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## Lesson 11. THERMAL PROPERTIES OF FROZEN FOODS

**Module 2. Food freezing**

**Lesson 11**

**THERMAL PROPERTIES OF FROZEN FOODS**

**11.1 Introduction**

The food product properties of interest when considering the freezing process include density, specific heat, thermal conductivity, enthalpy, and latent heat. These properties must be considered in the estimation of the refrigeration capacity for the freezing system and the computation of freezing times needed to assure adequate residence times. The approach to prediction of property magnitudes during the freezing process depends directly on the relationship between unfrozen water fraction and temperature.

It is important to study thermal properties of foods because they affect the design of food processing equipment. The food products undergo changes in composition during such process as freezing, evaporation and dehydration. There are different methods available to measure the thermal properties of food, but the available data differ depending on the method used. The important thermal properties of food are as follows:

**11.2 Density**

The influence of freezing on food product density is relatively small but a dramatic change does occur at and just below the initial freezing temperature. This change can be predicted by the following equation, as discussed by Heldman (2001):

* ρ * = 1/ ∑ * ( ** m * si * /ρ * si * ) *

** 11.3 Specific Heat **

A measure of the heat required to raise the temperature of a substance. When the heat Δ*Q* is added to a body of mass *m*, raising its temperature by Δ*T*, the ratio *C* given in Eq. (1) is defined as the heat capacity of the body.

_{p}= ΔQ/ ΔT

The specific heat capacity of a food product can be predicted, based on product composition and the specific heat capacity of individual product components. The following expression was proposed:

* Cp * = ∑ * (C * psi. * m * si * ) *

where each factor on the right-side of the equation is the product of the mass fraction of a product component and the specific heat capacity of that component. The specific heat values for product components were estimated by Choi and Okos (1986). The above equation can be used to predict the specific heat capacity of product solids by removing the term for the water fraction. These specific heat magnitudes for the product solids can be used in the prediction of product enthalpy and apparent specific heat.

C_{p} = 4.180 X_{w} + 1.711 X_{p} + 1.98 X_{f} + 1.547 X_{c} + 0/908 X_{a, ; }kJ/kg^{0}C _{……….}Cho’s and Oko’s Model

Where, X_{w}: water fraction

Xp: Protein fraction

X_{f}: Fat fraction

X_{c: }Carbohydrate fraction

X_{A: }Ash fraction

** 11.4 Thermal Conductivity **

Thermal conductivity (λ) is the intrinsic property of a material which relates its ability to conduct heat. Heat transfer by conduction involves transfer of energy within a material without any motion of the material as a whole. Conduction takes place when a temperature gradient exists in a solid (or stationary fluid) medium. Conductive heat flow occurs in the direction of decreasing temperature because higher temperature equates to higher molecular energy or more molecular movement. Energy is transferred from the more energetic to the less energetic molecules when neighboring molecules collide.

Thermal conductivity is defined as the quantity of heat (* Q *) transmitted through a unit thickness (* L *) in a direction normal to a surface of unit area (* A *) due to a unit temperature gradient (Δ* T) * under steady state conditions and when the heat transfer is dependent only on the temperature gradient. In equation form this becomes the following:

Thermal Conductivity = heat × distance / (area × temperature gradient)

*λ*=

*Q*×

*L*/ (

*A*× Δ

*T*)

The thermal conductivity magnitudes of most food products are a function of water content and the physical structure of the product. Many models suggested for prediction of thermal conductivity are based on moisture content and do not consider structural orientation. The Choi’s and Oko’s Model for prediction of thermal conductivity is as follows.

K = 0.58 X_{w} + 0.155 X_{p} + 0.25 X_{c} + 0.16 X_{f} + 0.135 X_{a , }W/m ºK _{……….}Cho’s and Oko’s Model

Where, X_{w}: water fraction

Xp: Protein fraction

X_{f}: Fat fraction

X_{c: }Carbohydrate fraction

X_{a: }Ash fraction

11.5 ** Thermal Diffusivity**

A measure of the rate at which a temperature disturbance at one point in a body travels to another point. It is expressed by the relationship *K/dC _{p},* where

*K*is the coefficient of thermal conductivity,

*d*is the density, and

*C*is the specific heat at constant pressure. Very little thermal diffusivity data are available, but it can be determined using relationship of specific heat, thermal conductivity and mass density of the food product.

_{p}** 11.6 Freezing Point Depresssion**

Probably one of the more reveling properties of water in food is the freezing point depression. Since all food products contain relatively large amounts of moisture or water in which various solutes are present, the actual or initial freezing point of water in the product will be depressed to some level below that expected for pure water.

The magnitude of this freezing point depression becomes a direct function of the molecular weight and concentration of the solute in the food product and in solution in the water.

(W_{b} = molecular weight of component in solution, M_{B} = mass in kg)

R_{g} is gas constant

R_{g} = w × W_{A} = 0.462 × 18

R_{g} = 8.316 Joules/mole ^{o}C

W_{A} = molecular weight of water = 18 moles/gm

w = fraction of water

** 11.8 Thermodynamics of Food Freezing **

Freezing is one the more common processes for the preservation of foods. It is well known that lowering the temp reduces the activity of microorganisms and enzyme systems, thus preventing deterioration of the food products. In addition to the influence of temp reduction on m.o. and enzymes, crystallization of the water in the product tends to reduce the amount of liquid water in the system and inhibit microbial growth or enzyme activity in the secondary action.

The engineering aspects of food freezing include several interesting areas. In order to design a refrigeration system that will serve a food freezing process, some indication of the refrigeration requirements or enthalpy change which occurs during product freezing is required. This aspect is related to the type of product being frozen. The second aspect of food freezing that is closely related to engineering is the rate at which freezing progresses. This aspect is related to the refrigeration requirement, but the temperature difference existing between the product and freezing medium are also of significance. The rate of freezing is also closely related to product properties and quality. Product properties resulting from very rapid freezing are significantly different from those obtained by slow freezing. This difference is dependent primarily on the manner in which ice is formed within the product structure. In addition, the rate of freezing will establish the rate of production for a particular food- freezing operation. For this purpose the most rapid rate of freezing is desirable provided that product quality is not sacrifice.

**Examples**

**Example 11.1**

A formulated food product contains the following components – water 80%, protein 2%, carbohydrate 17%, fat 0.1% and ash 0.9%. Predict the specific heat in W/kg K using Choi’s and Oko’s model.

** Solution : **

C_{p} = 4.180 X_{w} + 1.711 X_{p} + 1.98 X_{f} + 1.547 X_{c} + 0/908 X_{a}

= 4.180 (0.8) + 1.711 (0.02) + 1.98 (0.001) + 1.547 (0.17) + 0.908 (0.009)

= 3.651 kJ/kg^{o}C

= 0.8726 kCal/kg^{o}C

= 1.0147 W/kg^{o}C

**Example 11.2**

Calculate the thermal conductivity of milk using choi & OKOS model, if milk contains 87.5% water, 3.7% protein, 3.7% fat, 4.6% lactose and 0.5% ash at 10^{0}C.

**Solution**

K = 0.58 X_{w} + 0.155 X_{p} + 0.25 X_{c} + 0.16 X_{f} + 0.135 X_{a}

= 0.58 (0.875) + 0.155 (0.037) + 0.25 (0.046) + 0.16 (0.037) + 0.135 (0.005)

= 0.49 + 0.005735 + 0.0115 + 0.00592 + 0.000675

= 0.51383 W/m ºK

**Example 11.3**

Compute the temperature at which ice formation begins in an ice cream mix with the following composition: 10% butter fat, 12% solids-not-fat, 15% sucrose and 0.22% stabilizer.

The solute accounted for in the ice-cream mix is sucrose (W = 342) and lactose (W = 342), which represents 54.5 % of the SNF in the mix. – Molality is computed as:

Fraction solute = 0.15 + 0.545(0.12) = 0.2154 g/ g product

When expressed in terms of water fraction (62.78%), thus 0.2154/0.6278 = 0.3431 g solute/g solvent or 343.1 g solute / 1000g solvent

And m = 343.1/342 = 1.003

Therefore initial ice formation will occur at (273-1.86) 271.14 K or - 1.86^{o}C