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## Lesson 21. DESIGN PROBLEMS ON CONTINUOUS FREEZERS

*Module 2. Food freezing*

**Lesson 21**

**DESIGN PROBLEMS ON CONTINUOUS FREEZERS**

** 21.1 Introduction**

In the design of freezing systems, it is necessary to know the amount of energy that should be eliminated from the food to change from the initial to the final temperature of the frozen product. To do this, one must know the enthalpy of the food at the beginning and end of the freezing process. Since enthalpy is a function of state, it should be given with respect to a reference temperature that, in the case of freezing processes, is –40°C. This means that, at this temperature, the enthalpy of any product is considered null. In order to calculate the power needed to carry out the freezing process, it is necessary to determine the variation of enthalpy experienced by the product, since it is introduced in the freezer until the product reaches the final temperature. This can be achieved by using Equation 17.1. Another factor that should be calculated is the power that the freezing equipment should have to perform a given process. Such power is the total energy to be eliminated from the food per unit time and a measure of the capacity of the freezing system. Freezing power is calculated by the following equation:

Pow = m ΔH/t…………..Eq. 21.1

Here, * m *is the total quantity of food to be frozen, Δ*H *the increase of enthalpy experienced by the food from the initial to the final temperature, and * t *the time the food stays in the freezing equipment.

One of the basic considerations in the design of a system for the freezing process is the refrigeration requirement for reducing the food product temperature to the desired level. The enthalpy changes required will reduce the product from some temperature above the freezing point to some temperature below the freezing point and can be represented by

ΔH = ΔHs + ΔHu + ΔH_{L} + ΔH_{F}

where the terms on right hand side represent the sensible heat required to reduce the product temperature to the initial freezing point ( ΔH_{F}), the sensible heat removed to reduce the unfrozen portion of the product to the storage temperature( ΔH_{u}), the latent heat removed (ΔH_{L}), and the sensible heat removed to reduce the frozen portion of the product to the storage temperature( ΔH_{F}).

Sensible heat ΔHs is given by,

ΔHs = M Cp (Ti-T_{F}) where T_{F} = freezing point temperature

Evaluation of other components is somewhat complex because of changing state of product below initial freezing point. Mass of unfrozen product and frozen product are changing and are temperature dependant. Enthalpy change required to reduce the unfrozen portion of the product to various temperatures below initial freezing point, T_{F} is given by:

ΔH_{u} = M_{u }(T) C_{p},_{u} (T) (T_{F}-T)

Similarly,

ΔH_{F} = M_{F} (T) C_{p}, F (T_{F}-T)

these equations can between in differential form as:

ΔH_{u} = M_{u} (T) C_{p},_{u}(T) dT and

ΔH_{F } = M_{F }(T) C_{p},_{ F} dT

Latent heat portion is given by:

ΔH_{L} = M_{F} (T) L

Unfrozen and frozen portions of product at any temperature below the initial freezing point can be calculated by

ln X_{A} = λ’/R_{g} (1/T_{Ao} – 1/T_{A})

Where, T_{Ao} - freezing point of pure liquid, K

X_{A} - is mole fraction of water in solution

R_{g} - gas constant , 8.314 kJ/kg mol K.

T_{A} - absolute temperature of solute , K

λ’ - Latent heat of fusion, J/mol (6003 J/mol for dilute liquids)

After obtaining information on the frozen and unfrozen fractions as function of temperature and specific heat of unfrozen fraction the above equations can be evaluated by integration.