UNIT 1

Principles of Heat and

Mass Transfer

UNIT 1 PRINCIPLES OF HEAT AND MASS

TRANSFER

Structure

1.0 Objectives

1.1 Introduction

1.2 Heat Transfer System

Conduction

Convection

Radiation

Overall Heat Transfer Coefficients

Heat Transfer from Condensing Vapours

Heat Transfer to Boiling Liquids

1.3 Type of Food for Heat Processing

1.4 Heat Penetration

1.5 Heat Transfer Characteristics of Food

1.6 Devices for Determination of Heat Penetration

1.7 Determination of Cold Point in a Food Container

1.8 Calculation of Process Time

1.9 Factors Affecting Heat Penetration

1.10 Let Us Sum Up

1.11 Key Words

1.12 Answers to Check Your Progress Exercises

1.13 Some Useful Books

1.0 OBJECTIVES

By the time you have studied this unit, you should be able to:

• define the basic principles and methods of heat transfer;

• explain the role of heat transfer in heat preservation processes;

• identify the type of food for heat processing;

• determine the heat penetration and calculate the process time in a food;

and

• identify the factors affecting heat transfer and apply corrective measures to

enhance the process of heat transfer.

1.1 INTRODUCTION

Heat transfer is an important operation in the food industry. Whether it is

called cooking, baking, drying, sterilizing or freezing, heat transfer is part of

processing of almost every food. Heat transfer is a dynamic process in which

heat is transferred spontaneously from one body to another cooler body. The

rate of heat transfer depends upon the differences in temperature between the

bodies, the greater the difference in temperature, the greater will be the rate of

heat transfer.

Temperature difference between the source of heat and the receiver of heat is,

therefore, the driving force in heat transfer. An increase in the temperature

difference increases the driving force and, thus the rate of heat transfer. The

heat passing from one body to another travels through some medium, which in

general offers resistance to the heat flow. Both these factors, the temperature

difference and the resistance to heat flow, affect the rate of heat transfer.

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Food Preservation by

Application of Heat

1.2 HEAT TRANSFER SYSTEM

Heat can be transferred from one object to another in three ways: by

conduction, by convection and by radiation.

Conduction is the movement of heat by direct transfer of molecular energy

within solids. The molecules with greater energy communicating some of this

energy to neighbouring molecules with less energy. An example of conduction

is the heat transfer through the solid walls of a refrigerated store.

Convection is the transfer of heat by the movement of groups of molecules in

a fluid. The groups of molecules may be moved by either density changes or

by forced motion of the fluid. An example of convection heating is cooking in

a jacketed pan: without a stirrer, density changes cause heat transfer by natural

convection; while with a stirrer, the convection is forced.

Radiation is the transfer of heat energy by electromagnetic waves, which

transfer heat from one body to another, in the same way as electromagnetic

light waves transfer light energy. An example of radiant heat transfer is when

a foodstuff is passed below a bank of electric resistance heaters that are red-

hot (electric grill).

In general, heat is transferred in solids by conduction and in fluids by

conduction and convection (Figure 1.1). Heat transfer by radiation occurs

through open space, can often be neglected, and is most significant when

temperature differences are substantial. In practice, the three types of heat

transfer may occur simultaneously. For calculations it is often best to consider

the mechanisms separately, and then to combine them where necessary.

(a) (b)

Figure 1.1: Heat transfer in containers by (a) conduction and (b) convection

1.2.1 Conduction

In the case of heat conduction, the equation, heat transfer rate = driving

force/resistance, can be applied directly. The driving force is the temperature

difference per unit length of heat-transfer path, i.e., temperature gradient.

Instead of resistance to heat flow, its reciprocal, conductance, is used. This

changes the form of the general equation to:

Rate of heat transfer = driving force x conductance, which is:

dQ/dt = kA dT/dT x (1.1)

8

Principles of Heat and

Mass Transfer

Where, dQ/dt (JS

−1

)is the rate of heat transfer, the quantity of heat energy

transferred per unit of time, A (m

2

)is the area of cross-section of the heat flow

path, dT/dT x ( Cm )is the temperature gradient, that is the rate of change of

temperature per unit length of path, and

0 −1

k (Jm s K or Wm K )is the

thermal conductivity of the medium. Notice the distinction between thermal

conductance, which relates to the actual thickness of a given material (

−1 −1 0 −1 0 −1

k/x) and

thermal conductivity, which relates only to unit thickness. Eq. (1.1) is known

as the Fourier equation for heat conduction.

Thermal conductivity does change slightly with temperature, but in many

applications it can be regarded as a constant for a given material. Most

foodstuffs contain a high proportion of water and as the thermal conductivity

of water is about 0.7 J m

−1

s

−1

°C

-1

above 0°C, thermal conductivities of foods

are in the range 0.6-0.7 J m

−1

s

-1

°C

−1

. Ice has a substantially higher thermal

conductivity than water, about 2.3 J m

−1

s

−1

°C

−1

. The thermal conductivity of

frozen foods is, therefore, higher than foods at normal temperatures.

1.2.2 Convection

Convection heat transfer is the transfer of energy by the mass movement of

groups of molecules. It is restricted to liquids and gases, as mass molecular

movement does not occur at an appreciable speed in solids. It cannot be

mathematically predicted as easily as can transfer by conduction or radiation

and so its study is largely based on experimental results rather than on theory.

Newton found, experimentally, that the rate of cooling of the surface of a

solid, immersed in a colder fluid, was proportional to the difference between

the temperature of the surface of the solid and the temperature of the cooling

fluid. This is known as Newton's Law of Cooling, and it can be expressed by

the following equation.

q = h

s

A(T – T

a

TT

s

) (1.2)

Where, h

s

is called the surface heat-transfer coefficient, T is the temperature

of the cooling fluid and

T

a

TT

s

is the temperature at the surface of the solid. The

surface heat-transfer coefficient can be regarded as the conductance of a

hypothetical surface film of the cooling medium of thickness

x

f

such that

h

s

= k

f

/x

f

Where, k

f

is the thermal conductivity of the cooling medium. It is useful at

this point, however, to appreciate the magnitude of h

s

under various common

conditions and these are shown in Table 1.1.

Table 1.1: Approximate range of surface heat transfer coefficients

hs (J m

−2

s

−1

°C

−1

)

Boiling liquids 2400-24,000

Condensing liquids 1800-18,000

Still air 6

Moving air (3 m s

−1

)

30

Liquids flowing through pipes 1200-6000

1.2.3 Radiation

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Food Preservation by

Application of Heat

Radiation heat transfer is the transfer of heat energy by electromagnetic

radiation. Radiation operates independently of the medium through which it

occurs and depends upon the relative temperatures, geometric arrangements

and surface structures of the materials that are emitting or absorbing heat.

Radiation of wavelength 0.8-400 µm (infrared) is referred to as thermal

radiation or heat rays since electro magnetic radiation with this wavelength is

most readily absorbed and converted to heat energy. The infrared radiation is

used primarily for surface heating as it is transmitted rapidly to the surface. It

is used for dehydration of fruits and vegetables, freeze drying, baking, etc.

Radiation can be significant with small temperature differences as, for

example, in freeze-drying and in cold stores, but it is generally more important

where the temperature differences are greater. Under these circumstances, it is

often the most significant mode of heat transfer, for example in bakers' ovens

and in radiant driers.

The basic formula for radiant-heat transfer is the Stefan-Boltzmann Law

q = A σT

4

(1.3)

Where, T is the absolute temperature (measured from the absolute

zero of temperature at −273°C, and indicated in Bold type) in degrees

Kelvin (K) in the SI system, and  (sigma) is the Stefan-Boltzmann constant

= 5.73 × 10

−8

J m

−2

s

−1

K

−4

The absolute temperatures are calculated by the

formula K = (°C+273).

This law gives the radiation emitted by a perfect radiator (a black body as this

is called though it could be a red-hot wire in actuality). A black body gives the

maximum amount of emitted radiation possible at its particular temperature.

Real surfaces at a temperature T do not emit as much energy as predicted by

Eq. (1.3), but it has been found that many emit a constant fraction of it. For

these real bodies, including foods and equipment surfaces, that emit a constant

fraction of the radiation from a black body, the equation can be rewritten

q

= εA σT

4

(1.4)

Where, ε (epsilon) is called the emissivity of the particular body and is a

number between 0 and 1. Bodies obeying this equation are called grey bodies.

Emissivities vary with the temperature T and with the wavelength of the

radiation emitted. For many purposes, it is sufficient to assume that for:

* dull black surfaces (lamp-black or burnt toast, for example), emissivity is

approximately 1;

* surfaces such as paper/painted metal/wood and most foods, emissivities

are about 0.9;

* rough un-polished metal surfaces, emissivities vary from 0.7 to 0.25;

* polished metal surfaces, emissivities are about or below 0.05.

These values apply at the low and moderate temperatures, which are those

encountered in food processing. Just as a black body emits radiation, it also

absorbs it and according to the same law, Eq. (1.3). Again grey bodies absorb

a fraction of the quantity that a black body would absorb, corresponding this

time to their absorptivity α (alpha). For grey bodies it can be shown that α =

ε. The fraction of the incident radiation that is not absorbed is reflected, and

thus, there is a further term used, the reflectivity, which is equal to (1 – α).

The radiant energy transferred between two surfaces depends upon their

temperatures, the geometric arrangement, and their emissivities. For two

10

Principles of Heat and

Mass Transfer

parallel surfaces, facing each other and neglecting edge effects, each must

intercept the total energy emitted by the other, either absorbing or reflecting it.

In this case, the net heat transferred from the hotter to the cooler surface is

given by:

q = ACσ (T − T

1

4

TT

2

4

) (1.5)

where 1/C = 1/ε

1

+ 1/ε

2

− 1, ε

1

is the emissivity of the surface at temperature

T and ε is the emissivity of the surface at temperature T

1 2

TT

2

.

1.2.4 Overall Heat Transfer Coefficients

It is most convenient to use overall heat transfer coefficients in heat transfer

calculations as these combine all of the constituent factors into one, and are

based on the overall temperature drop. Radiation coefficients, subject to the

limitations discussed in the section on radiation, can be incorporated in the

overall coefficient. The radiation coefficients should be combined with the

convection coefficient to give a total surface coefficient, as they are in series,

and so:

h

s

= (h

r

+ h

c

) (1.6)

The overall coefficient U for a composite system, consisting of surface film,

composite wall, surface film, in series, can then be calculated as:

1/U = 1/(h

r

+ h

c

)

1

+ x

1

/k

1

+ x

2

/k

2

+ …+ 1/(h

r

+ h

c

)

2

(1.7)

In Eq. (1.7) often one or two terms are much more important than other terms

because of their numerical values. In such a case, the important terms,

signifying the low thermal conductance are said to be the controlling terms.

1.2.5 Heat Transfer from Condensing Vapours

The rate of heat transfer obtained when a vapour is condensing to a liquid is

very often important. In particular, it occurs in the food industry in steam-

heated vessels where the steam condenses and gives up its heat; and in

distillation and evaporation where the vapours produced must be condensed.

In condensation, the latent heat of vaporization is given up at constant

temperature, the boiling temperature of the liquid. Two generalized equations

have been obtained:

1) For condensation on vertical tubes or plane surfaces

h

v

= 0.94 [(k

3

ρ

2

g/μ) × (λ/LΔT)]

0.25

(1.8)

Where, λ (lambda) is the latent heat of the condensing liquid in J kg

−1

, L is

the height of the plate or tube and the other symbols have their usual

meanings.

2) For condensation on a horizontal tube

h

= 0.72 [(k

3

ρ

2

g/μ) × (λ/DΔT)]

0.25

(1.9)

1.2.6 Heat Transfer to Boiling Liquids

When the presence of a heated surface causes a liquid near it to boil, the

intense agitation gives rise to high local coefficients of heat transfer. A

considerable amount of experimental work has been carried out on this, but

generalized correlations are still not very adequate. It has been found that the

11

Food Preservation by

Application of Heat

apparent coefficient varies considerably with the temperature difference

between the heating surface and the liquid. For temperature differences greater

than about 20°C, values of h decrease, apparently because of blanketing of the

heating surface by vapours. Over the range of temperature differences from 1

to 20°C, values of h for boiling water increase from 1200 to about 60,000 J

m

−2

s

−1

°C

−1

. For boiling water under atmospheric pressure, the following

equation is approximately true:

h = 50(ΔT)

2.5

(1.10)

Where, ΔT is the difference between the surface temperature and the

temperature of the boiling liquid and it lies between 2 and 20°C. In many

applications the high boiling film coefficients are not of much consequence, as

resistance in the heat source controls the overall coefficients.

#

Check Your Progress Exercise 1

Note: a) Use the space below for your answer.

b) Compare your answers with those given at the end of the unit.

1. List the different methods of heat transfer.

………………………………………………………………………………

2. What is the relationship of conduction heat transfer rate with temperature

difference? What is the name of the equation used for determining the

conduction heat transfer rate?

………………………………………………………………………………

3. What is the name of the equation used for expressing the radiative flux

from an object? How is it related to temperature and properties of the

material?

………………………………………………………………………………

12

Principles of Heat and

Mass Transfer

………………………………………………………………………………

4. While estimating the rate of heat transfer between two objects, the

temperature of one of the objects is doubled. If convection and radiation

are the two modes of heat transfer between the two objects, which mode

would increase more and why?

………………………………………………………………………………

1.3 TYPE OF FOOD FOR HEAT PROCESSING

There are essentially two types of food when we talk of thermal processing:

1. Acid foods

2. Low acid foods

These two categories of foods differ significantly in their behaviour when

thermally processed. The acidity of the food, using the pH scale as a measure

of acidity, where 1 = very high acid and 4 = very low acid; the dividing line

for acid

foods and low-acid foods is pH 4.6. Acid foods can be canned at a

temperature of 100°C, while low-acid

foods must be pressure canned (to a

temperature of 115°C). The reason for this is that the toxin-producing,

potentially lethal organism, Clostridium botulinum, will not grow and produce

toxins at a pH below 4.6. Many spoilage microorganisms will not grow

between pH 1 and 4.6 either. The most common spoilage microorganisms

associated with acid foods are yeasts and moulds that can tolerate acid

environments.

1. Acid foods

High acid foods contain more natural acids. Many fruits are high acid

foods and the presence of these natural acids helps prevent growth of some

spoilage microorganisms. If the food product has a high enough acid level,

boiling-water temperatures are high enough to destroy spoilage organisms.

This is a prevention method for the deadly Clostridium botulinum bacteria.

2. Low acid foods

Low acid foods, such as vegetables and meat products, contain very little

natural acid. They must be processed at higher temperatures than boiling-

water to destroy any Clostridium botulinum bacteria. Water boils at

100°C, at sea level, and at a lower temperature at higher elevations.

Turning up the temperature under the pot or letting the water boil for a

13

Food Preservation by

Application of Heat

longer time does not raise the temperature of the water above its boiling

point. To make water boil at a higher temperature, it has to be put under

pressure, such as in a pressure canner. When a food is processed at 1.0

kg/cm

2

pressure, the water boils when it gets to 115°C, rather than at

100°C. This is high enough to kill the bacteria that causes botulism

poisoning.

Adjust for Altitude to Ensure Safety

The above values of temperatures have been determined for mean sea level.

As we move up the mountains, the atmospheric pressure goes down and water

boils at lower temperatures as altitude increases. Lower boiling temperatures

are less effective for killing bacteria. You must increase either the process

time or canner pressure to make up for lower boiling temperatures.

Because altitude affects pressure and the boiling point of liquid, adjustments

must be made when canning foods at altitudes of 300 m above sea level or

higher. When using the boiling water bath method, processing time must be

increased. Add 5 minutes to processing time for altitudes between 300 m and

1500 m above sea level. When using the pressure canner method, pressure

must be increased. If using a dial-gauge pressure canner, process foods at 0.8

bar pressure for altitudes between 600 m and 1200 m and at 0.9 bar pressure

for altitudes between 1200 m and 1800 m. If using the weight-gauge pressure

canner, use 1.0 bar of pressure.

When you mix low-acid and acid foods, assume that the mixture remains low-

acid. Although tomatoes used to be considered an acid food, some are now

known to have pH values slightly above 4.6, which means they are low-acid.

To safely can them as acid foods in a boiling-water canner, you must add

lemon juice or citric acid.

#

Check Your Progress Exercise 2

Note: a) Use the space below for your answer.

b) Compare your answers with those given at the end of the unit.

1. How are acid and low-acid foods distinguished?

………………………………………………………………………………

2. How is a thermal process for an acid food different than that for a low-acid

food?

………………………………………………………………………………

14

Principles of Heat and

Mass Transfer

3. What is the method used to raise the boiling point of water in food

processing?

………………………………………………………………………………

4. What changes are required for thermal processing of foods at high

altitudes?

………………………………………………………………………………

1.4 HEAT PENETRATION

Heat penetration studies are required to be conducted for verifying the

sterilizing temperature of a load (food) meant for moist heat sterilization.

These studies are conducted to ensure that the coolest unit within a pre-

defined loading pattern (including minimum and maximum loads) will

consistently be exposed to sufficient heat lethality (minimum “F”).

Heat penetration curve can be drawn by plotting the logarithmic difference

between either retort temperature and product temperature (heating curve) or

product temperature and cooling medium temperature (cooling curve) versus

time. The purpose of a heat-penetration study is to determine the heating and

cooling behaviour of a product/package combination in a specific retort

system for the establishment of safe thermal processes and evaluating process

deviations. The study is designed to adequately and accurately examine all

critical factors associated with the product, package and process, which affect

heating rates. A goal in conducting these studies is to identify the worst-case

temperature response expected to occur in commercial production as

influenced by the product, package and process.

Several product, process, package and measurement-related factors can

contribute to variations in the time-temperature data gathered during a heat-

penetration test. Establishment of a process requires expert judgment and

sound experimental data for determining which factors are critical and the

effect of changing those factors both within and beyond established critical

limits.

A typical heat penetration curve is shown in Figure 1.2. A broken heating

curve occurs when a food is initially heated by convective heating but then

undergoes a rapid transition to conductive heating (for example in foods,

which contain high concentration of starch, which undergoes a sol-to-gel

transition).

15

Food Preservation by

Application of Heat

Figure 1.2: Heat penetration curve

There are a number of ways of estimating how effective heat sterilization can

be. The thermal death time is the time microbes must be exposed to a

particular temperature before they are all dead. Similarly, the thermal death

point is the temperature at which all microbes in a sample are killed. Both are

very unsatisfactory, since they depend on many factors such as number of

microbes present in a sample, analytical conditions and techniques, etc.

1.5 HEAT TRANSFER CHARACTERISTICS OF FOOD

It is necessary to have information on both the heat resistance of

microorganisms or enzymes and the rate of heat penetration into the food for

determination of process time of a food.

Heat is transferred from steam or pressurized water through the container and

into the food. Generally the surface heat transfer coefficient is very high and is

not a limiting factor in heat transfer. The following factors influence the rate

of heat penetration into a food:

i) Type of product

ii) Size of the container

iii) Agitation of the container

iv) Temperature of the retort

v) Shape of the container. Tall containers promote convection currents in

convective heating foods.

vi) Type of container. Heat penetration is faster through metal than through

glass or plastics owing to differences in thermal conductivity.

In this section, the objective is to learn as to how the thermal properties of

food products affect the heat penetration and the quantity of heat. Two thermal

properties of importance are thermal conductivity and thermal diffusivity in

determining heat penetration. Specific heat and latent heat are important in

determining the quantity of heat required for the process

.

I. Thermal conductivity is the property indicating the rate at which heat

flows through a food product. A product with high thermal conductivity

lets the heat flow easily, whereas a material with low thermal conductivity,

also known as an insulator, puts resistance to the flow of heat. Fourier’s

heat conduction equation could be used to derive the units of thermal

conductivity, i.e., W/(m°C). It does change slightly with temperature, but

16

Principles of Heat and

Mass Transfer

in many applications it can be regarded as a constant for a given material.

Most foodstuffs contain a high proportion of water and as the thermal

conductivity of water is about 0.7 J m

−1

s

−1

°C

−1

above 0°C, thermal

conductivities of foods are in the range of 0.6-0.7 J m

−1

s

−1

°C

−1

. Ice has a

substantially higher thermal conductivity than water, about 2.3 J m

−1

s

−1

°C

−1

. The thermal conductivity of frozen foods is, therefore, higher than

foods at normal temperatures.

Typical thermal conductivities

Metals: k = 50-400 W/m°C

Water: k = 0.597 W/m°C

Air: k = 0.0251 W/m°C

Insulating materials: k = 0.035 - 0.173 W/m°C

For foods it is represented as

k = 0.25 m

c

+ 0.155 m

p

+ 0.16 m

f

+ 0.135 m

a

+ 0.58 m

m

Where m is mass fraction and subscripts c: carbohydrate, p: protein, f: fat,

a: ash and m: moisture.

or

k = 0.55p/100 + 0.26(100−p)/l00 J m

−1

s

−1

°C

−1

above freezing

= 2.4p/100 + 0.26(100 -p)/l00 J m

−1

s

-1

°C

−1

below freezing.

Where p is the percentage of water in the foodstuff.

II. Thermal diffusivity is the actual ability of a food to conduct heat to

adjacent molecules. Thermal diffusivity is a derived property that is the

ratio of thermal conductivity and the product of density and specific heat.

The units of thermal diffusivity, therefore, work out to be m

2

/s. Higher

value of thermal diffusivity means faster heat penetration and vice versa.

III. Specific heat: The specific heat is an important quantity that determines

the amount of energy that must be supplied or withdrawn from a unit mass

of material in order to increase or decrease its temperature by one degree.

Knowledge of the specific heat of a material is, therefore, important in the

design of processes such as chilling, freezing, warming, sterilization and

cooking. Specific heat has the units of kJ/(kg.K) in SI system of units.

Specific heat = 4.19p/100 + 0.84(100 − p)/100 kJ kg

−1

°C

−1

above freezing

= 2.1 p/100 + 0.84(100 − p)/100 kJ kg

−1

°C

−1

below freezing.

p is percentage of water in food stuff

IV. Phase transitions: It is important to determine the temperature at which

transitions occur, the enthalpy change associated with a transition, the type

of transition involved (exothermic or endothermic), and the quantity of

material that undergoes a transition. As an example, we will consider the

melting and crystallization of food components. When a material changes

its physical state from solid-to-liquid (melting) or from liquid-to-solid

(crystallization) it absorbs or gives out heat, respectively. A process that

absorbs heat is an endothermic process, whereas a process that evolves

heat is an exothermic process. Pure substances usually have very sharp

melting or crystallization points and, therefore, all the heat is absorbed or

evolved over a narrow range of temperature. Most foods are complex

17

Food Preservation by

Application of Heat

materials and, therefore, do not exhibit sharp transitions from one phase to

another. The amount of heat required for the phase change is called the

latent heat and has the units of kJ/kg.

Latent heat = 335p/100 kJ kg

−1

This equation and the ones given earlier for thermal conductivity and

specific heat represent a considerable over-simplification so they should be

used with caution, particularly in the region between −18°C to 0°C.

Freezing of foodstuffs occur over a range of temperatures and not at any

fixed point.

Some properties of liquids and thermal data for food products are depicted in

Tables 1.2 and 1.3, respectively.

Table 1.2: Some properties of liquids

Thermal

conductivity

Specific

heat

Density Viscosity Temperature

(J m

−1

s

−1

°C

−1

)

(kJ kg

−1

°C

−1

)

(kg m

−3

) (N s m

−2

)

(°C)

Water 0.57 4.21 1000

1.87 × 10

−3

0

4.21 987

0.56 × 10

−3

50

0.68 4.18 958

0.28 × 10

−3

100

Sucrose

20% soln.

0.54 3.8 1070

1.92 × 10

−3

20

0.59 × 10

−3

80

60% soln.

6.2 × 10

−3

20

5.4 × 10

−3

80

Sodium

chloride

22% soln.

0.54 3.4 1240

2.7 × 10

−3

2

Acetic

acid

0.17 2.2 1050

1.2 × 10

−3

20

Ethyl

alcohol

0.18 2.3 790

1.2 × 10

−3

20

Glycerine 0.28 2.4 1250

830 × 10

−3

20

Olive oil 0.17 2.0 910

84 × 10

−3

20

Rape-seed

oil

900

118 × 10

−3

20

Soya-bean

oil

910

40 × 10

−3

30

Tallow 900

18 × 10

−3

65

18

Principles of Heat and

Mass Transfer

Milk

(whole)

0.56 3.9 1030

2.12 × 10

−3

20

Milk

(skim)

1040

1.4 × 10

−3

25

Cream

20% fat

1010

6.2 × 10

−3

3

30% fat 1000

13.8 × 10

−3

3

Table 1.3: Thermal data for some food products

Specific heat

Above

freezing

Below

freezing

Freezing

point (°C)

Percent

water

(kJ kg

-1

°C

-1

)

Latent heat of

fusion

(kJ kg

−1

)

Fruit

Apples

−2

84 3.60 1.88 280

Bananas

−2

75 3.35 1.76 255

Grapefruit

−2

89 3.81 1.93 293

Peaches

−2

87 3.78 1.93 289

Pineapples

−2

85 3.68 1.88 285

Watermelons

−2

92 4.06 2.01 306

Vegetables

Asparagus

−1

93 3.93 2.01 310

Beans (green)

−1

89 3.81 1.97 297

Cabbage

−1

92 3.93 1.97 306

Carrots

−1

88 3.60 1.88 293

Corn

−1

76 3.35 1.80 251

Peas

−1

74 3.31 1.76 247

Tomatoes

−1

95 3.98 2.01 310

Water 0 100 4.19 2.05 335

1.6 DEVICES FOR DETERMINATION OF HEAT

PENETRATION

There are different types of thermometers available for measuring the

temperature in a thermal process and, thereby, permitting the determination of

heat penetration.

I. Mercury-in-glass (MIG) thermometer

Each retort system used for the thermal processing is equipped with a MIG

thermometer. Aseptic processing systems may have a temperature

indicating device other than MIG thermometer as the sole temperature

indicator. The MIG thermometer is the reference instrument for all

temperature readings, including vent temperature, come-up temperature

and process temperature during processing.

It is important that the MIG thermometer be tested/calibrated at the

operating temperature of the retort system (i.e., 115C, 120C, 125C

19

Food Preservation by

Application of Heat

etc.) and if possible in the heating medium used in the retort. If the retort is

operated at more than one processing temperature or over a wide range of

temperatures the MIG thermometer should be checked at all of the

temperatures normally used for processing. The MIG thermometers should

be tested against a thermometer that can be traced back to a BIS Standard

thermometer. The accuracy of the standard thermometer should be

checked at least once every 3 years depending upon how it is handled and

stored.

II. Temperature recording device

Each retort system is equipped with an accurate temperature-recording

device. The recording device provides a continuous record of the

temperature in the retort system during thermal processing. Common

systems in use are circular or strip charts, which are marked with ink pens,

electrical sparks, pressure pins, or which are created by graph plotters at

the time temperature readings are received. Electronic temperature

monitors and recorders are now available for the purpose and should be

utilized for greater accuracy and precision avoiding human errors. A band

or ribbon type surface pyrometer is used by processors to monitor

container surface temperatures.

III. Temperature sensors

Temperature measurement can be accomplished by essentially five basic

methods: (1) liquid-in-glass, (2) resistance thermometry, (3)

thermoelectric thermometry, (4) optical/radiation pyrometry, and (5) bi-

metal. Investigators are most familiar with the liquid (mercury or alcohol

usually) -in-glass and the bi-metal (dial gauge) types. It is possible now

that investigators will encounter the use of the optical/radiation pyrometers

as well.

i) Resistance thermometry

A resistance thermometer is a temperature-measuring instrument

consisting of a sensor (an electrical circuit element whose resistance

varies with temperature), a framework on which to support the sensor,

a sheath by which the sensor is protected, and wires by which the

sensor is connected to a measuring instrument, which is used to

indicate the effect of variations in the sensor resistance. Resistance

thermometers provide absolute calibration of temperatures in that no

reference junctions are involved, and no special extension wires are

needed between the sensor and the measuring instrument (as with

thermocouples).

The sensors can be of two types: resistance temperature detectors

(RTD’s) and thermistors. The RTD sensing element is formed of solid

conductors (usually in wire form) wound upon an insulating core. The

insulating core is usually made of mica or ceramic. The conductors,

which are wound in a helical coil to prevent mechanical restraints

during thermal expansion, are generally made of platinum; however

nickel and copper have been used. Platinum best meets the

requirements because being a noble metal, it can be highly refined, it

resists contamination, it is mechanically and electrically stable, and the

relationship between temperature and resistance is quite linear.

Thermistors (a contraction for “thermally sensitive resistors”) are

electrical circuit elements formed of solid semi conducting materials

20

Principles of Heat and

Mass Transfer

such as oxides of nickel, manganese, iron, cobalt, copper, magnesium,

titanium, and other metals. The powdered metal is formed under

pressure into the desired shape, usually a flat disc. The disc is sintered,

leads are attached, and encapsulated in epoxy. The finished thermistor

can also be encased in a sheath of plastic, stainless steel, copper or

aluminum. Both the RTD and thermistor can be obtained in various

configurations.

ii) Thermoelectric thermometry

The thermoelectric thermometer is a temperature measuring instrument

consisting of two continuous, dissimilar thermocouple wires extending

from a measuring junction to a reference junction with copper

connecting wires to a potentiometer. Unlike the resistance types, where

power must be supplied to the circuit, the thermocouple circuit

generates a measurable low voltage output that is almost directly

proportional to the temperature difference between the “hot” junction

and the “cold” junction. A unit change in this temperature difference

will produce some net change in electromotive force (emf or voltage).

Thermoelectric thermometry makes use of the known relationship

between a difference in junction temperatures and the resulting emf

developed by a thermocouple circuit. The temperature of one junction

(reference junction, T1) is held at a constant known value. This is

usually accomplished with an ice water (0°C) bath. The temperature of

the other junction (measuring junction, T2) is determined by

measuring the thermocouple circuit emf and referring to calibration

tables for the particular thermocouple materials. The thermocouple

junction usually is formed by twisting and fusing the two wires

together or they may be butt-welded. The finished element may be

used bare or enclosed in a sheath.

Check Your Progress Exercise 3

#

Note: a) Use the space below for your answer.

b) Compare your answers with those given at the end of the unit.

1. Write the full forms of the following abbreviations:

a) MIG thermometer

b) RTD sensor

………………………………………………………………………………

2. How is a thermocouple used for temperature measurement?

21

Food Preservation by

Application of Heat

………………………………………………………………………………

3. What is a thermistor? How does it differ from a RTD sensor?

………………………………………………………………………………

4. How is temperature in Kelvin scale related to temperature in Celsius

scale?

………………………………………………………………………………

1.7 DETERMINATION OF COLD POINT IN A FOOD

CONTAINER

In a study, determination of the cold spot was made using data collected for

heat penetration curves at 5 potential cold spot locations in the jars in 18

canner loads (Table 1.4). Two levels of two procedural variations were used in

testing for process calculations. Temperature profiles were compared for two

fill weights (450g, 480g) and two fill temperatures (direct-fill, and after a 10

minute wait, which had means of 84.4°C and 80.4°C, respectively). Process

calculation was accomplished by using thermocouples in each of six jars in

different canner loads of each of the three fill methods (standard, low initial

temperature, and high-fill weight). These jars were processed to 90.5°C plus

an additional 5 minutes. Processing was done in a boiling water canner using

the stovetop burners of a household gas range. Data were recorded using

Type T copper-constantan thermocouples.

Cold Spot Location

• The cold spot for this product and jar combination was located at the

geometric centre of the jar, Table 1.4.

22

Principles of Heat and

Mass Transfer

• The D value is the number of minutes it takes the straight line portion of

the heat penetration plot to pass through one logarithmic cycle.

• A larger D represents a slower rate of heat penetration.

Table 1.4: Cold spot determination of cranberry salsa in pint jars

Thermocouple

height in pint jar

Average D value

n = 18

Range Standard

deviation

Centre 54.86¹ 48.5-73.4 5.3

½" Below Center 53.89 48.6-64.7 3.9

1" Below Center 51.94 45.8-64.9 4.8

1½" Below Center 48.98 43.0-60.8 4.7

2" Below Center 47.00 41.4-58.0 4.5

¹Location of cold spot, as determined by largest individual D value (worst-case

scenario)

Heat penetration measures the rate at which a product heats during a thermal

process. A temperature sensor or thermocouple measures temperature changes

in the slowest heating region of the product or container and temperature is

monitored on a recording device. The time/temperature data, and heat resistant

data for the target microorganism, are used to calculate the scheduled process.

1.8 CALCULATION OF PROCESS TIME

The time/temperature relationship required for desired reduction of microbial

population is based on thermal resistance characteristics of the

microorganisms. The translation of this information into a form for use by the

operator of a commercial system requires integration with the heating and

cooling characteristics of the food product within the container. The methods

to be presented lead to the establishment of a processing system operator time

to ensure that the impact of the thermal process is equivalent to the desired

time/temperature for a given microbial population.

One of the first concepts to be understood when establishing process times is

lethality. The term lethality can be defined as the integrated influence of time

and temperature on a microbial population. Lethality is expressed as time at a

reference temperature.

Time, min

Lethal rate

0

0.1

0.2

10

20 30

40

Figure 1.4: Lethal rate curve for typical process in retort

23

Food Preservation by

Application of Heat

The lethal rate increases gradually with time as the temperature of the product

increases. As the product temperature begins to plateau at a magnitude near

the heating medium temperature, the lethal rate also plateaus and eventually

decreases as the product temperature decreases during cooling. Lethality is

expressed in time units for the process accomplished at the heating medium

temperature.

The time/temperature relationship representing the process is compared to the

process requirement needed to achieve product safety or an established

spoilage rate. For example, if the process under consideration is being used to

ensure the elimination of Clostridium botulinum as a health risk, the lethality

for the process must be equal to or greater than the thermal death time for the

microbial population.

The D-value or Decimal Reduction Time may be used as a measure. This is

defined as the time taken under specified conditions and at a particular

temperature to kill 90 per cent of the microbes in a sample. Only 10 per cent

or 1/10 of the original number of microbes survive the decimal reduction time:

hence its name. D-values can be determined from survivor curves when the

log of population is plotted against time.

D

reference temperature

= Time/(Log

a

-Log

b

)

Where a = the initial population, and b = the survivors after a time interval. F

value is a mathematically calculated number that describes the total lethal

effect of the process at the slowest heating point in a food container. It is the

equivalent, in minutes at a given temperature, of all heat considered with

respect to its capacity to destroy spores or vegetative cells of a particular

microorganism.

The effectiveness of a canning process is determined from a combination of

experimentation and calculation. Processing parameters are expressed in terms

of a series of symbols of which D, z, and F are key. When bacterial spores are

heated to a lethal temperature as during retorting of canned foods, the death of

most species approximates a first order chemical reaction that can be

described by a straight line on a semi-logarithmic graph paper. Figure 1.4

hows a hypothetical result from heating a species of spore at 115°C (240°F). s

In Figure 1.5, one minute is required to reduce the survivors from 10,000 to

1,000 or a 90 per cent reduction (one log reduction). Similarly, one minute is

required to reduce the survivors from 1,000 to 100 per gram of food and so on

until only 0.01 of a spore is present in 1 gram of food-which really means that

there remains only one living spore for each 100 grams of food. This time to

reduce the survivors by 90% is the Decimal reduction (D) value or in Figure 1,

D = 1 min. The subscript after the D indicates temperature at which the D

value was determined. Many factors affect the D value, such as the species of

spore, and the kind of food the spore is suspended in.

115

24

Principles of Heat and

Mass Transfer

Figure 1.5: Thermal death time curve for Clostridium botulinum

Check Your Progress Exercise 4

#

Note: a) Use the space below for your answer.

b) Compare your answers with those given at the end of the unit.

1. What is Decimal Reduction Time (D)? How is it determined?

………………………………………………………………………………

2. What is F value and how is it related to D value?

………………………………………………………………………………

3. Name the microorganism that is considered in the determination of

thermal processing.

25

Food Preservation by

Application of Heat

………………………………………………………………………………

4. What is meant by lethality in food processing? How is it related to various

process parameters?

………………………………………………………………………………

1.9 FACTORS AFFECTING HEAT PENETRATION

There are many factors, which affect the heat transfer into the food. Generally

the surface heat transfer coefficient is very high and is not a limiting factor in

heat transfer. The following factors are important which influences the rate of

heat penetration into a food:

1. Type of product: Liquid or particulate food (for example peas in brine),

where natural convection current is established, heat faster than solid food

(for example meat pastes and corned beef), where heat is transferred by

conduction. The low thermal conductivity of food is a major limitation to

heat transfer in conduction heating.

2. Size of the container: Heat penetration to the centre is faster in small

containers than in large containers.

3. Agitation of the container: End-over-end agitation (Figure 1.6) and, to a

lesser extent, axial agitation increases the effectiveness of natural

convection curie: and thereby increases the rate of heat penetration in

viscous or semi-solid foods (for example beans in tomato sauce).

26

Principles of Heat and

Mass Transfer

Figure 1.6: End-over-end agitation of containers

4. Temperature of the retort: A higher temperature difference between the

food and the heating medium causes faster heat penetration.

5. Shape of the container: Tall containers promote convection currents in

convective heating foods.

6. Type of container: Heat penetration is faster through metal than through

glass or plastics owing to differences in thermal conductivity.

1.10 LET US SUM UP

We have in this unit learnt the basic concept of heat transfer. Heat is

transferred by conduction, convection or radiation modes in a given situation.

The methods of temperature measurement include mercury-in-glass (MIG)

thermometers, resistance temperature detectors, thermistors, thermocouples

and radiation pyrometers. Temperature measurements permit us to evaluate

heat penetration rates in the thermal processes so as to determine the process

durations to achieve acceptable sterilization levels. These levels differ for

acid and less acid foods. If the pH level is below 4.6 the food is classified as

an acid food. However, if the pH is equal to or more than 4.6, the foods are

low-acid and the process temperatures would have to be more than 100°C.

Temperatures more than 100°C are achievable through raising process

pressure above that of the ambient. It is important to identify the cold spot in

the sterilization process because the heat penetration to that spot will control

the overall effectiveness of the process. Decimal reduction time at a given

reference temperature is used to fix the process time. Usually, 12 logarithmic

cycles are allowed for the microbial population reduction and, thus, the

process time F is equal to 12 D. The factors responsible for affecting the

temperature distribution and heat penetration rate need to be given due

consideration for finalizing the process durations.

1.11 KEY WORDS

27

Food Preservation by

Application of Heat

Conduction : Exchange of molecular energy directly

exchanged, from the hotter to the cooler regions.

Convection : Transfer of heat by the movement of groups of

molecules in a fluid.

Radiation : Transfer of heat energy by electromagnetic

waves.

Black body : It is a body which absorbs all incident light on it.

Grey body : Body which partially absorbs and partially

reflects incident light falling on it.

Fourier equation : It is the general equation guiding conduction

heat transfer.

Newton’s law of

cooling : It is the guiding principle behind convective heat

transfer.

Radiation

pyrometers : Measures temperature of a distant / hot object

without coming into contact with it.

Decimal reduction

time : Time required for reducing the microbial

population to one tenth of its initial number.

Microbial lethality : Time temperature combination to kill all

microorganisms including its spores.

28

Principles of Heat and

Mass Transfer

1.12 ANSWERS TO CHECK YOUR PROGRESS

EXERCISES

"

Check Your Progress Exercise 1

Your answers should include the following points:

1. The different methods of heat transfer are: Conduction, Convection and

Radiation.

2. The rate of conduction heat transfer increases as the temperature gradient

increases.

The equation, dQ/dt = kA dT/dT x is known as Fourier equation of heat

conduction.

3. The basic formula for radiant-heat transfer is the Stefan-Boltzmann

Law, q = ∈ σT

4

.

As indicated in the equation, the radiative heat flux q, is proportional to

the fourth power of temperature. That means for any increase in

temperature the flux increases much faster. The emissivity of the object,

∈, indicates its capacity in relation to a black body to emit thermal

radiation. The value of ∈ is in the range of 0-1; a black body has ∈ = 1

and a perfectly reflective body has ∈ = 0. The σ is Stefan-Boltzmann

constant.

4. If the temperature of one of the objects is doubled, it means the

temperature difference between the two objects has increased. Since

convection is directly proportional to the temperature difference, it will

increase in proportion to the temperature difference. On the other hand the

radiation heat transfer is proportional to the difference in the fourth power

of the temperatures of the two objects, the radiation heat transfer will

increase much more steeply. You can therefore, appreciate that the

radiation heat transfer increases much faster than the conduction or

convection when the temperature difference between two objects

increases.

Check Your Progress Exercise 2

Your answers should include the following points:

1. The acid and low-acid foods are distinguished on the basis of pH. The

foods with pH less than 4.6 are called acid and the foods with pH more

than 4.6 are called low-acid foods.

2. The thermal process for an acid food consists of treating it in a 100°C

boiling water bath, whereas the low-acid food must be pressure treated to a

temperature of 115°C or higher to kill the spoilage causing

microorganisms.

3. To make water boil at a temperature higher than 100°C in food processing,

it has to be put under pressure, such as in a pressure canner. When a food

29

Food Preservation by

Application of Heat

is processed at 1.0 kg/cm

2

pressure, the water boils when it gets to 115°C,

rather than at 100°C.

4. At higher altitudes the atmospheric pressure goes down and water boils at

lower temperatures. Thus, to make the thermal processing effective, either

the process time or canner pressure must be increased to make up for

lower boiling temperatures. That means pressure treatment may be

required even for acid foods.

Check Your Progress Exercise 3

Your answers should include the following points:

1. a) Mercury-in-Glass (MIG) Thermometer

b) Resistance temperature detector sensors

2. A thermocouple is made by joining two dissimilar metals. When one of

the junctions is at a different temperature than the surrounding

temperature, then a small voltage is developed which can then be

measured across the two leads at the other junction. When provision is

made in the circuit to take care of the reference point such as the freezing

point of water, then the resultant voltage is calibrated in terms of

temperature difference between the reference point and the temperature of

the junction.

3. A thermistor is normally a thermally sensitive material whose electrical

resistance changes with temperature. This change in resistance is

calibrated in terms of temperature. It differs from a resistance temperature

detection (RTD) sensor in terms of its sensitivity. As a result a thermistor

is able to sense very small changes in temperature as compared to a RTD

sensor.

4. K = (°C + 273), where K and C are units of temperature in Kelvin scale

and Celsius scale.

Check Your Progress Exercise 4

Your answers should include the following points:

1. The Decimal Reduction Time or D-value is defined as the time taken to

kill 90% of the microbes in a sample under specified conditions and at a

particular temperature. D-values are determined from survivor curves

when the log of population is plotted against time.

D

reference temperature

= Time/(Log

a

-Log

b

)

Where a = the initial population, and b = the surviving population after a

time interval.

2. The F value for a process is the number of minutes required to kill a

known population of microorganisms in a given food under specified

conditions. This F value is usually set at 12 D values and the resultant

microbial population is extremely low such as one microbe in 10,000 cans

(say).

30

Principles of Heat and

Mass Transfer

3. Clostridium botulinum is the reference microorganism, which is used in

determining the different parameters related to thermal processing.

4. Lethality is defined as the integrated influence of time and temperature on

a microbial population. It is expressed in time units for the process ac-

complished at the heating medium temperature. For e.g., a thermal process

may require 65 min at 115°C of steam temperature for a given food

product to achieve full lethality.

1.13 SOME USEFUL BOOKS

1. Henderson, S.M. and Perry, R.L. (1976) Agricultural Process Engineering.

AVI Publishing Co. West Port, Connecticut.

2. McCabe, W.L., Smith, J.C. and Harriott, P. (1993) Unit Operations of

Chemical Engineering. McGraw Hill, New York.

3. Nielsen, S.S. (1998) Introduction to Food Analysis. Aspen Publications

Inc., Maryland.

31