1. Thermal Properties and Moisture Diffusivity
BAE2023

2. Thermal Properties, Moisture Diffusivity
Processing and Storage of Ag Products
Heating
Cooling
Combination of heating and cooling
Grain dried for storage
Noodles dried
Fruits/Vegetables rapidly cooled
Vegetables are blanched, maybe cooked and canned
Powders such as spices and milk: dehydrated
Cooking, cooling, baking, pasteurization, freezing, dehydration: all involve heat transfer
Design of such processes require knowledge of thermal properties of material

3. Continue…. Heat is transferred by
Conduction: Temperature gradient exists within a body…heat transfer within the body
Convection: Heat transfer from one body to another by virtue that one body is moving relative to the other
Radiation: Transfer of heat from one body to another that are separated in space in a vacuum. (blackbody heat transfer)
We’ll consider
Conduction w/in the product
Convection: transfer by forced convection from product to moving fluid
Moisture movement through agricultural product is similar to movement of heat by conduction
Moisture diffusivity
Volume change due to moisture content change

4. Continue…. Terms used to define thermal properties Specific heat
Thermal conductivity
Thermal diffusivity
Thermal expansion coefficient
Surface heat transfer coefficient
Sensible and Latent heat
Enthalpy

5. Specific Heat
Specific Heat: Amount of heat required to raise temperature of unit amount of substance by one degree
Units:
𝐾𝐽 𝐾𝑔°𝐾 (SI System)
𝐵𝑇𝑈 lb°𝐹 (English System)
𝐶𝑎𝑙. 𝑔°𝐾 (if calories are used)
Conversion of units: 1 𝐾𝐽 𝐾𝑔°𝐾 = 𝐵𝑇𝑈 lb°𝐹 =0.239 𝐶𝑎𝑙. 𝑔°𝐾

6. Specific Heat Q = M Cp (T2-T1)
Once Specific heat of material is known, then the amount of heat (Q) needed to increase temp. from T1 to T2 is calculated by:
Q = M Cp (T2-T1)
Where,
Q = quantity of heat required to change temperature of a mass
Cp = Specific heat at constant pressure
M = mass or weight
Water is a major component of all agricultural products
Cp of water = = 1
Cp of oils and fats = ½ of Cp of water ………See Table 8.1 pg. 219
Cp of grains, powders = ¼ to 1/3 of Cp of water
Cp of ice = ½ Cp of H2O ( therefore, less heat required to raise temp. of frozen product then the same product when it is thawed)

7. Specific heat Eq. for calculating Cp based on moisture Content
For liquid H2O
Cp = M above freezing
For solid H2O
Cp = M below freezing
Eq. based on composition
Cp=4.18Xw+1.711Xp+1.928Xf Xc+0.908Xa
X is the mass or weight fraction of each component
The subscript denote following components: w=water, p= protein, f=fat, c= carbohydrate, a=ash

8. Thermal Conductivity (k)
Measure of ability to transmit heat
= -k A
K= coefficient of thermal conductivity
For one dimensional heat flow in x direction, k is numerically equal to the quantity of heat (Q) that will flow across a unit cross sectional area (A) per unit of time (t) in response to a temperature gradient () of 1 degree per unit distance in x direction
Units:
(SI system)
(English System) 1 = 1.731

9. Thermal Conductivity (k)
k water =0.566 at 0°C
= at 20°C
= at 60°C
At room temp. value of k for endosperm of cereal grains, flesh of fruits and veg., dairy products, fats and oil and sugar are less than that of water.
Higher the moisture content higher will be thermal conductivity of food product
Another factor is porosity e.g. freeze dried products and porous fruits like apple have low thermal conductivity.

10. Thermal Conductivity (k)
If we don’t know thermal conductivity, approximate using... K = kw Xw + ks(1-Xw) Where, Kw =Thermal conductivity of water Xw= Weight fraction of water Ks = Thermal conductivity of solids = 𝑊 m°𝐾 If the moisture in product is more than 50%, then K = Xw

11. Thermal Diffusivity (α)
α quantifies the materials ability to conduct heat relative to its ability to store heat.
α =
Where,
α = Thermal Diffusivity, Units () or ()
k = Thermal conductivity
= density of material
= Specific heat at constant pressure
Example : Estimate the thermal diffusivity of a peach at 22 C.

12. Surface heat transfer coefficient (h)
When a body is placed in flowing stream of liquid or gas, the body’s temperature will change until it eventually reaches in equilibrium with the fluid. In eq. form also known as Newton’s Law of cooling
𝑑𝑄 𝑑𝑡 = h A (Tf- Ts)
Where,
h = surface heat transfer coefficient and has same units as k i.e. 𝑊 m°𝐾
Tf = temp. of fluid
Ts = temp of solid body
h depends on fluid velocity, surface characteristics of solids, size and shape of solid and fluid properties ( density and viscosity)
Difficult to tabulate value of h, therefore experimentally determined

13. Sensible and Latent heat
Sensible heat: Temperature that can be sensed by touch or measured with a thermometer. Temperature change due to heat transfer into or out of product Latent heat: Transfer of heat energy with no accompanying change in temperature. Happens during a phase change...solid to liquid...liquid to gas...solid to gas

14. Latent heat (L) Latent Heat, L, (kJ/kg or BTU/lb)
Heat that is exchanged during a change in phase
Dominated by the moisture content of foods
Requires more energy to freeze foods than to cool foods (90kJ removed to lower 1 kg of water from room T to 0 °C and 4x that amount to freeze food)
420 kJ to raise T of water from 0 ° C to 100 ° C, 5x that to evaporate 1 kg of water
Heat of vaporization is about 7x greater than heat of
fusion (freezing)
Therefore, evaporation of water is energy intensive (concentrating juices, dehydrating foods…)

15. Latent heat (L)
Determine L experimentally when possible. When data is not available (no tables, etc) use…. L = 335 Xw where Xw is weight fraction of water Many fruits, vegetables, dairy products, meats and nuts are given in ASHRAE Handbook of Fundamentals

16. Enthalpy (h) Units: (kJ/kg or BTU/lb) Heat content of a material.
Used frequently to evaluate changes in heat content of steam or moist air
Combines latent heat and sensible heat changes
ΔQ = M(h2-h1)
Where,
ΔQ = amount of heat needed to raise temperature from T1 to T2
M = mass of product
h2= enthalpy at temp T1
h1 = enthalpy at temp T2

17. Enthalpy (h)
Approach useful when one of the temperatures is below freezing
Measurements based on zero values of enthalpy at a specified temperature e.g. at - 40°C, -18°C or 0°C.
Enthalpy changes rapidly near the freezing point
Change in enthalpy of a frozen food can be calculated from eq. below:
Δh = M cp(T2 – T1) + MXw L
Xw is the mass fraction of water that undergoes phase change(frozen fraction)
L is the latent heat of fusion of water
M is the mass of product
Δh = Change in enthalpy of frozen food

18. Example
Example 8.3: Calculate the amount of heat which must be removed from 1 kg of raspberries when their temperature is reduced from 25C to -5C. Assume that the specific heat of raspberries above freezing is 3.7 kJ/kgC and their specific heat below freezing is 1.86 kJ/kgC. The moisture content of the raspberries is 81% and the ASHRAE tables for freezing of fruits and vegs. Indicate that at -5C, 27% will not yet be frozen.

19. Homework Assignment Due February 20th
Problem 1: Determine the amount of heat removed from 1.5 kg of bologna (sausage) when cooled from 24C to -7C. Assume MC of 59% and at -7C, 22% won’t be frozen. Problem 2: Estimate the thermal diffusivity of butter at 20°C.