DRYING OF WHEAT GRAIN IN THIN LAYERS by VEERENDRA …

DRYING OF WHEAT GRAIN IN THIN LAYERS

by

VEERENDRA KUMAR BHARGAVA

B.Tech.(Hons.), Indian I n s t i t u t e o f Technology, Kharagpur, 1966

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

i n the Department of

A g r i c u l t u r a l E n g i n e e r i n g

We accept t h i s t h e s i s as conforming t o the

r e q u i r e d standard

THE UNIVERSITY OF BRITISH COLUMBIA

May, 1970.

In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r

an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t

t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y .

I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s

f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r

by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n

o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my

w r i t t e n p e r m i s s i o n .

Depar tment o f A g r i c u l t u r a l E n g i n e e r i n g

The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada

Date Mav. 19 7 0

ABSTRACT

The effect of drying parameters on the drying-rate

constant, the diffusion coefficient, and the dynamic e q u i l i

brium moisture content was investigated using the Park variety

of wheat. The i n i t i a l moisture content of a l l the grain used

in the drying tests was approximately 29 percent, dry basis.

A i r temperatures of 120, 100, 80 and 60 degrees Farenheit;

a i r flow rates of 120, 80, 20 and 5 feet per minute and

several relative humidities were employed as the drying

conditions during the tests. A closed cycle, heated a ir dryer

in which the a i r temperature and the relative humidity could

be controlled to + 2 degrees Farenheit and + 5 percent

respectively, was constructed for the investigation.

It was assumed that the mechanism of internal flow

of moisture within a kernel is that of diffusion. When the

i n i t i a l transit ion drying period was neglected, the drying-

rate constant and the diffusion coefficient were found to be

constant and the plot of log moisture ratio against time gave

an excellent f i t for each drying test. It was concluded that

the fa l l ing-rate period in thin layer drying could be

represented by a constant drying-rate constant and diffusion

coefficient. The effect of a i r temperature on the drying-rate

constant and diffusion coefficient was found to be inconsistent

with an Arrhenius type equation. There was no observable

effect due .to a i r flow rate and relative humidity of the drying

a i r .

The dynamic equilibrium moisture content increased

with increased relative humidity of the a i r . A plot of log

dynamic equilibrium moisture content versus log-log relative

humidity gave a straight l ine relationship and satisf ied

Henderson's equation. The equilibrium constants were found

to vary with the a ir temperature.

The dynamic equilibrium moisture content was found

to decrease with both the air temperature and a i r flow rate.

The effect of a ir flow rate was quite small except at low'

temperatures. When log a ir temperature was plotted against

dynamic equilibrium moisture content, i t followed a straight

l ine , indicating that an exponential relationship between the

two might exist . •

TABLE OF CONTENTS

PAGE

LIST OF TABLES i i i

LIST OF FIGURES v

TERMINOLOGY x

NOMENCLATURE x i i

ACKNOWLEDGEMENTS xiv

INTRODUCTION 1 REVIEW OF LITERATURE. 3

Nature of Drying Process 3 Equilibrium Moisture Content 10 Effect of Relative Humidity on the Static

Equilibrium Moisture Content 13 Drying Rate Constant and Diffusion

Coefficient 15 Air Flow Rate 15

THEORY 17 Drying Equations 17 Dynamic Equilibrium Moisture Content 18 Effect of Temperature on Equilibrium

Moisture Content 20 Drying Rate Constant 21 Effect of Air Temperature on the Drying Rate

Constant and the Diffusion Coefficient 21 APPARATUS 24

Instrumentation 24

- i -

MATERIALS AND MEASUREMENTS

Grain Used for Drying Experiments

Moisture Content

Temperature and Relative Humidity

Air Flow Rate

EXPERIMENTAL PROCEDURES

RESULTS AND DISCUSSION

Drying Curves

Dynamic Equilibrium Moisture Content

Effect of Relative Humidity on the Dynamic Equilibrium Moisture Content

Effect of A ir Temperature on the Dynamic Equilibrium Moisture Content

Effect of A ir Temperature on Drying Rate Constant

Effect of Relative Humidity of the Drying Air and Air Flow Rate on Drying Rate Constant

Effect of Air Temperature on Diffusion Coefficient

CONCLUSIONS

RECOMMENDATIONS FOR FURTHER STUDY

LITERATURE CITED

APPENDIX A

APPENDIX B

APPENDIX C

LIST OF TABLES PAGE

I Experimental Design Showing Temperature, Relative

Humidity and Air Flow Rates for Drying Tests

Conducted on Wheat, with the Code.Designation of

each Run. 32

II Computed Drying Results at 120 - 2 .5°F Drying A i r ;

Temperature for Several Relative Humidities and

Air Flow Rates. 35

III Computed Drying Results at 100 - 2 .0 °F Drying Air


Air Flow Rates. 36

IV Computed Drying Results at 81 - 2 . 0 ° F Drying A i r


Air Flow Rates. 37

V Computed Drying Results at 60 - 1 .0°F Drying Air


A i r Flow Rates. 38

VI Mean Values of Drying Air Temperature, Relative

Humidity, M £ and Calculated Values of Equilibrium

Constants, C and N (Equation [14]). HI

VII Computed Values of Constants b and d in Equation

[18] and those Presented by Henderson and Pabis

(24). 49

VIII Computed Values of Constants D q and E / R in Equation

[19]. 52

- i i i

- iv -

C - l Program for Computing Moisture Content (per

dry basis) , Dynamic Equilibrium Moisture Content

(percent, dry basis) and Moisture Ratio from .

Drying Weights and Relative Humidity from Dry

Bulb and Wet Bulb Temperatures with a Sample

Calculation for Drying Set E.

LIST OF FIGURES

FIGURES PAGE

1. Longitudinal section of wheat grain ij

2. Development of moisture gradient within a

kernel as drying progresses 20

3. Sketch of the dryer 2 5

4. Set of or i f ice plates used for controlling

a i r flow rate 2 9

5. A i r humidity and temperature recorder with

sensor 29

6. Effect of relative humidity of drying a ir on

mean values of dynamic equilibrium moisture

content.at 120 - 3°F, 100 - 2°F and 80 - 3°F 40

7. Relation between log mean values of dynamic

equilibrium moisture content and log-log

relative humidity for the a ir temperature

120 - 3°F , 100 - 2°F and 80 - 3°F 43

.8. Effect of drying a ir temperature on mean values

of dynamic equilibrium moisture content at

75 - 5%,.50 - 2% and 25 - 3% relative humidity

9. Plot of logarithm of drying a ir temperature

against mean values of dynamic equilibrium

moisture content at 75 - 5% and 50 - 2%

relat ive humidity

10. Relationship between the drying constant and the

reciprocal of absolute temperature of drying

a i r On the basis of Arrhenius equation

- v -

45

46

48

FIGURES - . v i - PAGE

11. Relationship between the diffusion coefficient

and the reciprocal of absolute temperature

of drying a ir on the basis of Arrhenius

equation 51

A - l Drying curves for a ir flov; rates of (111)

120 feet per minute, (112) 80 feet per

minute, (113) 20 feet per minute and (114)

5 feet per minute at 120 - 1°F and 78-2%

relative humidity 62

A-2 Drying curves for a ir flow rates of (121)



5 feet per minute at 120 - 1 .5°F and 50 - 2%


A-3 Drying curves for a i r flow rates of (131)



5 feet per minute at 122 - 1°F and 25 - 2%

relat ive humidity 64






FIGURES - v i i - PAGE




5 feet per minute at 100 - 1 .5°F and 50 +

1.5% relative humidity 66



minute, (2 33) 2 0 feet per minute and (234)

5 feet per minute at 100 - 1°F and 26 - 1.5%

relat ive humidity 67









5 feet per minute at 81 - 2°F and 50 - 1.5%







- v i i i -

Drying curves for air flow rates of (411)



5 feet per minute at 60 - l ° F and 75 - 1.5%

relat ive humidity

Drying curves for a i r flow rates of (421)




relative humidity

Plot of logarithm moisture ratio versus time

for drying set D, (211) a i r flow rate 12 0

feet per minute, (212) 80 feet per minute,

(213) 20 feet per minute and (214) 5 feet

per minute at 101 - 1°F and 72 - 2%

relative humidity

Plot of logarithm moisture ratio versus time

for drying set E , (221) a ir flow rate 120



per minute at 100 - 1 .5°F and 50 - 1.5%

relative humidity

FIGURES — ix -

B-3 Plot of logarithm moisture ratio versus time

for drying set F, (231) a i r flow rate 120



per minute at 100 - 1°F and 26 - 1.5%

relative humidity

TERMINOLOGY

Aleurone layer - - The protein layer in the periphery of the

grain lying at the base of pericarp.

Coefficient of determination - - In simple regression, the 2 . . '

quantity, r , representing the fraction of the

corrected sums of squares that is attributable to

simple l inear regression. - ^ ^ ^

Constant-rate period .-- The drying period during which the

rate of water removal per unit of drying surface

is constant.

C r i t i c a l moisture content — The minimum moisture content of \

the grain that sustains a rate of flow (of free . \

water to the surface of the grain equal \to the maximum .rate of removal of water vapor from the . \ grain under the drying conditions. At this moisture

content the constant-rate drying period ends. \

Diffusion - - The spontaneous mixing of one substance with

another due to the passage of molecules of each

substance through the empty spaces between molecules

of the other substance.

Drying rate constant — The slope of the l ine of plot of

logarithm moisture ratio against time.

Dynamic equilibrium moisture content - - The moisture retained

by the grain in equilibrium with i ts surroundings

under definite conditions of a i r temperature and

relative humidity. - x -

- XI -

Fall ing-rate period — The drying period during which the

instantaneous drying rate continually decreases.

Hygroscopic material - - The material that may contain bound

moisture.

Moisture gradient - - The distribution of water in a sol id

at a given moment in the drying process, the nature

of which depends on the characteristics of the

material.

Moisture rat io - - It is the ratio of the free moisture content

to the total moisture that can be removed from the--— /

grain under the definite drying conditions. ^

Pericarp - - The outer protective coat of grain. y

Thin layer drying - - Drying of grain which is entirely exposed

to the a i r moving through the product.

NOMENCLATURE 1

Constant

Equilibrium constant

Diffusion coeff icient, square feet per hour

Constant

Energy of activation factor, constant

Constant related to volumetric d i f fus iv i ty

Humidity of the drying a i r , pounds of moisture

per pound of dry a ir

Drying-rate constant, hour ^

Constant, factor varying with the material

Constant dependent on the shape of the part ic le

Moisture content, percent, dry basis

I n i t i a l moisture content, percent, dry basis

Dynamic equilibrium moisture content, percent,

dry basis

Equilibrium moisture content, pounds of moisture

per pound of dry matter

Static equilibrium moisture content, percent,

dry basis M MS - E Moisture r a t i o , ^—_•• ^ , a decimal

o E

Moisture content at any time 9, percent, dry basis

Equilibrium constant

Probability l eve l , ( 1 - 8), where 8 is the level

of significance

- x i i -

- X l l l -

R Gas law constant

T Absolute temperature

U Rate of specific chemical reaction

U Constant o

a Constant

b Constant

c Concentration at any point

d Constant

db Dry basis

df ' Degrees of freedom

f Constant

g Constant

n Constant

n' Exponent varying with material

Vapor-pressure at the surface under dynamic

conditions !

P g Uniform vapor-pressure within the kernel under

stat ic conditions 2

r Coefficient of determination

rh Relative humidity of a i r , a decimal

r^ Radius of the kernel equivalent to a sphere, feet

t • Temperature, degrees Farenheit

x Distance through the material in the direction of

diffusion

a Constant

0 Time, hour

- xiv -

ACKNOWLEDGEMENTS

The author wishes to express his deep sense of

gratitude and indebtedness to Professor E. L. Watson for

his incessant encouragement and guidance throughout the

progress of this study.

The author is grateful to Dr. E . 0. Nyborg for

the suggestions and assistance in the use of IBM 360

Computer.

Thanks are due to Mr. T. A. Windt (B.C. Department

of Agriculture, Agricultural Engineering Division) for

providing the wheat grain for this work and Mr. W. Gleave

for the help rendered during the construction of the dryer.

The f inancial support extended by the National

Research Council to carry out this study is very much

appreciated.

INTRODUCTION

In the modern practices of harvesting and processing

agricultural crops, drying of cereal grains has become an

essential operation. In view of the significance of this

development, the establishment of design requirements for

drying systems on a rational basis is very important.

The drying rate of grain in a thin layer is determined

by a ir temperature, relative humidity and by the rate of a ir

flow. A better knowledge of the effect of drying parameters

in thin layer drying is important in the anlysis of deep bed

drying.

In the past, both empirical and analytical approaches

have been made and several equations have been suggested to /

characterize moisture movement from a fu l ly exposed object. ^

The existing drying theory is based on the assumption that the

mechanism of internal flow of moisture within a kernel is that

of diffusion. The concept of dynamic equilibrium moisture

content has been used by many investigators but the relat ion

ships among a ir temperature, relat ive humidity and rate of a i r

flow have not yet been reported.

This study was therefore carried out to determine the

effects of a i r temperature, relative humidity and a ir flow

rate on the drying constant, the diffusion coefficient and the

dynamic equilibrium moisture content during thin layer drying

of-wheat grain. The drying experiments were conducted using

a ir at temperatures between 60 and 120 degrees Farenheit, with

relative humidity in the range of 25 to 80 percent and with

- 1 -

_ 2 -

a i r flow rates of 120, 80, 20 and 5 feet per minute. The

•wheat grain had an i n i t i a l moisture content of approximately

29 percent, dry basis.

REVIEW OF LITERATURE

Drying is of great importance to a l l grain handlers

and especially to farmers. The grain must be at the proper

moisture content for safe storage. High moisture content

causes deterioration from mold, microorganisms and insect

ac t iv i t i e s . Safe storage for wheat in most climates is assured

i f the moisture content is below 13.5 percent.

A wheat grain is a heterogeneous sol id consisting of

an outer protective coat, the pericarp within which l ies the

starchy endosperm and the wheat germ. A longitudinal section

of wheat grain is shown in Figure 1. Water enters the wheat

grain most readily at the germ end, the only part of the grain

not protected by the aleurone layer. Therefore, the resistance

to the water removal during drying is almost entirely concen

trated in the aleurone layer.

Nature of Drying Process

Investigations on drying have indicated that for a

material of high moisture content, drying can be divided into

two dist inct periods, a constant-rate drying period and a

fa l l ing-rate drying period. During the constant-rate period

the rate of drying is determined by the external conditions of

temperature, humidity and a ir flow while during the f a l l i n g -

rate period the rate of drying is governed by the internal flow

of l iquid or vapor (40)*. The fa l l ing-rate period of drying

Numbers in parentheses refer to the references l i s ted in the l i terature cited.

- 3 -

- 4 -

E N D O S P E R M /STARCHY ENDOSPERM -IALEURONE L A Y E R —

P E R I C A R P (EPIDERMIS C BEESWING ) CROSS LAYER

LTUBE CELLS S E E D C O A T S

JTESTA

(H VALINE LAYER

ENDOSPERM CELL-vvith starch granules ALEURONE CELL-

G E R M

ft SCUTELLUM Epithelium —

PLUMULE -

RADICLE

RADICLE CAP_

F i g u r e 1. L o n g i t u d i n a l s e c t i o n o f wheat g r a i n .

is controlled largely by the type of material and involves the

movement of moisture within the material to the surface by

l iquid diffusion and the removal of moisture from the surface.

Simmonds et al_. (44) found that for wheat grain which was

tempered to 66 percent moisture content, dry basis, a l l the

drying took place in the fa l l ing-rate drying period. Several

other workers are also of the opinion that most agricultural

products dry during the fa l l ing-rate period.

Many theories have been propounded in the past to

explain the nature of moisture movement. The phenomenon is

as the movement of water molecules due to:

(i) differences in vapor-pressure

( i i ) l iquid diffusion

( i i i ) capi l lary flow

(iv) pore flow

(v) multimolecular layer movement

(vi) unimolecular layer movement -

(vi i ) concentration gradient and so lubi l i ty of the absorbate

' The use of the diffusion equation to correlate the

drying data was f i r s t suggested by Sherwood (41, 42) and

Newman (37). The standard drying theory for porous media as

developed by Newman and Sherwood rests on the assumption that

water molecules diffuse through the material in such a way

that the rate of change of water concentration is proportional

to the rate of change of moisture gradient.

where D = di f fus iv i ty of moisture in the material

c = concentration at any point

0 = time

x = distance through the material in the direction of diffusion

Equation [1] is the fundamental basis of a great

deal of work which has been done in.drying. Experiments by

Sherwood (42, 43) have shown that for most materials the

d i f fus iv i ty is not a constant but is a function of the

moisture content. When equation [1] was used to correlate

drying data, Van Arsdale (46) stated that the di f fus iv i ty of

hydrophilic substances was highly dependent upon the moisture

content. Recognizing the inadequacy of equation [1], he

selected vapor-pressure instead of moisture concentration as

the diffusion producing potential in the diffusion equation.

Babbitt (2) has shown that the vapor-pressure is

the main driving force for the moisture movement during

drying. He observed in his experiments that in hygroscopic

materials the moisture can move against the gradient of

moisture concentration and the total migration is proportional

to the vapor-pressure difference. This relationship, however,

does not apply to relative humidities greater than 80 percent.

In a later publication Babbitt (4) derived di f ferent ia l

equations for the diffusion of vapors through sol ids.

Becker and Sallans (8) concluded, in a study of

- 7 -

wheat kernels that the di f fus iv i ty is independent of the

moisture content although i t is dependent upon the temperature

of the drying a i r , which is quite contrary to the works of

Wang and Hall ( 4 8 ) stated,

"If the temperature distribution within .the medium is uniform, the diffusion equation with concentration as the driving force is adequate in describing moisture movement in the medium. However, i f the temperature distribution within the medium is non-uniform, i t takes simultaneous equations of moisture and heat diffusion to describe moisture movement within the medium. The diffusion equation alone would be suitable for characterizing moisture movement in cereal grains i f temperature gradients in the individual kernels are negligible".

This is a reasonable assumption since the grain

response to temperature differences is much more rapid than

to moisture differences.

The analysis of the moisture diffusion in porous

media is simplified i f the material is of a simple geometric

shape, however, in general, moisture moves outward in a l l

directions. With this reasoning, Becker and Sallans ( 8 ) , Hustrulid and Flikke (31) and others have described moisture

flow in grain kernels using the diffusion equation.in

spherical coordinates assuming symmetry with respect to the

early investigators.

or ig in .

[ 2 ]

where c concentration at any point

e time

- 8 -

r . = radius of the sphere

D = diffusion coefficient

Chittenden and Hustrulid (16) found that the

diffusion coefficient varied with the i n i t i a l moisture content

of corn and concluded that the diffusion coefficient must

depend on moisture concentration. Sherwood (42), Hougen ert a l .

(28) and Van Arsdel (46) also concluded that the diffusion

coefficient is a function of concentration, but did not obtain

a solution of above equation [2] under these conditions. In

addition, because of variation in kernel structure, the diffusion

coefficient may depend upon the position of the kernel during

drying.

Whitaker e_t a l . (49) considered the diffusion

equation characterizing radial moisture diffusion in a sphere

whose diffusion coefficient was an arbitrary function of both

position and concentration. They concluded that a diffusion

coeff icient, which was a l inear function of concentration,

characterized the drying of sphere better than a constant

diffusion coefficient.

Chen and Johnson (13, 14), recognizing the discrepancy

between experimental and theoretically predicted values in the

later-part of the fal l ing-rate drying period, divided i t into

two phases. They.considered that during the f i r s t phase of

fa l l ing-rate period the moisture movement was due to the l iquid

flow above the maximum hygroscopic moisture where the diffusion

coefficient is independent of moisture content. During the

- 9 -

second phase of fa l l ing rate period the moisture movement

occurs below the hygroscopic moisture where both vapor and

l iquid flows occur within the material and the diffusion

coefficient is dependent upon the moisture content. This

resulted in two values for each drying constant and diffusion

coefficient, to describe a complete drying process.

Newman (36, 37) suggested that in a drying process

the moisture movement is by diffusion and is analogous to

that of heat conduction in a so l id . The equation given by

Henderson and Perry (27) for heated a i r drying of a slab

of in f in i te extent is

M Q~ M E T , -G0 .. 1 -9G0 . 1 -25G0 •» r , Vrrn; = L ( e + 9 e + 25 e + [ 3 ]

o E where M = moisture content (percent,dry basis)

after a time 0

M = i n i t i a l moisture content (percent, o dry basis)

Mj, = dynamic equilibrium moisture content (percent,dry basis)

G = constant related to volumetric di f fus iv i ty

L = constant dependent on the shape of the part ic le

0 = time

The left hand portion of equation is defined as the moisture

ratio (MR).

Hukil l (29) observed for thin layer drying of grain

that the drying rate was proportional to the difference between

grain moisture content and the equilibrium moisture content.

- 1 0 -

50 = - a CM - M£)

where a is a constant.

When integrated, this becomes

• M 6 - M E -aO M - M„ 6

O h

or MR = e"a G [ 4 ]

where the nomenclature is as previously defined. This

equation, commonly called the half response equation,

corresponds to a physical model that concentrates a l l the

resistance to moisture diffusion in a layer at the surface

of the kernel. The half response equation was derived and

employed by Simmonds et a l . ( 4 4 ) in their studies of wheat

grain drying.

Recognizing the inadequacy in describing the

complete drying process, Page (39) modified the half response

equation by adding an empirical constant.

MR = e L 5 J

where a and n are constants.

Equilibrium Moisture Content

The equilibrium moisture content is a function of

temperature and humidity and refers to the moisture content

which the material retains in equilibrium with i ts surroun

dings . When the value is obtained by static methods (21) i t is known as static equilibrium moisture content.

The concept of dynamic equilibrium moisture content

- 11 -

was introduced by Jones (32) to satisfy the preconceived

"logarithmic drying lav;" which fai led to give good agreement

between the theoretical and the experimental values as

observed by Babbitt (3), during his work'on adsorption of

water vapor by wheat. Jones postulated that during the

fa l l ing-rate drying period the surface moisture concentration

of a hygroscopic product remained above the stat ic equilibrium

at the so-called dynamic equilibrium moisture content', as

long as the "more loosely" held water has not been removed.

Simmonds et a l . (45) suggested that the discrepancy

between the values of dynamic and static equilibrium

moisture contents was due to the fact that grain is l iv ing in

nature and changes i t s physical and chemical nature according

to i t s environment. Whereas the drying process is a fast one,

the environmental adjustment of the grain's structure is a

slow process. These dynamic processes occurring simultaneously

give rise to the variation of the equilibrium moisture content

with rate of drying and the moisture content of the grain.

Allan (1) considered that the concept of dynamic

equilibrium moisture content had considerable merit as the

value obtained is found during an actual drying process and

refers to the pract ical range in a typical drying time. He

concluded that' for the purpose of predicting and describing

a grain drying process, the dynamic equilibrium moisture

content was the logical choice but for storage the stat ic

equilibrium moisture content was the appropriate quantity.

- 12 -

' Baker-Arkema and Hall (6) in the drying tests of

a l fa l fa wafers did not observe any dynamic moisture

equilibrium during the fal l ing-rate drying period, and even

doubted that such a quantity occurs during the drying of

other biological products.

Becker and Sallans (8, 9), Hustrulid and Flikke

(31) and Baker-Arkema and Hall (5) have used the term

effective surface moisture content instead of dynamic

equilibrium moisture content in the moisture ra t io . Hustrulid

and Flikke (31) assumed that, as soon as the drying starts ,

the surface is kept at a constant moisture content, and

called i t the effective surface moisture content. They did

not suggest any procedure for i ts calculation.

Baker-Arkema and Hall (6) found that the surface

moisture content in the drying of forage wafers varied

exponentially with time. Chittenden and Hustrulid (16)

found that surface moisture content decreased with time in

the drying of shelled corn.

Chu and Hustrulid (17, 18) used the effective

surface moisture content in the moisture ratio and suggested

the value as one which would give a straight l ine when free

moisture versus time is plotted on semilog paper for time in

the range of 4 to 10 hours. Though they used a-different

terminology for the dynamic equilibrium moisture content, i t

appears that the basic concept of the dynamic equilibrium

moisture content and the effective surface moisture content

- 13 -

is the same and the dynamic equilibrium moisture content may

represent some average of the surface moisture content.

Although the meaning of the term dynamic equilibrium

moisture content has always remained somewhat vague, many

workers have continued to use this concept because i t offers

the poss ib i l i ty of obtaining a straight l ine relationship

when the moisture ratio is plotted against time on a semi-

logarithmic paper, though without proper jus t i f i cat ion . For

instance, Hustrulid and Flikke (31) assumed a value for the

dynamic equilibrium moisture content for shelled maize of

7 percent to be called reasonable. Pabis and Henderson (38)

in two shelled maize drying tests chose values of 6.5 and

10.1 percent respectively for the dynamic moisture equ i l ibr ia ,

without explaining the reason for the difference in these two

values.

Effect of Relative Humidity on the Static Equilibrium Moisture" Content

Much work has been devoted to the development of

expressions showing the relationship between the equilibrium

moisture content and the relative humidity. The equilibrium

moisture content curves for a number of materials were found

to have the following mathematical characteristics (23).

1 - rh = e~K' ^ [6]

where rh = relative humidity of a ir expressed as a decimal

K 1 = factor varying with, material

- 14 -

n' = exponent varying- with material

^El = s tat ic equilibrium moisture content

Henderson (23) modified the above equation by

introducing a temperature factor in the exponential term.

McEwen and O'Callaghan (34) presented the re lat ion

ship between the equilibrium moisture content and relative

humidity by a more empirical equation.

M' = f + g . - [7] E t 2

where M! = equilibrium moisture content, pounds E of moisture per pound of dry matter

H = humidity of the drying a i r , pounds of moisture per pound of dry air

t = a ir temperature, degrees Farenheit and

f, g = constants

The relationships given by Henderson (23) and

McEwen and O'Callaghan (34) are applicable to the static

equilibrium moisture content and produce similar results

except at low and high relative humidities.

Chen (12), on the assumption made by Chen and

Johnson (13, 14) that the drying of hygroscopic materials is

considered as the moisture migration in a diffusion f i e l d ,

studied the equilibrium moisture isotherms for variable and

constant diffusion coefficients.

Although many attempts have been made by researchers

(Henderson (23), Young and Nelson (50), Chung and Pfost (19)

and Chen (12)) to develop mathematical models to correlate

- 15 -

e q u i l i b r i u m m o i s t u r e c o n t e n t w i t h the d r y i n g p a r a m e t e r s , none

o f the models are d i r e c t l y l i n k e d w i t h the e x i s t i n g t h e o r y o f

d r y i n g .

I t i s w e l l known t h a t the dynamic e q u i l i b r i u m

m o i s t u r e c o n t e n t depends on the t e m p e r a t u r e o f t h e d r y i n g a i r ,

i n a d d i t i o n t o r e l a t i v e h u m i d i t y but no d e f i n i t e r e l a t i o n s h i p

has been e s t a b l i s h e d as y e t .

D r y i n g Rate C o n s t a n t and D i f f u s i o n C o e f f i c i e n t

Becker and S a l l a n s ( 8 ) found t h a t the d r y i n g c o n s t a n t

i s a f u n c t i o n o f the a b s o l u t e t e m p e r a t u r e o f the d r y i n g g r a i n

and v a r i e s w i t h t e m p e r a t u r e a c c o r d i n g t o an A r r h e n i u s t y p e

e q u a t i o n . Henderson and P a b i s (25) and Boyce (10) o b s e r v e d

t h a t a f t e r one o r two hours o f d r y i n g , the t e m p e r a t u r e o f t h e

g r a i n r e a c h e s t h e • t e m p e r a t u r e o f the d r y i n g a i r and, t h e r e f o r e ,

s u g g e s t e d t h a t t h e a i r t e m p e r a t u r e may be used t o determine

t h e e f f e c t on the d r y i n g c o n s t a n t . The A r r h e n i u s t y p e

r e l a t i o n s h i p has been s t u d i e d and c o n f i r m e d by s e v e r a l o t h e r

i n v e s t i g a t o r s ( 8 , 17, 24, 4 4 ) .

The d r y i n g r a t e c o n s t a n t i s r e l a t e d t o the e f f e c t i v e

m o i s t u r e d i f f u s i o n c o e f f i c i e n t and the e f f e c t i v e k e r n e l r a d i u s

( 2 0 ) . C h i t t e n d e n and H u s t r u l i d (16) p o i n t e d out t h a t when

t h e r e i s . a v a r i a t i o n i n the e f f e c t i v e k e r n e l s i z e s , c o r r e l a

t i o n s t u d i e s must be done u s i n g v a l u e s o f t h e d i f f u s i o n

c o e f f i c i e n t r a t h e r than t h e d r y i n g c o n s t a n t .

A i r Flow Rate

Most p r e v i o u s i n v e s t i g a t o r s ( 5 , 16, 26, 44) have

- 16 -

found that the variation in the a ir flow rate past the kernels

of grain dried in a thin layer does not affect the drying time

or drying constant. This may be due to the high internal

resistance of the kernels to moisture movement as compared to

the low resistance to surface moisture movement.

Chilton and Colburn (15) correlated many resistance

data for fluids flowing through granular masses by means of

a modified Reynold's number using nominal particle diameter.

Their studies indicated that turbulance persisted above a

Reynold's number of 10 0 and laminar flow occurred below, a

Reynold's number of 2 0 but no dist inct break point was noted

between the two.

Henderson and Pabis (26) found that a ir rate had

no observable effect on drying when a ir flow was turbulent

and concluded that the variation in air-flow rate affects

the surface moisture transfer coefficient ins igni f icant ly ,

part icularly after the f i r s t two hours of drying.

THEORY

Drying Equations

As discussed previously, i t has been observed by

several workers (1, 31, 44, 47) that small grains exposed

in thin layers dry according to the equation

a ~ = - K (M - MP) . [8]

dQ E

Integrating and applying the boundary conditions,

0 = 0 , M = MQ

6 = 9, M = MQ

results in

M - M u E -K9 r o 1 M - M" = a 6 C 9 ]

0 E

where = i n i t i a l moisture content, percent, dry basis

= moisture content after a time 9, percent,dry basis

Mj, = equilibrium moisture content, percent,dry basis

9 = time, hours

K = drying constant, hour ^ and

a = constant

The above equation is based on the assumption that

the moisture movement.is by diffusion and a l l the resistance

to mass transfer is considered to be at the outer surface of

the kernel.

Assuming that the diffusional resistance is uniformly

distributed throughout the grain kernel and that the kernel

- 17 -

- 18 -

i s , a sphere of homogeneous material with a uniform i n i t i a l

moisture content, drying results have been expressed as

follows ( 5 , 8 , 3 0 , 3 8 )

M — M 0 0

0 E n=l n

For large, values of time, 9, the higher terms

of equation [10] are negligible and the equation reduces to

M n - M„ . -K9 9 E 6 n i l

M - M = iTi~ e C l 1 3

• 0 E

which is o comparable with equation [9] except for a constant.

The lef t hand term of equations [9], [10] and [11] is non-

dimensional and is called the moisture difference rat io .

In this study, equation [9] has been used to interpret the

experimental drying results.


The equilibrium moisture content CM£) in equation

[9] is a characteristic of the material and is a function

of the state conditions of the drying a ir (22, 2 4) and

therefore is assumed to be constant i f the a i r temperature

and humidity are constant.. The value of the dynamic e q u i l i

brium moisture content may be calculated as follows:

If a constant time interval A9 is taken during a

particular drying operation under constant conditions, then

the process of moisture reduction during drying is of a

nature such that

- 19 -

_MT, ' M M M 9+2A9 9 + A9 . -KA9 r n _ _ = = a e [12] M T 9 F N9+A9 b « b

The f i r s t two parts of the above equation, when

solved, give the value of the di'namic equilibrium moisture

'content as

M 2 - M M M 9 + A9 9 9 + 2A9 r

E " 9 Ft r~M -Ti ~ L J

9+A9 9 9+2A9 The dynamic equilibrium moisture content may also be

dM

calculated from equation [8] by plotting g- against moisture

content /dry basis) on a l inear graph paper after three

hours of drying for a drying test. The slope of the l ine

gives the value of K while the intercept gives the product

of K and M ,. This method is val id only when K is a constant

for a drying test.

The equilibrium moisture content in equations [9],

[10] and [11] when calculated from the experimental data

under the dynamic conditions, is called the dynamic equilibrium

moisture content.

It is assumed that a moisture gradient develops

within an individual kernel.as drying progresses. Under

static conditions, when the moisture is distributed uniformly

within a kernel, the vapor-pressure is uniform as shown by the

dashed line (Figure 2), with a surface vapor-pressure, p . s As the drying progresses, the vapor-pressure at the surface

of the kernel which is a function of moisture content at the

Figure 2. Development of moisture gradient within a kernel as drying progresses

surfacedecreases . Therefore, a moisture gradient is developed

within the kernel with vapor-pressure (P^) at the surface as

is shown by the so l id . l ine in Figure 2. The value of the

equilibrium moisture content (dynamic) thus calculated under

dynamic conditions is lower than the static equilibrium

moisture content and is preferred for use in a drying process.

Effect of Temperature on Equilibrium Moisture Content

The following relationship between relative humidity,

a ir temperature and equilibrium moisture content has been

established by Henderson (23) N . • . _

-CTM 1 - rh = e L [14]

where rh = equilibrium relative humidity, a decimal

Mg = equilibrium moisture content, percent dry basis

T = temperature, degrees Rankin

C,N = constants.

The above equation was developed to describe static

- 21 -

equilibrium moisture contents. However, in these studies

equation [14] has been used to describe "dynamic" values of

equilibrium moisture content.

Drying Rate Constant

Equation [9] can also be written as

In MR = In a - KG [15]

When MR is plotted against time 0 on a semilog

paper, the slope of the l ine represents the drying rate

constant (K). It was shown by Crank ( 2 0 ) that the drying

rate constant is related to the effective diffusion coefficient

and effective kernel radius by the equation

K = D ILl [16] rk

where D = diffusion coeff icient, square feet per hour

r, = radius of a kernel, equivalent to a sphere, feet.

Effect of Air Temperature on the Drying Rate Constant and the"Diffusion Coefficient "

Becker and Sallan ( 8 ) found that the drying constant

is a function of absolute temperature of the drying grain.

The drying constant and absolute temperature of the drying

a i r can be related by an Arrhenius type equation of the form:

d (In U) _ _ E _ dT R T 2

[17] E

or ~ W U = U e R T

o where U = rate of a specific chemical reaction

- 22 -

R = gas-law constant

E = energy of activation factor

U = constant o T = absolute temperature

Since moisture is assumed to be contained in small

grain as adsorbed moisture, the energy required to desorb

the moisture can be considered analogous to the energy of a

chemical reaction, and an equation of this type would apply.

Henderson and Pabis (24) established the following relat ion

ship and found i t to be satisfactory from the data of Allen

(1) and Simmonds et a l . (44) in addition to their own work.

d v i t + 460 K = b e

where b and d are .constants, and

t = temperature of the grain, degrees Farenheit

The temperature in the above equation refers to

the temperature of the grain but Henderson and Pabis (25),

Allen (1), Boyce (10) have indicated that the temperature

difference between the a ir and grain becomes insignificant

after 1 or 2 hours of drying. Because of the simplicity of

measuring a ir temperature rather than grain temperature, a i r

temperatures have been used in equation [18].

As the drying rate constant and the diffusion n 2

coefficient are related by a constant —j, for a given size r k

and shape of material, the effect of temperature on the

diffusion coefficient may also be represented by an equation

- 2 3 -

similar to equation [18] except for constants.

"*E/ D = D e [19] o

where R = gas-law constant -

T = absolute temperature, degrees Rankin and

D , E = constants

APPARATUS

Instrumentation

A closed-cycle, heated a ir dryer was constructed

to carry out the drying tests. The walls of the dryer were

insulated using two-inch-thick styrofoam. The drying area

was divided into three compartments and could be used for

tray drying, thin layer drying, deep bed drying and pot hole

drying. A sketch of the dryer is shown in Figure 3.

Steam coils were used for heating the a i r . A

cooling co i l was also placed within the dryer to make i t

possible to obtain low temperatures and relative humidities.

The cooling c o i l was connected to a refrigerating unit

instal led outside the dryer. Two temperature sensors, one for

dry bulb and the other for the wet bulb temperature, were used

to control and maintain the constant drying conditions during

the experiment. The sensors were effective over a temperature

range of -40 to + 160 degrees Farenheit.

A set of or i f i ce plates (Figure 4) was used to

control the a ir flow rate through the drying tray. The lower

plate was fixed while the upper plate could be rotated to

obtain the a i r flow rates between 0 and 1000 feet per minute

through the tray. In an attempt to.obtain a uniform velocity

profi le through the drying tray, the space between the tray

and or i f ice plate was f i l l e d i^ith spun fiberglass.

A i r drawn by a variable speed fan passed through

the steam heated coi ls and the adjustable or i f ice plates.

After passing through the -mixing zone, a part of the a i r was

diverted through the drying tray while the remaining a ir

- 24 -

Thin Layer or

D e e p B e d

D r y i n g C h a m b e r

Tray D r y i n g C h a m b e r

Sample

Pot Ho le D r y i n g C h a m b e r

A A

t>-s-tz_P=-------O r i f i c e Plates ^>°4^Dry Bulb Sensor

Wet Bulb Sensor D a m p e r

H e a t i n g Co i l (steam)

A A A G

->

A i r F low Path

->

v v

3>

Coo l ing C o i l

3>

F i g u r e 3 . Sketch o f the Dryer

- 26 -

passed through an adjustable damper. The path of the a ir

flow is indicated on Figure 3. The relative humidity of the drying a ir could be

increased by injecting steam into the drye?? at point A

(Figure 3). The injection of steam was controlled by the

wet bulb sensor and control valve.

MATERIAL AND MEASUREMENTS

Grain Used for Drying Experiments

Wheat grain of Park variety from the 19 6 8 crop,

grown in the Peace River area of Bri t i sh Columbia was used

for the drying tests in this study. The wheat grain was

stored in plast ic bags at 32 degrees Farenheit in order to

maintain i ts or ig inal moisture content. A sample of four to

five hundred grams was taken for each drying test. The

sample was cleaned and only the sound whole kernels were

collected. Prior to drying, the sealed sample was kept at

room temperature for ten to twelve hours to allow the grain

to come to room temperature. It was assumed that the moisture

was uniformly distributed throughout the sample. A l l tests

were conducted on grain at the i n i t i a l harvest moisture

content; no attempt was made to alter the moisture content by

adding water to the grain.

Moisture Content

A l l moisture content determinations were made using

the vacuum oven drying method at 95-100 degrees Farenehit (33).

Five samples, each weighing about 10 grams were used for each

moisture determination. The average loss of weight was used

to calculate the i n i t i a l moisture content and the f ina l weights

were Used as the dry matter content. The test samples were

found to have an average i n i t i a l moisture content of 29 percent,

dry basis.

Temperature^ and Relative Humidity

The dry bulb and wet bulb temperatures of the a ir

- 27 -

- 28 -

were determined both by mercury-in-glass thermometers and

the thermocouples placed in the stream of by-passed a i r at a

point where the a i r flow was greater than 1000 feet per

minute to ensure correct measurements, especially for the wet

bulb temperatures. The dry bulb and wet bulb temperatures

were also compared with the a ir temperature and relative

humidity recorded by a hygrometer (Hygrodynamic Inc. Model

15-4050E) shown in Figure 5. The sensing element was placed

inside the dryer. It was possible to read accurately up to

+ 2.0 percent relative humidity of the a ir on the chart of the

recorder". Because of this l imitation of determining the

relative humidity accurately, i t was mainly used to warn of

the changing conditions inside the dryer. The dry bulb and

wet bulb temperatures were used as a more accurate method of

calculating relative humidity of the a i r .

Air Flow Rate

Desired a ir flow rates could be obtained by adjusting

the slot width between the or i f ice plates and was measured with

a hot wire anemometer (Flowtronic Model 55 Bl a i r velocity

meter). A c ircular tray of eight inch diameter was used for

drying tests. The average velocity was determined by dividing

the area into five equal concentric areas and measuring the

a ir velocity at the center of each area. The mean of these

values was considered as the average a ir flow rate through the

tray (27). Settings for four different air flow rates of 5,

20, 80 and 120 feet per minute were obtained by adjusting the

- 29 -

Figure 5 A i r humid i ty a n d t e m p e r a t u r e recorder w i th sensor

- 30 -

openings between the or i f ice plates and the respective

positions were marked on the adjusting rod connected to the

upper or i f ice plate. Any a ir velocity setting could easily

be reproduced by s l iding the rod to the marked position.

The a ir velocity was further checked for each setting before

starting the drying test.

EXPERIMENTAL PROCEDURES

The drying tests were carried out at four a i r

temperatures of 1205 100, 80 and 60 degrees Farenheit with

relative humidities of 75, 50 and 25 percent. The experimental

design is given in Table I. Each drying set consisted of four

drying runs with a ir flow rates of 120, 80, 20 and 5 feet per

minute. Reynold's number varied from a minimum of 4- to a

maximum of 110, In a drying run where the dry bulb tempera

ture varied by more than + 2.0 degrees Farenheit or the relative

humidity varied by more than + 5.0 percent, the run was repeated.

The state conditions of the drying a ir were assumed to be

constant for each drying test.

The dry and wet bulb controls were set to give the

desired drying conditions. After the temperature and relative

humidity of the drying a i r had stabil ized the test sample was

placed in the dryer. About 24 5 grams of wheat was taken for

each drying test and was placed in the drying tray with screened

bottom, forming a layer five to six kernels deep. The tray

was removed from the dryer at specified time intervals , one

hour in most cases, and weighed to an accuracy of 0.01 gram

on a balance adjacent to the dryer. This operation was carried

out rapidly and i t was considered such brief interruptions did

not'interfere with the drying process. For the drying runs

included in sets C and F, where the air temperatures were high

but the relat ive humidities were low, a half-hour-interval

was taken between the successive weighing operations. For

drying sets J and K, a two-hour-weighing-interval was used

because of the low temperature and the high humidity of the

- 31 -

- 32 -

TABLE I. EXPERIMENTAL DESIGN SHOWING TEMPERATURE, RELATIVE HUMIDITY AND AIR FLOW RATES FOR DRYING TESTS CONDUCTED ON WHEAT, WITH THE CODE DESIGNATION OF EACH RUM

Drying Drying Air Drying run No. for a i r flow rate of Set —- : • -- :

Temp. R.H. 1 2 O 80 2 0 5 °F % ft/min ft/min ft/min ft/min

A 120 + 1.0 78 + 2 . 0 111 112 113 114

B 120 + 1.5 50 + 2. 0 121 122 123 124

C 122 + 1.0 25 + 2.0 131 132 133 134

D 101 + HO 72 + 2.0 211 212 213 214

E . 100 + •1.5 50 + 1.5 221 222 223 2 24

F 100 + 1.0 2 6 + 1.5 231 232 233 2 34

G 81 + 2 . 0 75 + 2.0 311 312 313 314

H ' 81 + 2.0 50 + 1.5 321 322 323 324

I 80 + 2.0 37 + 2 . 0 331 332 333 334

J 60 + 1.0 75 + •1.5 411 412 413 414

K 60 + 1.0 61 + 2.0 421 422 423 4 24

- 33 -

drying a i r .

The relative humidity of the drying a i r was calculated

from dry bulb and wet bulb temperatures using the mathematical

model of the psychrometric chart presented by Brooker (11).

The values were also compared with the relative humidities

recorded by the hygrometer and those calculated directly from

the psychrometric chart. A l l these values were found to agree

within + 2 percent.

The value of dynamic equilibrium moisture content

for each drying run was computed using equation [13]. Only

the moisture content data after the f i r s t three hours of

drying were used because the i n i t i a l drying period involved

transient conditions and was not suitable for analysis by the

methods used, in this work.

The computer program developed for computing the

moisture content (percent, dry basis) , the average dynamic

equilibrium moisture content (percent, dry basis) and the

moisture rat io from the drying weights, and the relative

humidity from the dry bulb and wet bulb temperatures is shown

in Appendix C along with a sample calculation for drying set

E.

RESULTS AND DISCUSSION

Drying Curves

The typical drying curves for wheat with an i n i t i a l

moisture content of 29 percent (dry basis) when exposed to

different a ir temperatures, relative humidities and a i r flow

•rates are shown in Appendix A. The computed drying results

for various drying conditions are shown in Tables II , III ,

IV and V.

From the drying curves i t is evident that the rate

of drying increases with increasing a i r temperature and a i r

flow rates, but decreases with increasing relative humidity

of the a i r . The effect of changes of a i r flow rate and

relative humidity is small as compared to the change in

temperature of the drying a i r .


The average dynamic equilibrium moisture content

calculated using equations [8] and [13] are shown in Tables

I I , I II , IV and V. These values are found to be in good

agreement though in general the values calculated from

equation [8] are s l ight ly higher.

Simmonds ejt aJL. (44) obtained the value of the

dynamic equilibrium moisture content for wheat at 80 degrees

Farenheit, 79 percent relative humidity and 32 feet per

minute a ir flow rate as 12.8 percent which is comparable to

12.7 percent found at 80 + 2 degrees Farenheit, 76 + 2 percent

relative humidity and for a i r flow rate of 2 0 feet per minute

in this study. These results indicate the dynamic equilibrium

- 34 -

TABLE II . COMPUTED DRYING RESULTS AT 120 - 2 . 5 °F DRYING AIR TEMPERATURE FOR SEVERAL RELATIVE HUMIDITIES AND AIR FLOW RATES

'Test Drying air A ir flow M„ K ' . . ^. No. Tern*. R.H. ft/min. E q n

E [ 1 3 ] -1 R e g r e s s i o n R a t i o n °F %(d.b.) %(d.b.) • hr

d. f. 9 DxlO5

v _ 2 M from 9 Eqn.[8]

ft /nr . %(d.b.)

SET A 111 119. 5 78. 0 120 4 . 5 0. 454 In MR=0.468-0.454(9) 5 0 . 99 0. 307 4.5

4 < 9 < 9 112 119. 5 78. 0 80 7. 2 0. 398 In MR=0.422-0.398(9) 5 0. 99 0. 269 7.3

4 < 9 < 9 113 119. 0 79. 0 •20 7. 6 0. 3 33 In MR=0.313-0.333(9) 5 0 . 98 0 .225 7.8

4 < 9 < 9 114 120. 0 78. 5 5 7. 6 0. 293 In MR=0.388-0.293(9) 5 0 . 99 0.198 7.9

4 < 9 < 9 SET B •

121 120. 5 51. 0 120 4. 3 0. 368 i n MR=0.607-0.368(9) 5 0. 99 0.249 4.4 4 < 9 < 9

122 121. 0 50. 0 80 5 . 0 0. 410 In MR=0.750-0.410(9) 5 0. 96 0. 277 4.7 4 < 9 .< 9

123 121. 0 51. 5 20 6. 0 0. 415 In MR=0.724-0.415(9) 5 0. 99 0.280 6. 1 4 < 9 < 9

124 121. 0 51. 5 5 5. 5 0. 288 In MR=0.588-0.288(9) 5 0. 96 0.194 5.8 4 < 9 < 9

SET C 131 122. 5 25. o • 120 4. 2 0. 378 In MR=0.385-0.378(9) 7 0. 98 0.256 4.6

3 < 9 < 6.50 132 122. 5 25. 5 • 80 3. 7 0. 316 In MR=0.426-0.316(9) 7 0 . 99 0.213 4.0

3 < 9 < 6.50 133 122. 0 26. 0 20 4. 2 0. 355 In MR=0.415-0.355(9) 7 0. 96 0 . 2.4 0 4.8

3 < 9 < 6.50 134 122. 0 25. 0 5 3. 5 0. 246 In MR=0.514-0.246(9) 7 0 . 98 .0.16 6 5.2

CO

< 9 < 6.50

TABLE III. COMPUTED DRYING RESULTS AT .100 - 2 . 0 ° F DRYING AIR TEMPERATURE FOR SEVERAL RELATIVE HUMIDITIES AND AIR FLOW RATES

. - 3 Test Drying air A ir flow M £ K DxlO M^from

No. Temp. R.H. ft/min Eon.[131 i Regression equation d.f . r 0 Eqn.[8] °F %(d.b.) %Cd.b.J h r _ 1 " .. * f t V h r . %(d.b.)

SET D 211 102. 0 71. 0 120 9. 5 0. 285 In MR=0.655-0. 285(9) 5 0. 99 0.192 9. 6

4 < 9 < 9 212 101. 0 72. 0 80 10. 4 0. 302 in MR=0.719-0. 302(9) 5 0. 99 0.186 10. 5

4 < 9 < 9 213 101. 0 73. 5 •• 20 11. 3 . 0. 280 In MR=0.7 31-0. 280(9) 5 0. 99 0. 204 11. 4

4 < 9 < 9 214 101. 5 72. 5 5 11. 2 0. 213 In MR=0.638-0. 213(9) 5 0. 99 0.144 11. 9

4 < 9 < 9 SET E

221 101. 0 50. 0 120 6. 9 0. 306 In MR=0.579-0. 306(9) 5 0. 99 .0.207 •7. 1 4 < 9 < 9

222 101. 0 50. 0 80 7. 2 0. 294 In MR=0.616-0. 294(9) 5 o. 99 0.199 7. 3 4 < 9 < 9

223 100. 5 50. 0 20 7. 9 0. 276 In MR=0.627-0. 276(9) 5 0. 99 0.186 8. 1 4 < 9 < 9

224 101. 0 50. 0 • 5 8. 5 0. 235 In MR=0. 616-0'. 235(9) 5 0. 99 0.159 8. 8 4 < 9 < 9

SET F 231 100. 5 26. 5 120 5. 8 0. 348 In M.R=0 . 665-0 . 348(9) 8 0. 99 0.235 6. 1

3. 5 < 9 < 7 232 100. 5 26. 5 80 6. 0 0. 293 In MR=0 . 62 3-0 . 293(9) 8 0'. 98 0.198 6. 5

3. 5 < 9 < 7 233 100. .5 26. 5 20 6. 4 0. 315 In MR=0.680-0. 315(9) 8 0. 99 0..213 • 6. 9

3. 5 < 9 < 7 . 234 100 . 5 26. 0 5 7. 5 0. 362 In MR=0.782-0. 362(9) 8 0 . 99 0. 245 7. 7

3.5 < 9 < 7

TABLE IV. COMPUTED DRYING RESULTS AT 81 - 2 .0°F DRYING AIR TEMPERATURE FOR SEVERAL RELATIVE HUMIDITIES AND AIR FLOW RATES

Test Drying a ir • A ir flow M £ K _ DxlO MEfrom No. Temp. . R.H. ft/min Eqn.[13] _ T Regression equation d.f . r 9 Eqn.[8]

°F %(d.b.) %Cd.b.) hr x . f t V h r . %("d.b.)

SET G 311 82. 0 75. 5 120 11. 7 0. 245 In MR=0.810-0. 245(9) 5 0. 99 0.165 11. 9

4 < 9 < 9 312 81. 5 76. 0 80 12. 2 0. 202 In MR=0.837-0. 202(9) . 5 0. 99 0.136 12. 4

4 < 9 < 9 313 82. 0 76. 0 20 12. 7 0. 215 In MR=0.912-0. 215(9) 5 0. 99 0.145 12. 8

4 < 9 < 9 314 82. 5 75. 0 5 12. 9 0. 183 In MR=0.919-0. 183(9) 5 •0. 99 0.124 13. 2

4 < 9 < 9 SET H

321 81. 5 50. 5 120 8. 4 0. 229 In MR=0.814-0. 229(9) 5 0. 99 0.155 8. 5 • 4 < 9 < 9

322 81. 5 49. 0 80 9. 3 0. 240 In MR=0.803-0. 240(9) 5 0. 99 0.152 9 . 5 4 < 9 < 9

32 3 82. 0 49. 5 20 9. 7 0. 235 In MR=0.819-0. 235(9) 5 0. 99 0 .15 9 9. 9 4 < 9 < 9

324 82 . 0 49. 5 5 9. 8 0. 214 In MR=0 ..821-0 . 214(9) 5 0. 99 0.144 10 . u 4 < 9 < 9

SET I 331 81. 5 37. 5' 120 5. 9 0. 210 In MR=0.563-0. 210(9) 5 0. 99 0.142 6 . 1

4 < 9 < 9 332 81. 0 37. 0 80 6. 2 0. 242 In MR=0.733-0. 242(9) 5 0. 99 0.163 6 . 5

4 < 9 < 9 333 80. 5 37. 5 2 0 8. 8 0. 167 In MR=0.769-0. 167(9) 5 0. 99 0.113 8. 9

4 < 9 < 9 334 80 . 0 38. 0 5 9. 4 0. 174, In MR=0.833-0. 174(9) 5 0. 99 0.117. 9. 5

4 < 9 < 9

TABLE V. COMPUTED DRYING RESULTS AT 60 - 1 .0°F DRYING AIR TEMPERATURE FOR SEVERAL RELATIVE HUMIDITIES AND AIR FLOW RATES

Test Drying a ir Air flow M £ K No. Temp. R.H. ft/min Ean.[13] T Regression equation d.f .

°F %(d.b.) U d . b . ) hr

SET J 411 60. 5 76. 0 120 14. 7 0. 103 In MR=0.795-0.

6 < 9 < 16 103(9) 5 o. 99 0. 069 14. 5

412 60. 5 75. 5 80 15. 5 0. 101 In MR=0.7 8 8-0. 6 < 8 < 16

101(9) 5 0. 99 0. 068 15. 1

413 60. 5 76. 0 20 16. 4 0. 111 In MR=0.817-0. 6 < 9 < 16

111(9) 5 o. 99 0. 075 16. 2

414 - 60. 5 76. 0 5 17. 1 0. 117 In MR=0.816-0. 6 < 9 < 16

117(9) 5 0. 99 0. 068 17. 1

SET K 421 60. 6 60. 0 120 7. 8 0. 107 In MR=0.845-0.

6 < 9 < 16 107(8) 5 0. 98 • : o. 072 8 . 4

422 60. 5 60. 5 80 8. 1 0. 101 In MR=0.851-0 . 6 < 9 < 14

101(9) 5 0. 98 0. 068 • 9. 2

42 3 60. 4 60. 5 20 9. 8 0. 077 In MR=0.774-0. 6 < 9 < 14

077(8) 5 0. 96 0. 053 11. 2

424 60. 0 62. 0 5 11. 8 0. 105 In MR=0.836-0. 105(9) 5 0. 99. • 0. 071 11. 6 6 < 8 < 16

-6 2 DxlO M£from

r 7 Eqn.[8] ft /hr . %(d.b.)

- 39 -

moisture content to be constant for a particular temperature

and relative humidity.

The plots of logarithm moisture ratio against time

(Appendix B) show a straight l ine relationship exceptionally

well after f i r s t three hours of drying for a l l the drying

runs. The departure from the straight l ine relationship

for the f i r s t 2 to 3 hours of drying is probably due to grain

adjusting to the drying conditions.. Under such conditions

the moisture loss may occur from the. surface of the kernels,

thus allowing proportionally greater drying rates. The

deviation from the straight line relationship is found to

increase as the drying potential increases ( i . e . at higher

a i r temperatures or at lower relative humidities of the

drying a i r ) .

The i n i t i a l drying period during the f i r s t three

hours of the test were not analyzed in this study as this

was-a transient situation. The grain temperature is probably

changing throughout this period which would produce a set of

values for the dynamic-equilibrium moisture content and the

drying rate constant which are different from that used for

the remainder of the drying run. It could also be possible

that the diffusion coefficient may change in character during

this period. It was fe l t that a better understanding of

"steady state" drying is required before attempting to study

the transient drying phase.

3 0 4 0 5 0 6 0 7 0 8 0

R e l a t i v e H u m i d i t y of D r y i n g A i r , p e r c e n t

Figure -6. Effect of relative humidity of drying a i r on mean value of dynamic equilibrium moisture

'. content at 120 + 3°F, 100 + 2°F and 80 + 3°F.

TABLE VI. MEAN VALUES OF DRYING AIR TEMPERATURE, RELATIVE HUMIDITY, M p AND CALCULATED VALUES OF EQUILIBRIUM CONSTANTS, C AND N (Equation [14]) . /

Drying Set

Drying a i r Mean Temp.

Mean R.H.

(d.b.)

Calculated constants for dynamic equilibrium

moisture C 1 N

Constants given by Henderson (2 3) for stat ic equilibrium moisture for wheat at 90°F.

C N

A B C

119. 5 121.0 122. 0

78.5 51.0 25.5

5.7 5.2 3.9 9.82x10 -6 2.97 5.59x10 3.03

D E F

101.5 101.0 10 0. 5

72.0 50.0 26.5

10.6 7.6 6.4 8.75x10 6 2.54

G H I

82.0 82.0 81. 0

75.5 50.0 37.5

12 .4 9.3 7.6 9.75x10 -6 2.22

J K

60.5 60.5

76. 0 60.5

15.9 9.4

- 42 -

The computed values of the dynamic equilibrium

moisture content were found to vary with a ir temperature,

relative humidity and a ir flow rate. The drying sets A,.B and C (Table II) do not show any definite pattern in the

variation of the dynamic equilibrium moisture content due

to a i r flow rate but for the other drying sets (Tables III ,

IV and V) i t can be seen that the dynamic equilibrium moisture

decreases s l ight ly with increasing a ir flow rate. This

variation seems to be more pronounced at the low temperature

drying sets (J and K, Table V). The variation in the dynamic

equilibrium moisture content due to the a ir flow rate was so

small that no relationship wither with the a ir flow rate or

the Reynold's number could be established.

Effect of Relative Humidity on the Dynamic Equilibrium Moisture Content

Results show that the dynamic equilibrium moisture

content increases with the relative humidity of the a ir which

is in accordance with the effect on static equilibrium

moisture content.

To study the relationship between the relative

humidity and the dynamic equilibrium moisture content in

equation [14] the mean values of the dynamic equilibrium

moisture content have been computed for each set of drying

tests. As the effect of a i r flow rate is small, i t has been

neglected. The plot of mean value of the dynamic equilibrium

moisture content against the relative humidity is shown in

Figure 6, and does not show any definite pattern.

- 43 -

i i I I — I L 1 1 80 70 60 50 40 30 20 10

Log - l o g R e l a t i v e H u m i d i t y , percent

ure 7. Relation between log mean values of dynamic equilibrium moisture content and log-log relative humidity for the a ir temperature 120 + 3°F, 100 + 2°F and 80 + 3°F.

- 44 -

A plot of log dynamic equilibrium moisture content

versus log-log relative humidity (Figure 7) at. a constant

temperature shows a l inear relationship. This indicates that

the relationship in equation [14] is val id even for the

dynamic equilibrium moisture content as found in this study.

The calculated equilibrium constants for the dynamic equilibrium

moisture content, C and N are compared in Table VI with those

given by Henderson (2 3) for the stat ic equilibrium moisture

content values at 90 degrees Farenheit for wheat.

Effect of A ir Temperature on the Dynamic Equilibrium Moisture Content

The computed values of the dynamic equilibrium

moisture content decrease considerably as the drying a ir

temperature increases at a given relative humidity. These

data indicate that the effect of a ir temperature on the

dynamic equilibrium moisture content is more significant than

the effect of relative humidity or a i r flow rate (Tables II ,

III , IV and V).

For a constant relative humidity of the a i r , the

equation [14] becomes

' T . -J- [20] E

The plot of logarithm temperature against the

logarithm dynamic equilibrium moisture content does not show

any satisfactory linear relationship. Therefore, i t seems

that equation [14] fa i l s to account correctly for the

temperature dependence of the dynamic equilibrium moisture

- 45 -

I 6 r

0 60 70 80 90 100 110 120 T e m p e r a t u r e of D r y i n g A i r (degrees Fa renhe i t )

Figure 8. Effect of drying a ir temperature on mean value of dynamic equilibrium moisture content at 75 + 5%, 50 + 2% and 25 + 3% relative humidity.

- 46 -

150r

CD

- £ 1 0 0

£•80 1/1 0 £ 6 0 D) 0) ~o

4 0

a E

2 0

10 5 7 9 11 13 15

D y a m i c Equ i l ib r ium M o i s t u r e C o n t e n t , percent , d r y b a s i s

1 7

Figure 9. Plot of logarithm of drying a ir temperature against mean values of dynamic equilibrium moisture contents at 75 + 5% and 50+2% relative humidity.

- 47 -

content because the intercepts do not remain constant as

shown in Figure 7. This has also been observed by Flail and

Rodriguez-Azias (22). Therefore, other relationships were

examined in this study.

The mean values of the dynamic equilibrium moisture

content for drying sets A, D, G and J , and B, E and H

(Table VI) could be grouped together since the relative

humidities are 7 5 + 5 percent and 5 0 + 3 percent respectively

to determine the effect of a ir temperature on the dynamic

equilibrium moisture content.'

A l inear regression of the a ir temperature on a l l

the values of dynamic equilibrium moisture content gave a 2

coefficient of determination (r ) of 0.45 for the data in

Tables II , III , IV and V. The plot of temperature and the

mean values of the dynamic equilibrium moisture content is

shown in Figure 8. The curves appear to have a definite

convex shape. A semilogarithm plot of logarithm temperature

and the dynamic equilibrium moisture content indicates a

straight l ine relationship (Figure 9). It would appear that a relationship of the form

-M E

t = A + e , where A is a constant, may describe the

variation of the dynamic equilibrium moisture content with

a i r temperature. Further tests w i l l be required to confirm

this .

Effect of A ir Temperature on Drying Rate Constant

The computed values of the drying rate constant (K)

T (degrees Rankin) Figure 1 0 . Relationship between the drying constant and the reciprocal of

i absolute temperature of drying a i r on the basis, of Arrhenius equation.

- 49 -

in. equation [9], neglecting the f i r s t three hour's of drying,

are shown in Tables II , III , IV and V for each run. The

l inear regression of the logarithm of drying rate constant

on the reciprocal of the absolute temperature (Figure 10)

resulted in a coefficient of determination (r~) of 0.83

(significant at P < 0.01). The values of constants b and

d in equation [18] are shown and compared with those

presented by Henderson and Pabis (24) in Table VII.

TABLE VII. COMPUTED VALUES OF CONSTANTS b and d IN EQUATION [18] AND THOSE PRESENTED BY HENDERSON AND PABIS (24)

Computed constants Constants given by Henderson and Pabis (24) for wheat

b d df r 2 b d r 2

9231 5858 43 0.83 10 + 7 9354 0.90

The constants computed in this study appear to be

lower than those presented by Henderson and Pabis (24) for

rewetted wheat grain with 6 6 percent i n i t i a l moisture

content when dried for 25-30 hours at a ir temperatures from

70 to 170 degrees Farenheit.

Henderson and Pabis (24) found while using the

data of Allen (1) that the Arrhenius relationship between

the drying rate constant and a ir temperature was independent

of relative humidity though the former may be a function of

relative humidity of the drying a i r .

- 50 -

?^fj^J- °,f Relative Humidity of the Drying Air and Air Flow Rate on Drying Rate Constant

The computed values of the drying rate constant

in Tables I I , III , IV and V do not show any definite pattern

in the variation either due to' the relative humidity of the

a i r or the air flow rate. The values of the drying rate

constant were plotted against both the relative humidity and

a ir flow rate (Reynold's number) separately on regular

coordinate, semilog and log-log paper but no meaningful

relationship could be obtained.

Allen (1) while drying maize and rice found that

the drying rate constant was a function of relative humidity

but did not give any relationship, whereas other authors

(2, 31) have offered no evidence that relative humidity is

related independently to the drying rate constant.

Effect of A i r Temperature on Diffusion Coefficient

The diffusion coefficient, the factor governing the

mechanism of the internal movement of the moisture within a

grain, is related to the drying constant by a constant factor 2

as described in equation [16].

The average effective diameter of wheat kernels

was computed from one hundred sound kernels considering the

volume of each kernel equivalent to a sphere and was found — 3 •

to be 8.2 x 10 feet. The diffusion coefficients as

calculated from the values of the drying rate constant are

presented in Tables I I , III , IV and V.

1.68 1 . 7 3 1 . 7 8 _ 1 1 . 8 3 1.88 1 . 9 3 x l 0 ~ T (degrees Rankin )

Figure 11. Relationship, between the diffusion coefficient and the reciprocal of absolute temperature of drying a ir on the basis of Arrhenius equation

- 52 -

As expected, the plot of logarithm diffusion

coefficient (D) versus the reciprocal of the absolute

temperature of the drying a i r (~) , Figure 11, was found to

be a straight l ine since the drying rate constant and the

diffusion coefficient are direct ly related. The intercept

and slope of the regression line gives the value of the

constants D q and E / R respectively in equation [19]. . The

constants have been computed by regression analysis and

are shown in Table VIII.

TABLE VIII. COMPUTED VALUES OF CONSTANTS D AND E/ IN EQUATION [19] ° K

D o

E / R E df 2 r

7096xl0"7 59 30 3.85 43 0.83

Since the diffusion coefficient is direct ly related

to the drying constant the effect of relative humidity and

a ir flow rate on the diffusion coefficient would be similar

to those already reported for the drying constant.

CONCLUSIONS •

. In this study the effect of drying parameters on

the dynamic equilibrium moisture content, the drying rate

constant and the diffusion coefficient in thin layers was

investigated. The results of this work support the' follow

ing conclusions.

1. A constant drying rate period occurred for a very short

time and most of the drying period for wheat grain with

approximately 29 percent moisture content, dry basis,

occurred in the fal l ing-rate drying period.

2. The average dynamic equilibrium moisture content

calculated using equation [13.] from the drying data after

f i r s t three hours of drying satisf ied the logarithmic

drying law sat is factori ly for the drying period considered

in this study.

3. The effect of a i r flow rate on the dynamic equilibrium

moisture content was found to be ins ignif icant , except +

at low temperatures of 6G - 1 degree Farenheit.

4. The dynamic equilibrium moisture content increased with

the relative humidity of the drying a ir and appeared

to follow Henderson's equation.

5. With increasing a i r temperature, the dynamic equilibrium

moisture content increased, and perhaps there might

exist an exponential relationship.

6. The drying rate constant and diffusion coefficient were (

found to increase with a ir temperature in accordance

- 53 -

- 54 -

with an Arrhenius type equation.

7. It was observed that the drying process in thin layers

could be related by a constant drying-rate constant

and a constant diffusion coefficient, except during

the i n i t i a l transit ion period.

RECOMMENDATIONS FOR FURTHER STUDY

It is known that as drying progresses, the surface

temperature of grain increases from the wet-bulb temperature

of the drying a ir to near i t s dry-bulb temperature, but the

time, when i t starts increasing and the rate of increase are

not known. A knowledge of the surface temperature of the

grains at various times during drying and information on the

temperature gradients through the kernel would be of value

in analyzing the i n i t i a l transit ion drying period.

On the basis of a limited number of drying tests

conducted in this study, i t was found that the dynamic

equilibrium moisture content varied with a ir flow rate,

relative humidity of the a i r and the temperature of the

drying a i r . The effect of a ir flow rate was found to be very

small except at low temperatures. The effect of relative

humidity of a ir on the dynamic equilibrium moisture content

was in agreement with the Henderson's equation. The equilibrium

constants were found to vary with the a ir temperature. This

needs further veri f icat ion by conducting more drying tests

under similar conditions. The dynamic equilibrium moisture

content has been found to decrease with a ir temperature but

no mathematical relationship could be obtained. It has been

suggested that there might exist an exponential relationship

and this needs further study.

The results of this study do not show any significant

effect of relative humidity of the .air on'drying rate constant,

- 55 -

- 56 -

Even the basic theory precludes an.independent relative

humidity effect on the drying-rate constant. This factor,

perhaps, should be investigated further.

LITERATURE CITED

Al len , J .R. Application of grain drying theory to the drying of maize and r i ce . J . Agri . Engng. Res., 5 .(4) 363 , 1960 .

Babitt, J .D. Observation on the permeability of hygroscopic materials to water vapor. Canadian J . of Res. 18 (a): 105-121, June 1940.

Observations on the adsorption of water vapor by wheat. Canadian J . of Res. 27, Sec. F, 55, 1949 .

Observations on the d i f ferent ia l equations of drying. Canadian J . of Res. 28, S e c . A , 449, 1950.

Bakker-Arkema, F.W. and H a l l , C.W. Static vs dynamic moisture equi l ibr ia in the drying of biological products. Approved Journal art ic le 3708 of the Michigan Agricul tural Experiment Station.

* _______ Importance of boundary conditions in solving the diffusion equation for drying forage wafers. Trans. ASAE 8 (3): 382-383, 1965.

Becker, H.A. Study of diffusion in solids of arbitrary shape, with application to drying of wheat kernel. J . Applied Polymer S c i . , 1212, 1951.

Becker, H.A. and Sallans, H.R. A Study of internal moisture movement in the drying of wheat kernel. Cereal Chemistry, Vol . 32, (3): May, 195 5.

. A Study of the desorption isotherms of wheat at 25°C and 50°C. Cereal .Chemistry', 33: 79, 1956.

Boyce, D.S. Grain moisture and temperature changes with position and time during through drying. J . Agri . Engng. Res., 1965 , 10(4) : 333.

Brooker, D.B. Mathematical model of the psychrometric chart. Trans. ASAE 10(4 ): 558-60 , 1967.

Chen, C.S. Equilibrium moisture curves for biological materials. ASAE Paper No. 69-889, ASAE, St. Joseph, Mich. , 19 69 .

Chen, C.S. and Johnson, W.H. Kinetics of moisture movement in hygroscopic materials I. Trans. ASAE 12(1): 109-113, 1969.

- 58 -

14. Chen, C.S. and Johnson, W.H, Kinetics of moisture movement in hygroscopic materials II . Trans ASAE 12(4): 478-481, 1969. '

15. Chilton, T.H. and Colburn, A.P. Pressure drop in packed tubes. Indust. Engng. Chem. 23: 913, 1931.

16. Chittenden, D.H. and Hustrulid, A. Determining drying constant for shelled corn. Trans. ASAE, vol . 9, No. 1, 1966.

17. Chu, S.T. and Hustrulid, A. Numerical solution of diffusion equations. Trans. ASAE, Vol. 11, No. 5, 1968.

18. __. General characteristics of . variable d i f fus iv i ty process and the dynamic equilibrium moisture content. Trans. ASAE, 11(5): 709-715, 1968.

19. Chung, D.S. and Pfost, H.B. Adsorption and desorption of water vapor bv cereal grains and their products. Trans. ASAE, 10(4): 549, 1967.

20. Crank, J . The mathematics of diffusion. Oxford University Press, Amen House, London, E .C .4 , 1956.

21. H a l l , C.W. Drying farm crops ( f i f th pr int ) . Edwards Brothers Inc. , Michigan,. 1966.

22. H a l l , C.W. and Rodriguez-Azias, J . H . Equilibrium moisture content of shelled corn. Agric. Engng. 39(8): 466, 1958.

23. Henderson, S.M. A basic concept of equilibrium moisture. Agri . Engng. 33: 23-32, 1952.

24. Henderson, S.M. and Pabis, S. Grain drying theory I. Temperature effect on drying coefficient. J . Agri . Engng. Res., 6(3):169, 1961.

25. .. Grain drying theory III . -The a ir /grain temperature relationship. J . of Agri . Engng. Res., Vol. 7, 1962.

26. . Grain drying, theory IV. The "effect of a i r flow rate on the drying index. J . of Agri . Engng. Res., 7 (2): 85-89, 1962.

27. Henderson, S.M. and Perry, R.L. Agricultural process engineering (second edit ion) , J . Wiley S Sons, Inc. , New York, 1966. '

- 59 -

28. Hougen, O.A. , McCauley and Marshal, W.R. Limitations of diffusion equation in drying. Trans. Am. Inst. Chem. Engrs. , Vol. 36, 1940.

29. H u k i l l , W.V. Basic principles in drying corn and sorghum. Agri . Engng. 28: (8), 1947.

30. Hustrulid, A. Comparative drying rates of naturally moist, re-moistened and frozen wheat. Trans. ASAE 6(4): 304-308 , 1963.

31. Hustrulid, A. and Flikke, A.M. Theoretical drying curves for shelled corn. Trans. ASAE 2(1):112, 1959.

32. Jones, C.R. Evaporation in low vacuum from warm granular material (wheat) during the fa l l ing rate period. J . Sc i . Food. Agric. 2: 565-571, 1951.

33. Lepper, H.A. Of f i c ia l and tentative methods of Analysis. Asso. of O f f i c i a l Agricultural Chemists, p. 404, 1945.

34. McEwan, E. and O'Callaghan, J .R. Through drying of deep beds of wheat grain. Trans. Instn. Chem. Engrs. , 198 , 1954. . .

35. . • The effect of a i r humidity on through drying of wheat grain. Trans. Instn. Chem. Engrs. 33: 135-154 , " l 9 55.

36. Newman, A.B. The drying of porous solids: Diffusion calculations. Trans. Am. Inst. Chem. Engrs. 27: 310, 1931.

37. . The drying of porous solids: Diffusion and surface emission equations. Trans. Am. Inst. Chem. Engrs. 27: 203, 1931.

38. . Pabis, S. and Henderson, S.M. Grain drying theory II. A c r i t i c a l analysis of the drying curve for shelled maize. J . of Agr. Engng. Res. , 6(4 ) : 272 , 1961.

39. Page, G.E. Factors influencing the maximum rates of ' a i r drying shelled corn in thin layers. M.S. thesis,

M.E. Department, Purdue University, 1949.

40. Perry, J . H . Perry's chemical engineer's handbook. McGraw-Hill Book Co. , New York, 1963.

41. Sherwood, T.K. The drying of solids I. Ind. Engng. Chem. 21: 12, 1929.

- 60 -

42 . Sherwood, T.K. The drying of solids II. Ind. Engng. Chem. 2 1 : 976 , 19 29.

43 . . Air drying of sol ids. Trans. Am. Inst. Chem. Engrs".' 32: 150-168 , 19 36.

44 . Simmonds, M.A. , Ward, G.T. and McEwen, E. The drying, of wheat grain, Part I. The mechanisms of drying.

.Trans. Instn. Chem. Engrs. (London) 31 : 2 6 5 - 2 7 8 , 1953 .

4 5 . ^ . Part III . Interpretation"in terms of i t s biological structure. Trans. Instn. Chem. Engrs. 3 2 : 1 1 5 , 19 54.

46 . Van Arsdale, W.B. Approximate diffusion calculation for the fa l l ing rate phase of drying. Trans. Am. Inst. Chem. Engng. 4 3 : 1 3 - 2 4 , 1947 .

4 7 . Van Rest, D .J . and Isaacs, G.W. Exposed-layer drying rates of grain. Trans. ASAE, 11( 2 o") : 2 36-2 39 , 1968 .

48 . Wang, J . K . and H a l l , C.W. Moisture movement in hygroscopic materials. Trans. ASAE Vol. 4 , No. 1, 1 9 6 1 .

49 . Whitaker, T . , Barre, H . J . and Hamdy, M.Y. Theoretical and experimental studies of diffusion in spherical bodies with a variable diffusion coefficient. Trans. ASAE, V o l . 1 2 , No. 5 , 19 69 .

50 . Young, J . H . and Nelson, G.L. Research of hysteresis between sorption and desorption isotherms of wheat. Trans. ASAE, 1 0 ( 1 0 ) : 7 5 6 - 7 6 1 , 1967 .

- 6 i -

©

APPENDIX A

- 62 -

•Figure A - l Drying curves for a ir flow rates of (111) 120 feet •per minute, (112) 80 feet per minute, (113) 20 feet per minute and (114) 5 feet per minute at 120 + 1°F and 78+2% relative humidity.

- 63 -

° 1 2 3 4 . 5 6 7 8 Time, hour

Figure A-2. Drying curves for a ir flow rates of (121) 120 feet per minute, (122) 80 feet per minute, (123) 20 feet per minute and (124) 5 feet per minute at 120 + 1 .5°F and 5 0 + 2% relative humidity.

- 64 -

3 0 r

Time, hour

Figure A-3 Drying curves for a ir flow rates of (131) 120 feet per minute, (132) 80 feet per minute, (133) 20 feet per minute and (134) 5 feet per minute at 122 + 1°F and 2 5 + 2% relative humidity.

- 65 -

3 0 r

4 5

Time, hour 8

'Figure A-4 Drying curves for a ir flow rates of (211) 120 feet per minute, (212) 80 feet per minute, (213) 20 feet per minute and (214) 5 feet per minute at 101 + 1°F and 72 + 2% relative humidity.

- 66 -

3 0 i

5

0

5

0 7224 a 2 2 3

! 2 2 5221

0 4 5 T ime, hour

8

A-5. Drying curves for a i r flow rates of (221) 120 feet per minute,.(222) 80 feet per minute, (223) 20 feet per minute and (224) 5 feet per minute at 100 + 1 .5°F and 50 + 1.5% relative humidity.

- 67 -

30r

5 r

T i m e , hour

Figure A-6. Drying curves for a i r flow rates of (231) 120 feet per minute, (232) 80 feet per minute, (233) 20 feet per minute and (234) 5 feet per minute at 100 + 1°F and 26 + 1.5% relative humidity.

- 68 -

•Figure A-7. Drying curves for a i r flow rates of (311) 120 feet per minute, (312) 80 feet per minute, (313)20 feet per minute and (314) 5 feet per minute at 81 + 2°F and 75 + 2%,relative humidity.

- 69 -

3 0 r

._ 2 5 on D _D

X

g 2 0

<_•

d

c c o U <L> —. _)

1/1

'o

15

10

324 323 322 321

0 4 5 Time, hour

8

Figure A-8. Drying curves for a i r flow rates of (321) 120 feet per minute, (322) 80 feet per minute, (323) 20 feet per minute and (324) 5 feet per minute at 81 + 2°F and 50 + 1.5% relative humidity.

- 70

30

.£ 25} </>

o JQ

X

~o

£ 20 u

a

c t y

-*—

c o U a> -4— CO

O

15

,-334 5333

10

»332 131

0 4 5 T i m e , h o u r

8 _ i 9

Figure A -9 . Drying curves for a ir flow rates of (331) 120 feet per minute, (332) 80 feet per minute, (333) 20 feet per minute and (334) 5 feet per minute at 80 + 2°F and 37 +2% relative humidity.

- 71 -

3 0 r

c o c o u CD —.

2 5 IA

D

13 £ 2 0

CD a

15

'o 10

0 8 10 12

Time, hour

14 16

Figure A-10 Drying curves for a ir flow rates of (411) 120 feet' per minute, (412) 80 feet per minute, (413) 20 feet per minute and (414 5 feet per minute at 60 + 1°F and 75 + 1.5% relative humidity.

- 72 -

Ti m e . hour

Figure A - l l . Drying curves for a ir flow rates of (421) 120 feet per minute, (422) 80 feet per minute, (423) 20' feet per minute and ( 424) 5 feet per minute at 60. + 1°F and 61 + 2% relative humidity.

- 73 -

APPENDIX B

- 74 -

0.02

0.011 i i I l i - J _ J 1 0 1 2 3 4 5 6 7 8

Time, hour

Figure B - l . Plot of logarithm moisture ratio versus time for drying set D, (211) a ir flow rate of 120 feet per minute, (212) 80 feet'per minute, (213) 20 feet per minute and (214) 5 feet per minute at 101 + 1°F and 72 + 2% relative humidity.

- 75 -

0 01 0 1 2 3 4 5 6 7 8

Time, hour

F i g u r e B-2.

0 . 0 4

0 . 0 2

0.01 0 1 2 3 4 5 6

T i m e , hour

Figure B-3.• Plot of logarithm moisture ratio versus time for drying set F , (231) a ir flow rate of 120 feet per minute, (232) 80 feet per minute, (233) 20 feet per minute and (234) 5 feet per minute at 100 + 1°F and 26 + 1.5% relative humidity. ~

- 77 -

APPENDIX C

T A B L E C - l . PROGRAM FOR COMPUTING M O I S T U R E CONTENT ( P E R C E N T , DRY B A S I S ) , DYNAMIC E Q U I L I B R I U M M O I S T U R E CONTENT ( P E R C E N T , DRY B A S I S ) AND M O I S T U R E R A T I O FROM D R Y I N G WEIGHTS AND R E L A T I V E H U M I D I T Y FROM DRY BU L B AND WET BU L B T E M P E R A T U R E S WITH A S A M P L E C A L C U L A T I O N FOR D R Y I N G SET E.

01 MENS ION NR.UN( 2 0 ) » N M E A ( 2 C) , 1 I ME ( 2 0 ) , T UB ( 2 0 ) , TO B ( 20 ) , AI RF ( 2 0 ) T W G ( 2 10 ) , ACT ( 2.0 )

99 NU-0 0 0 1 I = 1 T 2 0 . .

. READ(5,2)NRUIU I ) » N M E A ( I ) , T I ME( I ) , T W B ( I ) t T D B { I > ,A IRF( I ),WG( I ) IF(NRUN(T).EQ.9^9) GO TO 3

__2 ..FOR.MAT.f 2 I 3 t F .6 .2 . »_4F7. .2 . ) „ _ „ 1 NU = M + 1 3 NV=NU

NW=NU . ; ; AC A = ( ( WG ( N U - 2 } *WG(NU ) )- ( W G i N U - 1 )**2 ) ) / (WG (NU- 2)+WGIN U ) - 2.0*WG(N U - 1

1) ) .. NU.= N U - . l • .. ..

A OB = ( ( WG ( MJ -2 ) * W G ( NU ) ) - (W G { NU- 1 j * * 2 ) )/( WG ( NlJ-2 ) + W G ( NU ) - 2 . 0 * WG ( N U- 1 1) )

N U = N U - 1 " A G O ! ( W<G ( NU-2 ) *WG (NU ) )- (WG (NU-l ) * * 2 ) ) /( WG(NU-2 ) + WG ( N U ) - 2. C* KG < N U - l

1) ) NU=NU-1. ... ; _ ._ _ A00=((WG(NU-2)*WG(NUj)- (WG(NU-l)**2 ) ) / (WG(Nu~2)+WG(NU)-2.0*WG(NU-1

1) ) NU=NU-1 AGE = ( ( W G ( NU-2 ) *W G (NU ) ) - (W G (NU-1 ) * * 2 ))/( WG ( Nil- 2 ) + WG ( NU ) - 2. 0* WG {NU-l

1) ) AOF= ( ( WG ( NV-4 ) * WG ( N V ) ) - ( WG ( Ny-21**2 )_) / ( WG ( NV-4 ) + WG ( NV ) -2 .0*WG (NV-2

1 ) ) NV=NV-2 AOG= ( ( W G( NV-4 ) * WG ( N V ) )- ( WG ( N V - 2 ) »*2 ) )'/ ( WG ( N v-4 ) +WG(NV) -2 . 0*WG ( Ny-2

1 ) ) NV=NK-l AOH= ( (WG<NV -4)*UG(NV) )-( KG(NV-2)**2> ) / < WG ( N V - 4 ) + WG.( N V )-2 . 0* W G ( N V-2

I ) ) A 0 I = ( ( W G ( N W - 6 ) * Iv G (N W ) ) - ( W G ( N W - 3 ) * * 2 ) ) / ( WG ( N W - 6 ) + K G ( N W ) - 2 . 0 * W G ( N W - 3

V ) ) l :

AOJ=(A0A+ACB+A0C+AOr+AOE+A0F+ACG+AGF+A0l)/9.O WR1TF(6,1G) NRUN(NW) - -

. 1 0 F O R M A T (5.0X » !.RUN_NC_..!.t 13.) _ WRITE(6,2C) AGJ

2 0 FORMAT (//, lOXf « EQUIL . MOISTURE CONTENT, WB •= ' F11.5) WRI TE (6 ,70)

7 0 FOR MAT ( / / , 1 0 X » ' R IN MG DB EQUIL NC FREE f.C V. RATIO RH ' ) ' DO 30 I=1,NW

AO K - 0 . 7 7 5 2 8 * WG ( 1 ) A 0 L =(KG(IJ-AUK)*1CO.OC/AOK A H ' = AGJ -ACK

' AGN=AGM*100. OO/A.CK

- 7 8 -

- 7 9 -

A G O ( I )= A O L - A O N AG.C = AGC•{ I ) / A G C ( 1 ) AOW= 54 . 6 3 2 9 - < 1 2 3 0 1 . 6 8 8 / T D B ( I ) ) - 5 . . 16 9 2 3 * A L 0 G (T C B I D ) . A O R = E X P ( A Q W ) A C X = 5 4 . 6 3 2 9 - 1 1 2 3 0 1 . 6 8 B / T W f i ( 1 ) ) - 5 . 1 6 9 2 3 * A L 0 G ( T W O l 1 ) ) A O S = E X P { AOX) - ACT= 1 0 7 5 . 3 9 6 5 - 0 . 5 6 9 8 3 - ( 1 M B { I ) - 4 9 1 . 6 9 ) A C U - - 1 . 0 * ( C . 2 4 0 5 * ( AO S - l 4 . 6 9 9 6 ) ) / ( C . 6 2 19 A-!'ACT )

. A O V - U O S - A 0 U * ( T C t S ( I l - T W B l I ) ) ) /AOP. 30 W R I T E ! 6 , 6 C ) N M E A ( I} , AOL , A ON , A C O ( 1 j , A O C , A O V 6 0 F O R M A T { 1 0 X , 1 3 , 5 F 1 0 . 5 )

GO TO 9 9 5 5 S T O P __ •

END

$ R U N - L G A L "ii E X E C U T I O N B E G I N S

RUN NO. ° 2 21

E G U I L . M O I S T U R E C O N T E N T , WD = 2 0 3 . 9 3 8 9 0

R I N MC DB E Q U I L MC FRF.E MC M R A T I O RH 1 2 8 - . 9 8 5 6 4 6 . 9 7 5 17 2 2 . 0 1 0 4 7 I . 0 0 0 0 0 0 . 4 9 9 5 4 2 1 3 . 6 5 2 1 1 6 . 9 7 5 17 1 1 . 6 7 6 9 4 0 . 5 3 0 5 2 0 . 4 9 9 54 3 1 4 . 3 7 7 0 7 6 . 9 7 5 1 7 7 . 4 C 1 9 0 0 . 3 3 6 2 9 0 . 4 9 9 5 4 4 12 . 1 0 0 5 5 6 . 9 7 5 1 7 5 . 1 2 5 3 8 0 . 2 3 2 8 6 0 . 4 9 9 5 4 5 1 0 . 6 7 9 0 4 6 . 9 7 5 1 7 3 . 7 0 3 8 6 0 . 1 6 8 2 8 0 . 4 9 9 5 4 6 9 . 7 0 8 6 2 6 . 9 7 5 1 7 2 . 7 3 3 4 5 0 . 1 2 4 1 9 0 . 4 9 9 54 7 9 . 0 2 6 7 1 6 . 9 7 5 1 7 2 . 0 5 1 5 4 0 . 0 9 3 21 0 . 4 9 9 5 4 .-8 8 . 4 9 1 6 7 6 . 9 7 5 1 7 1 . 5 1 6 5 0 0 . 0 6 8 9 0 0 . 4 9 9 54 9 . 8 . 0 8 2 5 3 6 . 9 7 5 1 7 1 . 1 0 7 3 6 0 . C 5 C 31 0 . 4 9 9 5 4

1 0 7 . 7 6 7 8 1 6 . 9 7 5 17 0 . 7 9 2 6 4 0 . 0 3 6 0 1 0 . 4 9 9 5 4

RUN NO. 222 EGUIL. M O I S T U R E C O N T E N T , WB •= 2 0 4 . 2 7 5 6 3

R I N MC DB E Q U I L MC F R E E MC M R A T I O RH 1 2 8 . 9 8 5 6 4 7 . 1 5 1 8 0 21 . 8 3 3 8 3 1 . 0 0 0 0 0 0 . 4 8 7 4 1 2 1 9 . 2 8 1 5 7 7 - 1 5 1 8 0 . 1 2 . 1 2 9 7 7 C . 5 5 5 5 5 0 . 4 8 7 4 1 3 1 5 . 1 3 7 6 7 7 . 1 5 1 8 0 7 . 9 8 5 8 7 0 . 3 6 5 7 6 0 . 4 9 9 5 4 4 12.8 29 6 7 7 . 1 5 1 8 0 5 . 6 7 7 8 6 0 . 2 6 0 0 5 . 0 . 4 9 9 5 4 5 11 . 2 7 7 0 2 7 . 1 5 1 8 0 4 . 1 2 5 2 1 0 . 1 8 8 9 4 0 . 5 C 4 6 3 6 10.2 0 6 9 4 7 . 1 5 1 8 0 3 . 0 5 5 1 4 0 . 1 3 9 9 3 0 . 5 0 4 6 3 7 9 . 4 7 2 5 8 7 . 1 5 1 8 0 "2. 3 2 C 7fi C . 1 0 6 2 9 0 . 5 C 4 6 3 8 8 . 8 9 5 5 8 . 7 . 1 5 1 8 0 1 . 7 4 3 7 7 0 . 0 7 9 8 7 C . 4 9 8 5 0 9 8. 4 4 9 7 2 7 . 1 5 1 8 0 1 . 2 9 7 9 2 0 . 0 5 9 4 5 0 . 4 9 2 4 1

10 8 . 0 8 2 5 3 7 . 1 5 1 8 0 "0 . 9 3 C 7 3 0 . 0 4 2 6 3 0 . 4 9 2 4 1

80

RUN NO. 22 3

EQUIL. MOISTURE CONTENT , WB ~ ; 20 5.75696

R IN MC D8 EGUIL MC FREE MC M RATIO RH 1 28.96564 7.92832 21 .05681. 1.00000 0.49747 2 20.27820 7.928 82 12.34938 0.5 864 8 C.49747 3 16.02939 7.92882 8.100 57. 0.38470 0. 5 C 3 6 C 4 13.82631 7.92882 5.89748 0.28007 0.50978 5 12.33135 7.92882 4.4C253 0.209C8 C.5C463 6 11 .22980 7 .9 28 8 2 3.30098 0. 15677 C . 4 9 R 5 0 7 10.44823 7.92 8 82 2.51941 0. 1196.5 0 .4924 1 8 9.85550 7.9 28 82 1.52667 0.09150 0.48741 9 9.40963 7.92882 1 .48081 0.07032 0.49345

10 9.02147 7.92882 1.05265 0.05189 0.499 54

TON~N0T~2 m

EQUIL. MOISTURE CONTENT, WB = 2C6.87781

R IN MC DB EQUIL HC FREE KC M RATIO RH 1 28 .98564 8 . 51676 20 .468 3 7 1. 00000 0.49954 2 21.74692 8. 51676 13 .23016 0 . 64636 0 .49954 3 17.44566 8. 51676 8 .52890 C. 43622 0.4 99 54

_ 4 . 14.92785 8 . 5 1676 6 .41109 0 . 31321 0.49954 5 13.40667 8. 5167 6 4 .8 8991' " 0. 23 8 89 ' 0.50463 6 12.38381 8. 51676 3 .86705 C. 18892 0.4 9 345 7 11.6 2321 8. 51676 3 .10645 0. 1517 6 0 .4924 1 8 10.99376 8. 51676 2 .477GC C. 12101 0.49241 9 10 .44298 8. 51676 1 .92622 0. 09411 0.499 54

10 10.C18 10 8. 5 1676 1 .5 0134 0. 07335 0.50463

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