Drying Technology: An International Journal ...

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PARAMETERS AFFECTING GRAIN DRYING BY IMMERSION IN A HOT PARTICULATE MEDIUM a

K. J. Sibley & G. S. V. Raghavan

a

a

Department of Agricultural Engineering , Macdonald College of McGill University , 21, 111 Lakeshore Road, Ste.-Anne-de-Bellevue, Quebec, Canada , H9X 1C0 Published online: 27 Sep 2010.

To cite this article: K. J. Sibley & G. S. V. Raghavan (1985) PARAMETERS AFFECTING GRAIN DRYING BY IMMERSION IN A HOT PARTICULATE MEDIUM, Drying Technology: An International Journal, 3:1, 75-99, DOI: 10.1080/07373938508916256 To link to this article: http://dx.doi.org/10.1080/07373938508916256

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DRYING TECHNOLOGY, 3(1),

75-99 (1985)

PARBIIETRRS BPPEClTNG GRAIN DRYING BY

Downloaded by [McGill University Library] at 11:58 26 January 2015

IlMBRSION I N A HOT PAiU'ICUUTB HEDIDM

K. J. Sibley and G. S. V. Baghavan Department of Agricultural Engineering Macdonald College of McGill University 21,111 Lakeshore Road Ste.-Anne-de-Eellevue, Quebec, Canada H9X 1CO

KEY WORDS AND PHRASES High temperature; m o i s t u r e r a t i o ; sand; batch; conduction; c o n t a c t time; e q u i l i b r i u m m o i s t u r e ; h i g h temperature; models; m o i s t u r e r a t i o ; p a r t i c l e s i z e ; sand.

ABSTRACT

High temperature particulate medium conduction grain drying is a very promising technique. However, lack of basic drying characteristic information has resulted in unsuccessful attempts to develop an efficient, economical, continuous flow dryer. In this study, the effects of initial grain moisture content, initial medium temperature, medium particle size, medium to grain mass ratio, and contact time on the drying of shelled corn immersed in hot sand are evaluated. Moisture losses ranged between 0.2 and 5.2 percentage points (wb).

Traditionally, air has been used for convection drying of agricultural grains, even though it has been shown to be an

Copyright @ 1985 by Marcel Dekker.

lnc.

0737-3937/85/0301-0075$3.50/0

76

SIBLEY AM) RAGHAVAN

inefficient heat transfer medium, for lack of knowledge of a better medium. The convection drying process as represented on a psychrometric chart reveals that air will reach saturation before all its sensible heat can be utilized for moisture removal,


resulting in extended drying times (Foster, 1973). These slow drying times create bottlenecks in the harvesting and storage process which often causes a partial loss of the crop. Conduction heating of the grain, by intimate contact with a hot particulate medium, has been shown to greatly increase drying rates (Raghavan and Harper, 1974; and others); hence greatly reducing drying times. The drying method, called "Particulate Medium Conduction Grain Drying", consists of immersing the grain in a hot bed of granular material, such as sand or salt, for a very short "contact time" during which most of the drying takes place.

The mixture is

continuously agitated by means of a rotating drum or fluidized bed and then separated through a sieving operation; following which the medium is re-cycled to be re-heated and used again.

Further

drying is induced by large temperature gradients as the product cools to ambient temperature after separation from the medium. Although many of the parameters that affect the particulate medium conduction drying process, either directly or indirectly, have been found, (Table 1) specific relationships between them have not been determined adequately. Of the parameters studied to date, as presented in Table 1, the main parameters of initial grain moisture content, initial


78

SIBLN AND RAGHAVAN

medium temperature, medium particle size, medium to grain mass ratio, and contact time can be singled out as having the most influence on drying and should be studied in greater detail. Therefore, the objective of this study was to perform expereiments using the conduction drying technique to determine


the effects of the above main parameters on the rate of moisture loss from shelled yellow dent corn immersed in hot sand.

Experimental Design

A completely randomized factorial experimental design was set up involving four replicates, two grain initial moisture contents, three initial medium temperatures, three medium particle sizes, three medium to grain mass ratios, and three contact times. The factors and their experimental levels are listed in Table 2. Treatment combinations were coded by a five digit number in the following manner: Integer number refers to factor level while position in the code refers to actual factor. i.e.,

Code 12132

would correspond to a treatment of Al, B2, C1, D3, and E2.

Only

two initial moisture content levels were used in the experiments so that the size of the experiment could be kept within manageable limits. Initial temperature of the grain and ambient relative humidity were measured as co-variables, but were maintained as uniform as possible.

PARAMETERS AFFECTING GRAIN DRYING TABLE 2 Experimental Factors and their Levels


FACTOR

INDEPENDENT VARIABLE

1

A

Grain initial moisture content (%wb)

B

Initial medium temperature

C

LEVEL 2

3

1 7 . ~ 3 ~-

23.74' 232

200

150

Medium particle size3 (pm)

SO0

300

250

D

Medium to grain mass ratio

4

6

8

E

Contact time (sec)

30

60

120

(OC)

'herage value representing range of 21.57% to 24.63% '~vera~evalue representing range of 17.03% to 18.91% 3~anu~acturer's specifications

The dependent variable of grain final moisture content was measured on random independent sub-samples aEter the application of a treatment combination to an initial grain sample.

Kxperimental Materials

The particulate medium used in the experiments was a commercialy available pre-washed and pre-graded sand. Three factory grades of 30, 55, and 65, which correspond to USA sieve numbers of 35, 52 to 55, and 62 respectively were selected. These three particle sizes fall into the USDA textural classes of coarse, medium and fine. A sufficient amount (400 kg) of yellow dent corn grown at the Macdonald College farm, harvested at approximately 18% moisture

SlBLEY AND RAGHAVAN

80

content(wb), was randomly selected for use in the experiments. The grain was placed in airtight plastic garbage cans, each lined with a sealable plastic bag to prevent changes in moisture content. One half of the grain was randomly selected to be remoistened to approximately 24% moisture content (wb).

A pre-calculated


quantity of water was added to the grain and uniform mixing was carried out for 30 minutes. stored in a refrigerator at 4

After initial mixing, the grain was OC

for two days.

The grain was then

uniformly mixed a second time for 15 minutes and placed back in the reErigerator at 2

OC

to be stored for a minium of five more

days. The

18% moisture content (wb) grain was kept in the

refrigerator during this time, and was not mixed.

The above

procedure resulted in uniform moisture distribution throughout the grain samples.

Equipment and Instrumentation

A small hatch dryer was fabricated for the experimental investigations. The main component of the dryer was an aluminium pot 27 cm. inside diameter and 22 cm. deep.

A cover was attached

to the pot with a hinge and quick release closure.

All outside

surfaces were insulated with R-10 fiberglass insulation which was protected with an industry standard paper backing. In order to approximate atmospheric conditions that would be encountered deep within a continuos flow, flighted rotary dryer, vents were not constructed in the dryer lid, as was done in wheat

81

PARAMETERS AFFECTING GRAIN DRYING drying studies by Lapp et a1.(1975)

and Lapp et al. (1976a,b).

Therefore, the only means of moisture escape from the dryer was through the minimal void spaces created at the contact surface between the pot rim and cover. A table top primary separating screen was constructed out of


aluminium screening which would facilitate quick separation of the grain and sand after an experimental run. A sand catch pan, to fit beneath the separating screen and a grain catch pan to fit at the end of the separating screen were constructed using aluminium. All outside surfaces of the catch pans were also insulated with R-10 fiberglass insulation.

A Mettler

pc-1200 electronic balance accurate to 0.01g was used for all weighings. within 1

A drying oven which maintained a constant temperature OC

oE the set temperature was used for moisture content

determinations. The sand was heated to initial test temperature by an electric convection oven which maintained cabinet temperature within 1

OC

of the set temperature.

Atmospheric dry bulb and wet bulb temperatures were measured by a sling-psychrometer accurate to 0.5' Auxiliary

F.

laboratory equipment included: standard moisture

content determination cans, thermometers, a time clock, enameled sand heating trays, grain sample trays, oven mitts, air tight grain containers (plastic garbage cans lined with sealable plastic bags), sand containers and sieves.

82

SIBLEY AND RAGHAVAN

Bxperimental Procedure

Before any actual experimental runs were conducted, all equipment and instrumentation were set up and calibrated to assure that they were in proper working condition. All moisture content determination cans were cleaned, labelled, and weighed.


A preliminary experimental procedure was formulated and several trial runs were conducted for familiarization and to pinpoint any changes that should be made in operating procedures. A final experimental procedure was formulated and the actual tests were started. All ovens were set to the desired temperature and allowed to stabilize for at least 24 hours before each trial. A

quantity of grain was brought to the laboratory from the

refrigerator and allowed to warm up before each test period.

A

treatment combination, to be applied to a grain sample, was selected from a master list. The appropriate amount of sand was weighed out in the enameled heating trays, which were then placed in the heating oven. The sand was heated for a minimum of seven hours and checked with a thermometer to ensure that it had reached the desired initial temperature before each test run. When the medium was ready, the appropriate number of moisture content determination cans were p l a ~ e d ~ i n t readily o accessible positions.

A sample of grain was weighed out, placed in a holding

tray and its temperature was recorded. A grain sample was also taken for intial moisture content determination. An extra tray of hot sand was taken from the oven, placed in the dryer, agitated for two minutes to pre-heat the dryer, and

PARAMETERS AFFECTING GRAIN DRYING removed from the dryer. The grain sample was then placed in the dryer immediately followed by the hot sand and the time count began. The mixture was agitated by rotating the dryer through a figure-eight motion by hand for the prescribed contact time. The


dryer was opened and the mixture was poured on to the separating screen. Three samples of grain were immediately taken for moisture content determinations. Room dry bulb and wet bulb temperatures were then measured and recorded.

The above procedure was repeated for each

experimental run. The rotation of the dryer was kept as uniform as possible between tests. Moisture content determinations were carried out according to ASAE standard S352 for corn as outlined in ASAE (1982). Moisture contents were calculated on a wet basis according to the relation:

MC(wb)

where MC(wb)

=

weight of water weight of wet material

x

100%

is moisture content (wet basis).

RESULTS rn

nxswssm

An analysis of variance, using Statistical Analysis Systems (SAS) procedure ANOVA, was performed on the experimental drying data with grain final moisture content as the dependent variable. Complete descriptions of the statistical procedure used in the anlaysis of the experimental data are contained elsewhere (SAS

SIBLEY AND RAGHAVAN

(1982), Steel and Torrie (1980)).

Results of this analysis are

shown in Table 3. The factorial model used in the experimental design accounted for 99.6% of the variation in final grain moisture content indicating that the independent variables considered in the


experiments were, indeed, the major parameters affecting drying. The coefficient of variability of 1.02X indicated properly controlled experimental conditions and high precision of experimental technique. Factor main effects and interaction effects among the factors were all found to be significant at the 0.01 alpha level. Interaction indicates failure of the simple effects of each factor to behave the same over the different levels of the other factors. Therefore, factor simple effects and/or effects due to treatment combinations should be examined in order to see the true effects of each main factor on final grain moisture content. Examination of the magnitudes of the F-values for the interaction effects in Table 3, relative to those for the factor main effects revealed that even though interaction effects were statistically highly significant, they accounted for only a very small portion of the variability in grain final moisture content; consequently they are of little practical importance. An analysis of variance on final grain moisture content using only the main effects model was performed to varify the above conclusions. Results oE the analysis are shown in Table 4. The main effects model accounted for 96.7% of the variation in final grain moisture content showing that interaction effects did, in fact, account for only 2.9% of the total variation.

PARAMETERS AFFECTING GRAIN DRYING

TABLE 3 A n a l y s i s of Variance on G r a i n F i n a l Moisture Content: F a c t o r i a l Model

ss*


SOURCE MODEL

4960

ERROR

18

CORRECTED TOTAL SOURCE A B A*B C A*C B*C A*B*C D A*D B*D A*B*D C*D A*C*D B*C*D A*B*C*D E A*E B*E A*B*E C*E A*C*E B*C*E A*B*C*E D*E A*D*E B*D*E A*B*D*E C*D*E A*C*D*E B*C*D*E A*B*C*D*E

*Values

*

MS

F-VALUE

*

PR

F>R'*

ROOT MSE

4978

*

SS*

F VALUE

4375 194 39 5 3 12 6 36 1 5 13 1 2 4 6 203 3 9 2 1 1 1 1 16 3 8 2 1 1 1 2

99999 2551 516 70 42 78 43 474 14 35 88 8 11 14 19 2667 36 62 11 4 5 4 4 104 22 27

8 3 3 2 3

have been rounded o f f due t o s p a c e l i m i t a t i o n s

C.V.(%)

*

MCf MEAN

SIBLEY AND RAGHAVAN TABLE 4 Analysis of Variance on Grain Final Moisture Content: Main Effects Model

DF

ss*

MS*

F-VALUE

MODEL

9

4813

535

2065

ERROR

638

165

0.259

CORRECTED TOTAL

647

4978


SOURCE

SOURCE

DF

SS*

F VALUE*

*

PR> F

*'R

.C.V.(%)

0.0001

0.97

2.66

ROOT MSE

MCf MEAN

0.509

19.12

PR> F

*

Values have been rounded off due to space limitations

Locating differences in effects among the main factor levels, using Duncan's new multiple range test, revealed that all levels for each of the factors produced a difference in mean final grain moisture content, statistically significant at the 0.01 alpha level.

Mean, here, refers to average effect among all factor

levels other than the ones being considered in the test. Examination of the means for each factor showed that final grain moisture content decreased with decreased initial grain moisture

*

content, decreased with increased initial sand

temperature, decreased with increased sand to grain mass ratio, and decreased with increased contact time.

Sand particle size



18

20

-22

24

l N I T 1 A L NO l STURE CONTENT (%wb)

FIGURE 1. Average effect of initial moisture content on drying.

showed an optimum condition at 300 pm, although differences in final moisture content were practically negligible. These results are graphically illustrated in Figures 1, 2, 3, 4, and 5. Differences in final moisture content among treatment combinations were also found using Duncan's test.

Treatment

combinations 11223 and 11323 gave the lowest final moisture content values for an initial grain moisture content of 23.74%

(wb).

Differences between the mean final moisture contents for these two combinations were not significant at the 0.01 alpha level.

Here,

mean refers to the average value of final moisture content between the four experimental replicates. Therefore, a treatment combination of: Initial sand temperatures of 232 OC, sand grain mass ratio of 6:1, contact time


SIBLEY AND RAGHAVAN

125

175

225

I N I T l A L SAND TEMPERATURE

FIGURE 2 .

275 (OC)

Average e f f e c t of i n i t i a l sand temperature on drying.

SAND P A R T I C L E S I Z E (p)

FIGURE 3 .

Average e f f e c t of sand p a r t i c l e s i z e on drying.


2 0

5

UI

-

g 5 z b I " ' " ' '

FINAL M O l STURE CONTENT ('Zwb) a3

b

0

SIBLEY AND RAGHAVAN

90

of 120 seconds, with either a sand particle size of 300 or 500pm, produces the optimum drying conditions for an initial corn moisture content of 23.74% (wb).

Final moisture content was approximately

18.5% for a moisture loss of 5.2 percentage points (wb).


Treatment combinations 21133 and 21333 gave the lowest final moisture contents for an initial moisture content of 17.93% (wb), with differences between the means not significant at the 0.01 alpha level. Therefore, a

treatment combination of: Initial sand

temperature of 232 OC, sand grain mass ratio of 8:1, contact time of 120 seconds, with either a sand particle size oE 250 or 500 um, produces the optimum drying conditions for an initial moisture content oE 17.93%

(wb).

The final 'moisture content was

approximately 14.5% (wb) for a moisture ldss of 3.4 percentage points (wb). From the above optimum conditions, it is seen again that sand particle size does not greatly affect drying since the use of any size will produce an optimum condition. Graphs illustrating the above results are shown in Figures 6,and 7. Moisture losses for all treatment combinations ranged between 0.2 and 5.2 percentage points (wb) and are similar to the moisture loss ranges reported by Raghavan and Harper (1974) and Mayfield (1974) shown in Table 1 for drying corn immersed in hot granular salt and to the range reported by Tessier (1982) for drying corn immersed in hot sand.

Similarity, in the above ranges indicates


-

I-

Z

m

SRNO SIZE : 500.0 urn SAND TEMP. : 232.0 C TIME : .x 30.0 scc 60.0 5ec 0 120.0 sec


e

SRNO GRAIN MASS RRTIU

FIGURE 6.

Optimum d r y i n g c o n d i t i o n s f o r 23.74% i n i t i a l m o i s t u r e c o n t e n t corn.

SflNO SIZE

- SRNO TEMP. TIME

:

: :

500.0 Urn 232.0 C 30.0 scc A 60.0 scc 0 120.0 SCC

SAND GRAIN NRSS RATIO

FIGURE 7.

Optimum d r y i n g c o n d i t i o n s f o r 17.93% i n i t i a l m o i s t u r e c o n t e n t corn.

92

SIBLEY AND RAGHAVAN

that the drying parameters of initial medium temperature, medium to grain mass ratio and contact time are more influencial than dryer type and mechanical operating conditions. In essence, then, the above parameters are, and should be, controllable in a sucessful dryer design.


An empirical model, involving the main factors with two co-variables of initial grain tmperature and ambient relative humidity of, f = a + ~ ( M c ~+)c(tc) + d(T s,1. ) + e(SGMR) +f(T . ) + B(RH) + h(dp) (2) g,l was found to fit the experimental data very well, where MCi is MC

initial grain moisture content (Xwb),

tc is contact time (sec),

T S s i is initial sand temperature (K), SGMR is sand to grain mass ratio, T is initial grain temperature (K), RH is ambient g,i relative humidity ( X ) , and d is sand particle size (m). P Coefficients for Equation 2 were determined using SAS procedure S'IEPWISE and are ehown in Table 5 .

All variables were significant

at the 0.01 alpha level. Procedure STEPWISE is a multiple linear regression procedure in which variables enter the proposed model in order of contribution. Therefore, conclusions about the relative importance of a certain variable to the model can be made. Initial moisture content was the first variable to enter the model, followed by contact time, initial sand temperature, and sand to grain mass ratio, indicating that these four variables had the major influences on final grain moisture content. Improvement in R-square by the entrance of initial grain temperature, ambient

PARAMETERS AFFECTING GRAIN DRYING TABLE 5 Coefficients for Final Moisture Content Models of Equations 2 and 3

COEFFICIENT

MODEL


EQUATION 2

---

EQUATION 3

relative humidity and sand particle size was small, indicating that these variables have only minor influences on particulate medium grain drying. In fact, neglecting them would only reduce R-square to 0.96. Therefore, for simplicity, the grain final moisture content model of Equation 1 was reduced to: MCf = a + b(MC.1 + c(tc) + d(Ts,;) 1

+ e(SGMR)

(3)

94

SIBLEY AND RAGHAVAN

Coefficients for Equation 3 are also presented in Table 5.

The

arithmetic signs in front of the coefficients further demonstrates that fins1 grain moisture content increases with initial moisture content, and decreases with increased initial sand temperature, SGMR, and contact time.


For convenience and generalization of results, correlations with the drying data were performed on grain average moisture ratio.

The empirical model of:

MR

(MCf

- MCe)/(MCi - MCe)

+ d(SGMR) + e(Tg,;)

= a + b(tc)

+ c(T~,~)

(4)

+ f(dp)

where MCf is final grain moisture content, and MCe is equilibrium moisture content (Xwb), gave the highest correlation of the models tested. Equilibrium moisture content was calculated using the Chung Equation presented in ASAE (1982) for standard D245.4 of, MCe = 0.33872

-

(0.05897 ln(-(~,

+ 30.205) ln(RH)))

(5)

where MCe is equilibrium moisture content ( X d b ) , ~ ~is the temperature of ambient air (OC), and RH is ambient relative humidity (decimal).

Coefficients for Equation 4 are presented in

Table 6. Contact time, initial sand temperature, and SGMR also entered this model first, respectively, followed by initial grain temperature and lastly, sand particle size; all variables were significant at the 0.01 alpha level.

From the analysis, entrance

of initial grain temperature and sand particle size into the model produced little improvement in R-square, even though their effects were statistically significant.

PARAMETERS AFFECTING GRAIN DRYING TABLE 6 Coefficients for Drying Models of Equations 4 and 6

COEFFICIENT

MODEL


EQUATION 4

EQUATION 6

Therefore, for practical purposes, the moisture ratio model was reduced to: MR = a + b(tc)

+ c ( T ~ , ~ )+ d(SGMR)

(6)

Coefficients for Equation 6 are also shown in Table 6. A contour plot of obtainable moisture ratios was drawn (Fig. 8) using Equation 6 to illustrate the relationship between the drying parameters of contact time, initial sand temperature, and sand to grain mass ratio over the range of experimental conditions studied.

For a given initial grain moisture content, the plot

enables quick selection of the proper drying parameter levels to achieve a desired final moisture content.


SIBLEY AND RAGHAVAN

150

175

200

INITIAL SAND TEMPERATURE

CURVE i)

FIGURE 8.

225

PC1

MOISTURE RATIO SAND TO GRAIN MASS RATIO 4.0 6.0 8.0

I

0.980

0.955

0.930

2 3

0.970 0.960

0.945 0.935

0.920 0.910

4

0.950

0.925

0.900

8

0.940

0.915

0.890

6

0.930

0.905

0.880

7 8

0.920

0.895

0.870

0.9 10

0.885

0.860

9 10

0900 0.890

0.875 0.865

0.850 0.840

II

0.880

0.835

0.830

I2 13

a870 0.860

0.845 0.835

0.820 0.810

14

0.850

0.825

0.800

I5 16

0.840 0830

0.815 0.805

0.790 0.780

Contour p l o t of m o i s t u r e r a t i o s from Equation 6.


97

CONCLIISIONS

From the work carried out in this study, several conclusions were drawn.

These were:

1) The independent parameters of initial grain moisture

content, initial sand temperature, sand to grain mass ratio, and


contact time were the main variables affecting the particulate medium drying process and they should be controllable in future dryer designs. 2) Sand particle size did not practically influence drying, although its effects were statistically detected due to very low experimental error 3) Final corn moisture content was satisfactorily modelled by an empirical function of initial corn moisture content, contact time, initial sand temperature, and sand to grain mass ratio. 4)

Moisture losses ranged between 0.2 and 5.2 percentage

points (wb) verifying that the particulate medium drying process can be used to succeasfully dry agricultural grains if the right combination of drying parameters is used.

5)

Over the range of variables studied, optimum drying was

achieved when the following conditions were used: For 24% (wb) initial corn moisture content;

i

SGMR = 6

iii) tc = 120 sec iv) dS = 300 or 500 pm and for 18% (wb) initial corn moisture content;

SIBLEY AND RAGHAVAN iii) tc = 120 sec

6)

Moisture loss was satisfactorily modelled by an empirical

function of contact time, initial sand temperature, and sand to


grain mass ratio. 7) Drying parameter interaction effects accounted for only 2.9% of the total variation in final grain moisture content, and for practical purposes may be neglected.

ASAE. 1982. Agricultural engineers yearbook. ASAE, St. MI 49085.

Joseph,

Foster, G. H. 1973. Heated-air grain drying. In Grain storage: Part of a system. R. N. Sinha and W. E. Muir, eds., AVI Publishing Co., Westport, Conn., p. 189-208. Khan, A. U., A. Amilhussin, J. R. Arboleda, and W. J. Chancellor. 1973. Accelerated drying of rice using heat conducting media. ASAE Paper No. 73-321, ASAE, St. Joseph, MI 49085. Lapp, H. M. and L. R. Msnchur. 1974. Drying oilseeds with a solid heat transfer medium. Can. Agric. Eng., 16(2): 57-59. Lapp, H. M., P. S. K. Leung, and J. S. Townsend. 1975. Solid heat transfer mediums for processing grains and oilseeds. ASAE Paper No. 75-302-NCR, ASAE, St. Joseph, MI 49085. Lapp, H. M., G. S. Mittal, and J. S. Townsend. 1976a. Drying and processing of small grains using solid heat transfer media. CSAE Paper No. 76-108. Lapp, H. M., G. S. Mittsl, and J. S. Townsend. 1976b. Cereal grain drying and processing with solid heat transfer media. ASAE Paper No. 75-3524, ASAE, St. Joseph, MI 49085. MayEield, R. L. 1974. High temperature grain treatment with a particulate bed. Unpub. M.Sc. Thesis, Colorado State University, 85 p. Mittal, G. S., H. M. Lapp, and J. S. Townsend. 1982. Continuous drying of wheat with hot sand. Can Agric. Eng., 24(2): 119-122.


99

Raghavan, G . S. V. and J . M. Harper. 1974. High t e m p e r a t u r e d r y i n g u s i n g a h e a t e d bed o f g r a n u l a r s a l t . Trans. ASAE., 1 7 ( 2 ) : 108-111. SAS.

1982. SAS u s e r ' s g u i d e : S t a t i s t i c s . Cary, North C a r o l i n a , 584 p.

SAS I n s t i t u t e I n c . ,


S t e e l , R. D. G . and J. H. T o r r i e . 1980. P r i n c i p l e s and procedures o f s t a t i s t i c s . Second e d i t i o n , Mc Graw H i l l Book Co., New York, 633 p. T e s s i e r , S. 1982. Heat t r a n s f e r and d r y i n g i n a s o l i d medium r o t a t i n g drum. Unpub. M.Sc. T h e s i s . , Mc G i l l U n i v e r s i t y , 145 P.

F i n a n c i a l a s s i s t a n c e Lor t h i s s t u d y was provided by t h e N a t i o n a l S c i e n c e s and E n g i n e e r i n g Research Council (NSERC) o f Canada.

CBBNGE OF ADDRESS Kevin J . S i b l e y C h e r r y f i e l d Foods I n c . P.0. Box 128 C h e r r y f i e l d , Maine U.S.A. 04622