with the thickness, results in the following equation: Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Fig. 1 Freezing of a slab Eqs. 7.1 – 7.3 Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
For conditions when t=0, x=0 and t=tf, x=a/2 (at the center of slab), this leads to Eq. 7.5 Also Lf = mm L (for a food material) where mm = moisture content of food (fraction) L = latent heat of fusion of water, 333.2 kJ/(kg.0C) Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
The general form of Plank’s equation is where P’ and R’ are constants accounting for the product shape with P’=1/2, R’=1/8 for infinite plate; P’=1/4, R’=1/16 for infinite cylinder; and P’=1/6 and R’=1/24 for sphere or cube. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Brick-shaped solids have values of P’ and R’ lying between those for slabs and those for cubes, which can be obtained from the graph in Fig. 2. In this figure, β1 and β2 are the ratios of the two longest sides to the shortest. It does not matter in what order they are taken. Fig. 2 Chart providing P and R constants for Plank’s equation when applied to a brick or block geometry. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Example: Freezing time(Example 7.1) • A spherical food product is being frozen in an air-blast wind tunnel. The initial product temperature is 10 oC and the cold air -15 oC. The product has a 7-cm diameter with density of 1,000 kg/m3. The initial freezing temperature is -1.25 oC, and the latent heat of fusion is 250 kJ/kg. Compute the freezing time. Given: Initial product temperature Ti = 10 oC Air temperature T = -15 oC (Not – 40oC) Initial freezing temperature TF = -1.25 oC Product diameter a = 7 cm (0.07 m) Product density = 1000 kg/m3 Thermal conductivity of frozen product k = 1.2 W/m.k Latent heat HL = 250 kJ/kg Shape constants for spheres: P’ = 1/6, R’ = 1/24 Convective heat-transfer coefficient hc = 50 W/m2.k Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Example: Freezing time • Solution: calculate the freezing time tF will be o.72 hr if the if the air temperature is assumed - 40oC. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Plank's equation results in the under-estimation of freezing times because of the assumptions made in its derivation. • The initial freezing temperature (TF) for most foods is not reliably known. Although the initial freezing temperature is tabulated for many foods, the initial and final product temperatures are not accounted for in the computation of freezing times. • Also we often do not know for sure what values of ρf and kf to select. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Despite the limitations, Plank’s equation is the most popular method for predicting freezing time. • Most other available methods are based on the modification of Plank’s equation. • Because of data uncertainty alone, freezing time estimates should be treated as being accurate to within ±20% at best. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Pham (1986) presented an improvement of Plank’s equation for prediction of freezing times. The approach is based on the following equations: • The mean freezing temperature is defined as (7.8) where Tc is final center temperature and Ta is freezing medium temperature. The freezing time is given by (7.9) Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
where dc = characteristic dimension ‘r’ or shortest distance Ef = a shape factor (‘1’ for slab, ‘2’ for cylinder and ‘3’ for sphere) (7.10) (7.11) (7.12) (7.13) ΔH1 = Enthalpy change during pre-cooling, J/m3 ΔH2 = Enthalpy change during phase change and post- cooling period, J/m3 Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
Freezing Time of Finite Shaped Objects In Pham’s method, the value of Ef is adjusted (Eq. 7.16): Ef = G1 + G2E1 + G3E2 where the values of G1, G2 and G3 are given in Table 7.1 and E1 and E2 are calculated from Eqs. 7.17 & 7.19 and Eqs. 7.18 & 7.20, respectively. We can now follow Example 7.2 (Singh and Heldman) and compare the freezing time calculations based on Pham’s approach and Plank’s equation. Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal
