**THERMAL PROPERTIES(i)**

The transfer of heat is a very important factor to understand and to be able to control during the processing and storage of many food and agricultural products. There are a number of thermal properties that must be understood for the successful process design of all procedures that involve heating and cooling of foods.

Specific Heat

The most basic thermal property is specific heat (c_{p}). The p subscript
indicates that the value is the specific heat at constant pressure. The specific heat of
any material is the amount of heat required to raise one unit of mass of the material by
one degree. The most commonly used units for specific heat are kJ/(kg-K), Btu/(lb-F), and
cal/(g-K). An important equation relating specific heat, mass of the sample (M), the
amount of heat that must be added (Q), and the initial and final temperatures of the
sample (T1 and T2) is seen below.

There are several equations that can be used to predict unknown specific heats for food
and agricultural products. The first two equations are based on the wet basis moisture
content (M) of the product. Wet basis moisture content, introduced here, will be covered
more extensively in a later section. For the sake of these equations use wet basis
moisture content in decimal (rather than percentage) form. These equations predict
specific heat in kJ/(kg-K).

Above freezing: c_{p} = 0.837 + 3.348M

Below freezing: c_{p} = 0.837 + 1.256M

Another equation commonly used to estimate the specific heat for foods in kJ/(kg-K) takes into account the mass fraction (X) of all of the solids that compose the product. As seen as subscripts in the following equation, w is water, p protein, f fat, c carbohydrate, and a ash.

c_{p} = 4.180X_{w} + 1.711X_{p }+ 1.928X_{f} + 1.547X_{c}
+ 0.908X_{a}

Thermal Conductivity

Thermal conductivity (k) is another important thermal property. Normally expressed in the units W/(m-K) or Btu/(h-ft-F), it is a property that tells how well a material conducts heat. Heat conduction is the transfer of energy between neighboring molecules within a material. The following equation relates the thermal conductivity to the amount of heat that flows through the material per unit of time (dQ/dt), the cross sectional area of the material through which the heat flows (A), and the temperature difference per unit of length of the conducting material (dT/dx).

Thermal conductivity can be greatly influenced by a number of factors such as the water
content, porosity, and even fiber orientation of the material. However, there are a couple
of equations that allow for the estimation of k when experimental data are not available.
The following equation yields the best results when used at higher moisture contents. It
relates the weight fraction of water X_{w}, thermal conductivity of water k_{w},
and the thermal conductivity of the solids portion of the material k_{s}, which is
assumed to be 0.259 W/(m-K).

k = k_{w}X_{w} + k_{s}(1 – X_{w})

Below is another equation for estimating thermal conductivity. It is only considered useful for materials containing greater than 50% water.

k = 0.056 + 0.57 X_{w}

**Thermal Diffusivity**

Thermal Diffusivity (a) is a thermal property to describe a
homogeneous, isotropic material where k, r, and c_{p}
are constant throughout the material for the entire temperature range being considered.
This quantity reveals the material’s ability to conduct heat relative to its ability
to store heat. Thermal diffusivity is equal to k/(r*c_{p})
and is usually expressed in the units of m^{2}/s or ft^{2}/s. Its primary
use is in the following partial differential equation, Fourier’s general law of heat
conduction. This equation expresses the temperature (T) variation within a three
dimensional object (x,y,z)

Thermal Diffusivity can also be estimated based on the weight fraction of its water, fat,
protein, and carbohydrate components using the following equation.

a = 0.146*10^{-6}X_{w} + 0.100*10^{-6}X_{f
}+ 0.075*10^{-6}X_{p} + 0.082*10^{-6}X_{c}

**Latent Heat**

Latent heat (L) is the heat that is exchanged with a material during a phase change, when the heat exchanged does not result in a change in the temperature of the material. The units for latent heat are kJ/kg or Btu/lb. Latent heat is usually subdivided into latent heat of freezing and latent heat of vaporization. An example of latent heat of freezing is the 335 kJ that 1 kg of water releases while maintaining its temperature at 0 C when changing from the liquid to the solid state. Latent heat of vaporization is represented by the 2257 kJ that 1 kg of water must absorb while temperature remains constant at 100 C to evaporate from liquid into vapor. Latent heat can represent a huge expenditure of energy in food processing when freezing or evaporation is involved. Latent heat is best determined through experimentation, but it also can be estimated based on the mass fraction of water in the product.

L = 335X_{w}

_{Heat Capacity }

i. Stroshine and Hamann. 1994. Physical Properties of Agricultural Materials and Food Products. 143-150.