Prof. DAN Dharmasena Professor in Postharvest Engineering ... -1... · 1. Design of new machines,...

3/11/2017 1DAN Dharmasena

Prof. DAN Dharmasena

Professor in Postharvest Engineering & Technology

Dept. of Agric. Engineering

PHYSICAL PROPERTIES OF

AGRICULTURAL PRODUCTS

References:

1. Nuri N. Mohsenin, Physical Properties of Plant and

Animal Materials (1986) Gordon and Breach Science

publishers, New York.

2. Nuri N. Mohsenin, 1980. Thermal properties of foods

and agricultural materials

3. P. H. Pandey, Principles and Practices of Postharvest

Technology, Third edition (2002) Kalyani Publishers.

ISBN 81-7096-632-9


1.0 Introduction

Agricultural produce (plant and animal

material) is subjected to various handling and

processing practices.

Ie. Mechanical handling,

Thermal processing,

Optical testing,

Microwave heating,

Electromagnetic testing, washing and

handling in water etc. Applications are ever increasing.3/11/2017 3DAN Dharmasena

Little is known about basic physical

characteristics and other properties:

•Specific heat and other thermal characteristics

•Electrical conductivity

•Dielectric constants

•Light transmittance characteristics

•Mechanical properties: stress-strain behaviour

Resistance to compression, Impact & Shear

Coefficient of friction etc.


Incident

ray

Air (ε’ =1)

Reflected rays

(40 <ε’<70)

Food

Transmitted

rays

Air (ε’ =1)ε’ =dielectric constant/permittivity


Exposure to electro

magnetic radiation

What is the importance?

Information of physical properties is essential in

1. Design of new machines, structures, processes and

controls

2. For the determination of machine or operation

efficiency

3. Developing new consumer products of plant or animal

origin

4. In quality evaluation for final product consistency

3/11/2017 7D A N Dharmasena

Who needs this information?

• Agric/Food. Engineers

•Food scientists

•Food processors

•Plant and animal breeders/Biotechnologists


As Livestock Forage

Resistance to cutting, chopping,

Shredding

Aerodynamic properties: Blowing,

conveying

Compaction and load distribution

in silo (for Loading, storage and

unloading

As Grain

Resistance to detachment from the cob,

Aerodynamic properties: in cleaning

Electrical, Optical properties: MC

determination

Thermal Prop: Drying, Heat treatment,

Cooling

Frictional Prop: Silo design, Conveying

Flow properties: Conveying

As Livestock Feed

Mechanical Prop: Grinding and

mixing

Flow properties:

Mechanical/pneumatic conveying

Rheological Prop: Conveying as

liquid feed

As Food

Moisture sorption properties: storage,

drying, packaging

Viscoelastic properties: Milling

Rheological Prop: Extrusion

Aerodynamic & Hydrodynamic: Cleaning,

Conveying

Physical Processes: Shelling, Cleaning,

Polishing, drying, aspiration …etc.

Corn in the field

Physical properties to predict harvest maturity

Harvesting

Applications

example


1.2 Physical characteristics

Shape size Volume Surface area

Density Porosity Colour Appearance

Applications:

Shape and dimensions

•Design of grain cleaners, Cooling time calculation

of fruits

•Design of grain and other conveyors

•Quality control of fruit and vegetables3/11/2017 10D A N Dharmasena

Skip next

Physical characteristics conti..

Density and specific gravity

• Cleaning and separation,

• sorting and grading

Surface colour and appearance:

• Colour sorting, Selective

harvesting, grading


1.3 Mechanical Properties:

Load deformation characteristics,

•Impact and shear resistance: in size reduction-

energy estimation

•Static and sliding coefficient of friction: Handling

& processing machine design, Design of storage

structure

•Compressibility: bailing, silo design, method of

compressing


Ideal elastic – demonstrated for less than 0.1%

strains – Reiner 1960

Not in existence for real materials!!!!!

Linear elasticity

Steel

Non-linear

elasticity of

rubber

Inelasticity of

dry corn kernel

LoadingLoading

Loading

Unloading Unloading Unloading

HookeanNon-Hookean

Elastic

Inelastic (viscoelastic)


Static

Vibration

Density

kg/m3

Time minutes

Impact

compression

The highest compression of silage is obtained by?


•Shearing resistance and cutting forces:

•Agric. Structures

•Manual harvesting or Harvesting machines

(Cutting forces)

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http://images.google.com/imgres?imgurl=http://photos1.blogger.com/img/19/1850/640/Harvesting Rice4.jpg&imgrefurl=http://www.andyinasia.blogspot.com/&h=640&w=507&sz=146&tbnid=lKQ-5wnwvP4J:&tbnh=134&tbnw=106&hl=en&start=12&prev=/images?q=+harvesting++of+paddy&hl=en&lr=&sa=G

http://images.google.com/imgres?imgurl=http://photos1.blogger.com/img/19/1850/640/Harvesting Rice4.jpg&imgrefurl=http://www.andyinasia.blogspot.com/&h=640&w=507&sz=146&tbnid=lKQ-5wnwvP4J:&tbnh=134&tbnw=106&hl=en&start=12&prev=/images?q=+harvesting++of+paddy&hl=en&lr=&sa=G

1.4 Thermal properties

•Specific heat: Design of dryers,

heat-processing systems

•Other thermal properties:

Thermal conductivity,

T. Diffusivity,

Surface conductance,

Emmisivity


1.4 Electrical Properties

• In handling and processing

• Electrical conductance – In MC

determination

• Capacitance – In MC determination

• Dielectric properties – heating, microwave

heating

• Reaction to electromagnetic fields–

electrostatic separation, Electroporation of

Cell Membranes3/11/2017 17D A N Dharmasena

1.4 Optical properties

• Light transmittance and

reflective properties for:

• Sorting and grading

• Maturity and surface colour determination

• Grain cracks

• Blood spots and green rot in eggs


2.0 PHYSICAL PROPERTIES

2.1 Roundness:

Is a measure of the sharpness of the

corners of the solid

(diagrams TP)

1. Roundness = Ap/Ac

Ap – Largest projected area of the solid in natural resting position

Ac – Area of smallest circumscribing circle

Area measurement by tracing or Projection


2 Roundness = ∑r

NR

Where,

• r- radius of curvatures of corners

• R – Radius of the maximum inscribed circle

• N- Total number of corners


3. Roundness ratio: = r/R

R- Mean radius of the object

r – Radius of curvature of the

sharpest corner


2.3 Resemblance to geometric bodies

In some cases the shape can be approximated by one of the

following geometric shapes. Based on the shape, surface area

and volume can be calculated.

1. Prolate spheroid – When an ellipse rotates about its major

axis (like a lemon)

V = 4/3 (Лab2)

2. Oblate spheroid – When an ellipse rotates about its minor

axis (“Heen naran”grapefruit)

V = 4/3 (Лa2b)


Where, a, and b are respectively semi-major

and semi-minor axes of the ellipse of rotation.

Volume =4/3Л r1*r2*r3 – Tri-axial ellipse (a>b>c)

Semi-major axis: The longest radius of an ellipse.

Semi-minor axis: The shortest radius of an ellipse.

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Oblate: c<a

Prolate

Prolate: b>ab=c

a=c

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Ellipsoidal Objects

The sphericity, Ψ, of an oblate spheroid (similar to the shape of the planet Earth ) is defined as such: {An oblate spheroid can be formed by rotating an ellipse about its minor axis.} (a>c)

where a, b are the semi-major, semi-minor axes, respectively.

3. Right circular cone or cylinder like

cucumbers

V = (Л/3) h(r12+r1r2+r2

2) Right circular cone

V = 1/3Лr2h (when r2=0)

r1 and r2 are respectively radii of base and top

and h is the height


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2.2 Sphericity:

Schematic representation of difference in grain shape. Two parameters are shown: sphericity (vertical) and rounding (horizontal).

http://en.wikipedia.org/wiki/File:Rounding_&_sphericity_EN.svg

http://en.wikipedia.org/wiki/File:Rounding_&_sphericity_EN.svg

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Sphericity is a measure of how spherical (round) an object is. As such, it is a specific example of a compactness measurement of a shape.

Defined by Wadell in 1935, the sphericity, Ψ, of a particle is the ratio of the surface area of a sphere (with the same volume as the given particle) to the surface area of the particle:

where Vp is volume of the particle and Ap is the surface area of the particle

3/11/2017 29

Derivation

Hakon Wadell defined sphericity as the surface area of a sphere of the same volume as the particle divided by the actual surface area of the particle.First we need to write surface area of the sphere, As in terms of the volume of the particle, Vp

therefore

Hence we define Ψ as:

3/11/2017 30

V p & As relationship

Volume of a sphere = Sum of the volume of n # of square pyramids

Sq. Pyramid volume = 1/3 x surface area of the base (a) x Vrt. height (h)

If the sphere is divided in to n # of square pyramids;

The volume of all pyramids = volume of the sphere

V= 1/3 * a * r + 1/3 *a*r + 1/3*a*r…….

V= 1/3 * r (a + a+ a+ a+..) ----Total surface area

V=1/3 * r * (4πr2)

Therefore the volume of a sphere = 1/3 * r * (surface area)

V= 1/3 * (4πr3) = 4/3 πr3

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Sphericity of common objects

GO to MS Words slide

a>c

= (Л /6) abc 1/3

(Л /6) a3

= bc 1/3

a2

a- longest intercept

b – longest intercept normal to a

c- longest intercept normal to a & b

(The intercepts need not intersect each other at a common point)


When solid volume is

assumed as an ellipsoid with

a,b,c

2.2 Sphericity: Some other formulas

1. Three-dimensional expression

= de/dc

• de- Dia of a sphere of the same volume as

the object

• dc – Diameter of the smallest

circumscribing sphere or usually the longest

dia of the object


2. Sphericity = di/dc

• di- Diameter of the largest inscribed circle

• dc – Diameter of the largest circumscribed

circle


3. % Sphericity of a perfect sphere = 100%,

McIntosh apple = 90%


3.0 VOLUME AND DENSITY

Platform scale

Specific gravity balance

Specific gravity bottle or Pycnometer method

Specific gravity gradient tube

True density & Bulk density

QUIT NEXT slide


3/11/2017 37

Platform scale

Volume (cm3)= Mass of displaced water (g)

Density of water (g/cm3)

Specific gravity = Mass in air * Sp. Gravity of water

Mass of displaced water

3/11/2017 38

Specific gravity balance

For Solids heavier than water

Small fruits, beans, kernels of corn

Volume (cm3) = Mass in air - Mass in liquid (g)

Density of water (g/cm3)

Specific gravity = Mass in air * (SG)L

[Mass in air - Mass in water (g)]

3/11/2017 39

For Solids lighter than water

Attach a sinker to the object

Calculate specific gravity as follows:

Sp.gravity = (Ma) object * (SG)L

[(Ma – Mw)both - (Ma – Mw) sinker]

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Specific gravity gradient tube

Specimen must be impervious to the liquid until it reaches the

equilibrium, Fast method

Principle

x

y

z

b

a

SPg at x = a+ (b-a) * (x-y)

(z-y)

a & b - SPG of

standard floats

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Liquid Specific Gravity

Methanol-benzyl alcohol 0.08-0.92

Isopropanol-water 0.79-1.00

Ethanol-carbon tetrachloride 0.79-1.59

Carbon tetrachloride-

Trimethylene dibromide 1.60-1.99

Trimethylene dibromide-

ethylene bromide 1.99-2.18

Ethylene bromide-bromoform 2.18-2.89

Liquids suitable for preparation of

solutions

SKIP NEXT

3/11/2017 42

Specific gravity bottle or Pycnometer method

For seeds and some grains:

Steps:

1. Take empty weight and weight after filling it with distilled

water at 20 oC.

2. Determine the SPG of toluene (C6H5CH3)

SPG of Toluene = Weight of toluene

Weight of water

Why toluene? Doesn’t soak into the grain, low surface tension

(flow well through grain surface), less solvent property (fats),

high boiling point, specific gravity not affected by exposing

to air, low SPG

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3. Place 10 grains in the pycnometer and pour toluene to cover the

sample.

4. Exhaust entrapped air by gradually increasing the vacuum by a

vacuum pump.

5.Vacuum and release several cycles until no air bubbles coming

up and fill it with toluene. Cool it to 20 oC

6. Weigh the bottle and calculate the SPG as follows.

SPG of grains = Weight of the grain x SPG of toluene

Weight of the toluene displaced by grains

Weight of the toluene displaced by grains = Wgt. of grains –[Tot

Wgt with (Tolu+Grains) –Tot Wgt. With Tolu]

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Or

Wgt of Toluene + Wgt of grain = (Wgt of

Toluene+Grain) + Wgt of Displaced Toluene

Wgt of DT = [Wgt of Grain + Wgt of Toluine]-

(Wgt of Toluene+Grain)

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Eg.

Weight of 16 grains of corn = 4.598g

Weight of pycnometer = 55.6468g

Weight of pycnometer + Toluene = 78.2399g

Weight of Pyc + Tolu + Sample = 79.6226g

Weight of Pyc + water = 81.7709g

SPG of toluene =

= 78.2399-55.6468 =0.8648

81.7709 – 55.6468

SPG of corn=

= 4.4598 * 0.8648

[4.4598-(79.6226-78.2399)]

= 1.256

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Volume of grain = sample weight

SPG of grain

Sample weight

Sample wgt/Wgt of equal volume of water

=4.4598/1.256

= 3.558 cm3

3/11/2017 47

Volume measurement

Air comparison Pycnometer

1. Close v1 valve, push A to stop point

2. To balance pressure -have to push B forward

3. Keep tare sample cup, to maintain the same pressure, have

to move B backwards – get the tare volume

4. Place the sample – measure the true volume

4.0 POROSITY

•Porosity is defined as the percentage of volume of inter

grain space (pores) to the total volume of grain bulk.

•Porosity can be determined by using the ratio of bulk

density to true density values. Rice 780kg/m3 /

1360kg/m3=?

•The percent void of different grains in bulk are often

needed in drying, airflow, and heat flow studies of grains.

•It depends on shape, dimensions and roughness of the

grain surface.


3/11/2017 49

ρs – ρb x 100 = % porosity

ρs

ρs = ms/vs

ρb = ms/vb

vb-vs * 100 = porosity

vb

Can you derive the above equation?

Porosity values of grains

The porosity of rice and rough rice ranges from 46 to 60


3/11/2017 51

To manometer

Valve 2

Valve 1

a

Valve 3

Tank 1 Tank 2

Material filled in T2, Close V2 & air is supplied to T1

Get manometer reading P1 after closing V1

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From the perfect gas low

P1V1 = nRT1--- n = m/M

P1- pressure n – number of gas moles

V1 –Tank 1 volume m-mass of air,

P1V1 = m RT1

M

M- average molecular weight of air

R-gas constant

T1-absolute temperature

Now close valve 3 and open valve 2

Read pressure P3

Under this situation air Mass m is divided to m1 + m2 = m

m2 to fill V2 pore space in Tank 2

Assume RT1 = RT2 = RT

P1V1 M = P3V1 M + P3V2 M P3 V2 = V1(P1-P3)

RT RT RT V2/V1 = (P1-P3)/P3

5.0 Angle of Repose and angle of Friction

Depends on grain shape, surface characteristics and moisture

content.

Angle of Repose

The angle of repose is the angle between the base and the

slope of the cone formed on a free vertical fall of the grain

mass through a nozzle to a horizontal plane.

Referred to as -Dynamic angle of repose or poured angle

2. Static Angle of repose- measured on a tilted surface

Coated with a layer of granules

3.Angle of slide – Above measure, without

A particle layer3/11/2017 53D A N Dharmasena

Angle of repose of some grains

Dynamic angle of repose is more applied in grain flows in hoppers etc.


3/11/2017 55

Angle of Friction (Angle of Internal Friction)

A measure of the frictional forces within the

particulate materials, or coefficient of friction between

granular particles

Applications

Design of shallow bins – Rankine equation

σ3 = 9.81 N/kg x wy tan2 (45-φi /2)

σ3 –Lateral pressure against the wall at a point “y” feets below the top

φi - Angle of Internal Friction

w –bulk density kg/m3

φi

3/11/2017 56

Deep Bins

Angle of repose line

intersects below the

grain surface

Lateral pressure/Vertical

pressure = k

k = 1-sin φi

1 + sin φi

φi

Further

information;

Mohsenin

751-758

How to Measure Angle of Int. friction φi ?

Two simple methods &

Use of tri axial chamber (Soil

mechanics)

φi

slot

Angle of

friction

Flowing

solids

3/11/2017 58

Vertical tube and piston

dt

Lc –longest

movable plug

of solids

Tan φi = Lc/dt

The piston cannot be moved at all at a critical

height!!

3/11/2017 59

Improtant Design Applications of Phy. Properties

1.Brown’s equation for flow of granular materials

through an orifice

G = ᴫ ρs d2.5eff g0.5 [1-cosβ]

4 2 sin3β

G- mass flow rate

ρs – particle true density

deff –effective diameter of the orifice (true for

30<orifice:particle diam)

= orifice dia – (1.5 x particle diam)

g – gravitational acceleration

β -angle between cone wall and horizontal

SI Units

3/11/2017 60

2.Franklin and Johanson (1955) equation (horizontal orifices)

Well accepted even today

Q = wsB2.93

(6.29 tanφi +23.16) (d +1.89) – 44.9

Flow rate – pounds/minute

B- diameter of the orifice in inches

d – average diam of particles in inches

ws - particle true density (solid density) pounds per cubic foot

φi – internal angle of kinetic friction

Another equation is available for inclined orifices (refer tp Moshinin’s book)

QUIZ Next

Application of physical prop.s

Static Pressure Drop

•The pressure drop for air flow through grain/biomass is very

important in designing dryer or aeration systems as well as in choosing

correct fan.

•The pressure drop for air flow through grain depends on the air flow

rate, the surface and shape characteristics of grain, the number, size and

configuration of the voids, the variability of the particle size and bed

depth.

•It has been found that the pressure drop is influenced by the extent of

packing and the amount of the foreign material.

•Number of mathematical models are available to estimate SPD


3/11/2017 62From PDF file LD266

Hakil & Shedd (1955) Model revised by

ASAE

Condition: For the air flow range 0.01 -0.2

m3/sm2

ΔP/L = aQ2

ln (1 + bQ) ΔP-Static pressure (Pa)

L – bed depth m

Q- air flow rate (m3/sm2)

a, b – constants – need to find values for different crops

Where are the parameters for physical characteristics?

3/11/2017 64

3/11/2017 65

gc = 1

• Further reading - Key words “resistance of grain beds”

Airflow through packed columns/grain beds)

• Still use crop specific empirical equations

Principles of Grain Drying and Aeration- Grain Physical and Thermal

Properties Related to Drying and Aeration

• Chong-Ho Lee* and Do Sup Chungt (PDF grain drying and aeration)

• http://books.google.lk/books?id=NVmhnmaIMtwC&pg=PA236&lpg=PA236

&dq=Equation+for+static+pressure+drop+through+grain+beds&source=bl&ot

s=m75-

hy_MxL&sig=LSsCgNKxW__CVQTB8c6FEDHwm80&hl=en&ei=V9X5TO

i_GcWwhQe-

sriqCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBMQ6AEwA

DgK#v=onepage&q=Equation%20for%20static%20pressure%20drop%20thro

ugh%20grain%20beds&f=false

3/11/2017 66

3/11/2017 67

3.0 AERODYNAMIC PROPERTIES

The knowledge of aerodynamic and hydrodynamic properties of

agricultural products is necessary for designing air and water

conveying and separating systems (i.e., pneumatic or hydrodynamic

systems).

Terminal velocity and drag coefficient

The air velocity at which an object remains in a suspended state in a

vertical pipe under the action of an air current is called terminal

velocity of the object. When a paddy grain moves in air stream of a

grain dryer, it experiences resistance to motion which is a function of

its velocity and density of air.


Considering free fall of an object which

attains a constant terminal velocity Vt

when the gravitational accelerating

force, Fg becomes equal to the resisting

upward drag force Fd'

Hence, Fg = Fd' When V = Vt

3/11/2017 69

Terminal velocity of different grains


3/11/2017 71

Aero-hydrodynamic properties

Continue with TP presentation

Quiz next

4. HYGROSCOPIC PROPERTIES

Moisture content definitions

Moisture content wet basis (%MCwb)

MC = Mass of water x 100

Mass of undried grain

Moisture content dry basis (%MCdb)

MC = Mass of water x 100

Mass of dry mater


•Conversions - Wet basis to Dry basis & Dry basis to wet basis

(wb)100

(wb) xMC100c(db)m

MC

(db)100

(db)100xMCMC(wb)

MC

•A sample of 100g paddy is placed in an oven at

1300C for 24h and all of its moisture is driven off.

The final weight is 80g. What is the original

%MC in wet basis and dry basis?


3/11/2017 74

Methods of moisture analysis:

Depends on the type of food

Need to use AOAC standard method for a particular food

Association Of Analytical Chemests

They update techniques time to time

You need to give only the AOAC standard No in reporting the

method in documents

Water activity (aw)The typical water activity of some foodstuffs

Type of product Water Activity (aw)

Fresh meat and fish 0.99

Bread 0.95

Aged cheddar 0.85

Jams and jellies 0.8

Plum pudding 0.8

Dried fruit 0.6

Biscuits 0.3

Milk powder 0.2

Instant coffee 0.2


Microorganisms grow at

this aw and above

Food

examples

0.95

Pseudomonas, Escherichia, Proteus, Shigella,

Klebsiella, Bacillus, Clostridium

perfringens, some yeasts

Highly perishable foods (fresh and canned fruits,

vegetables, meat, fish), milk, cooked

sausages, breads, foods with up to 4 oz

sucrose or 7% NaCl

0.91Salmonella, Vibrio parabaemolyticus, C.

botulinum, Lactobacillus, some molds

Some cheese (Cheddar, Swiss, Provolone), cured

meat, fruit juice concentrates with 55%

sucrose or 12% NaCl

0.87Many yeasts, Candida, Torulopsis, Hansenula

micrococcus

Fermented sausage, sponge cakes, dry cheese,

margarine, foods with 65% sucrose or 15%

NaCl

0.80Most molds, most Saccharomyces spp.,

Debaryomyces, Staphylococcus aureus

Most fruit juice concentrates, condensed milk,

syrup, flour, high-sugar cakes, pulses

containing 15-17% moisture

0.75Most halophilic bacteria, Mycotoxigenic

aspergilli

Jam, marmalade, glace fruits, marzipan,

marshmallows

0.65 Xerophilic molds, Saccharomyces bisporusRolled oats with 10% moisture, jelly, molasses,

nuts

0.60 Osmophilic yeasts, few moldsDried fruits with 15-20% moisture, caramel,

toffee, honey

0.50

No microbial proliferation

Noodles with 12% moisture, spices with 10%

moisture

0.40 Whole egg powder with 5% moisture

0.30Cookies, crackers, bread crusts with 3-5%

moisture

0.03Whole milk powder with 2-3% moisture,

dehydrated soups


3/11/2017 77

Estimated mold-free shelf life in days at 21° C:

Source: http://en.wikipedia.org/wiki/Water_activity

•A measure of the free moisture (unbound) in

a food.

•The water activity of a food is not the

same thing as its moisture content.

•Water activity is in practice usually

measured as equilibrium relative humidity

(ERH).


Water activity or aw is the relative availability of

water in a substance.

It is defined as the vapor pressure of water divided

by that of pure water at the same temperature.

Therefore, pure distilled water has a water activity of

exactly 1 (one).

•If we multiply this ratio by 100, we obtain the

equilibrium relative humidity (ERH) that the foodstuff

would produce if enclosed with air in a sealed

container at constant temperature.


The air and the grain are then said to be in equilibrium.

This moisture content of the grain is called equilibrium moisture

content (EMC) and the corresponding relative humidity (RH) is

called Equilibrium Relative Humidity (ERH).

At

T = Constant


Food

Stand

Sat.

salt

Air tight

chamber

3/11/2017 81

Go to EMC presentation – L4

5.0 THERMAL PROPERTIES

For processing raw materials thermal treatments are given like

heating, cooling, drying and freezing. It has been found that the

change of temperature depends on the thermal properties of the

product which are:

1. Specific heat

2. Thermal conductivity

3. Thermal stability

4. Thermal diffussivity

5. Heat of vaporisation.


Specific heat:

Amount of heat required to raise the temperature of a unit mass

through 1OC.

The specific heat of grain

This equation is used for the grains above 8 percent moisture

content only.

Where Cdr = Specific heat of the bone dry grain

Cw = Specific heat of water taken to be unity

M = moisture content of grain (percent dry basis)


Grains 0.35-0.45kcal/kg0C SI unit- * 4.187kJ/kg 0C

One calorie equals 4.187 joules

Siebel’s equation for fat free materials

Above freezing Cavg = 3349M + 837.36 J/kgK

Below freezing Cavg = 1256M + 837.36 J/kgK

M- Mass fraction of water (ie. 0.8 or moisture wet basis)

Modified Siebel’s

Above freezing Cavg = 1674F + 837.36 SNF+4186M J/kgK

Below freezing Cavg = 1674.72F + 837.36 SNF+ 2093.4M J/kgK


Specific heat choi & Okos.pptx

Specific heat choi & Okos.pptx

Thermal Conductivity

It is defined as the amount of heat flow through unit thickness of

material over a unit area per unit time for unit temperature

difference.

Thermal conductivity of a single grain varies from 0.3 to 0.6

kcal/m hour °C whereas the thermal conductivity of grains in

bulk is about 0.10 to 0.15 kcal/m hour °C which is due to the

presence of air space in it. The thermal conductivity of air is

0.02 kcal/m hr °C. It has been seen that the therma1

conductivity of the single grain is three to four times greater

than that of the grain bulk.


Generally during heat treatment a calculated quantity of heat is

passed through the grains at a particular thermal conductivity

which will not reduce the food balance and also maintain the

viability of the grain. According to Fourier's Law the rate of heat

now can be calculated as:

A = Area

The values of thermal conductivity of rice range from 0.68 to 1.9

W/m K depending on the variety, the initial temperature, measuring

methods and moisture content of grain.


Thermal Stability

The ability of grain to preserve, and in some cases to improve

its seed, food and other technological qualities in the drying

process is usually called the thermal stability. It is mainly

connected with the properties of the components of its

chemical composition.

Thermal Diffussivity

Thermal diffussivity is caused by vapour movement due to

temperature differences. Can be estimated using mathamatical

models.


Heat of Vaporisation

The heat of vaporisation of water in rice and corn is

defined as the energy required to vaporise moisture from

the grain.

Equilibrium moisture content curves furnish the data

necessary to calculate the heat of vaporisation for

moisture.

From data tables in materials hand books

Number of mathematical models are available for

different products.


Heat of vaporization of grain moisture with respect to

temperature variation


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When solid volume is assumed as an ellipsoid with a,b,c

Degree of Sphericity = Volume of solid) 1/3

Volume of circumscribed sphere

= (Л /6) abc 1/3

(Л /6) a3

= bc 1/3

a2

a- longest intercept

b – longest intercept normal to a

c- longest intercept normal to a & b

(The intercepts need not intersect each other at a common point)


When solid volume is assumed

as an ellipsoid with a,b,c

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is degenerate:

• Tri-axial or (rarely) scalene ellipsoid;

• oblate ellipsoid of revolution ( oblate spheroid );

• prolate ellipsoid of revolution ( prolate spheroid );

• the degenerate case of a Sphere;

http://en.wikipedia.org/wiki/Oblate_spheroid

http://en.wikipedia.org/wiki/Prolate_spheroid

http://en.wikipedia.org/wiki/Sphere

Prof. DAN Dharmasena Professor in Postharvest Engineering ... -1... · 1. Design of new machines,...

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