11 - Moisture Content and Drying Rate Calculations

7/30/2019 11 - Moisture Content and Drying Rate Calculations

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MOISTURE CONTENTAND DRYING RATE

CALCULATIONS

SOLIDS


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MOISTURE CONTENT

RELATIONSHIPSMOISTURE/SOLIDEQUILIBRIUMRELATIONSHIPSFIGURES 9.4-1 AND 9.4-2 FOR SEVERAL TYPESOF SYSTEMSDEFINED ON THE BASISOF RELATIVE HUMIDITYAT A SPECIFICTEMPERATUREEQUILIBRIUM AMOUNTOF MOISTURE TENDSTO DECREASE WITHINCREASINGTEMPERATURE


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MOISTURE CONTENT

VARIABLES

BASED ON THE MASS OF MOISTURERELATIVE TO THE MASS BONE DRY SOLID

)(

.

%100@

)25.9(

15.9

*

*

MoistureSurface

X X Bound AboveContent Moisture X

MoistureUnbound H withSaturationContent Moisture X

X X Content MoistureFree X

Content Moisturem Equilibriu X

BDS Solid Dry Mass Liquid Mass

X

Bt U

R B

t

t


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DRYING RATE CURVES

DEPEND ON WHETHER HEAT ORMASS TRANSFER CONTROLS

FREE MOISTURE VS. TIME DRYING RATE VS. MOISTURE CONTENT

http://www.ias.ac.in/sadhana/Pdf2005Oct/PE1280.pdf
http://www.ias.ac.in/sadhana/Pdf2005Oct/PE1280.pdfhttp://www.ias.ac.in/sadhana/Pdf2005Oct/PE1280.pdfhttp://www.ias.ac.in/sadhana/Pdf2005Oct/PE1280.pdfhttp://www.ias.ac.in/sadhana/Pdf2005Oct/PE1280.pdf


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DRYING REGIMESCONSTANT RATE - NO LIMIT TO MASS

TRANSFER IN SOLID PHASE SURFACE MOISTURE TRANSFER NEAR SURFACE

FALLING RATE

MOISTURE FLUXTHROUGH THE SOLIDIS HINDERED

CRITICAL POINTS OCCURBETWEEN CONSTANT

RATE AND FALLING RATEWITH A CHANGE IN THE

FALLING RATE DRYINGMECHANISM


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DRYING MODELS

RATES FROM EMPIRICAL DATA

CONSTANT RATE DRYING CONTROLLED BY HEAT TRANSFER TO

VAPORIZE THE MOISTURE OR MASS

TRANSFER

)35.9(t A

X L R S

76.9)( H H M k T T h R W B yW

W C


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HEAT TRANSFER

CORRELATIONS

TO PREDICT CONSTANT RATE DRYING

RADIATION CAN ALSO BE A FACTOR

)106.9(37.017.1

:

)96.9(0128.00204.0

:

37.02

37.02

8.02

8.02

G

R f t

BTU hG

K m

W h

SURFACE TO LARPERPENDICU

G R f t BTU

hGK mW

h

SURFACE TOPARALLEL


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FACTORS THAT AFFECT h

AIR VELOCITY (G)GAS HUMIDITY (T TW) AND (H W-H)GAS TEMPERATURE (T TW) AND (H W-H)SOLID THICKNESS - NO EFFECT ON RATE

FOR SURFACE MOISTUREMATERIALS SURFACE FINISH OR ANYCONDITION THAT STIMULATESTURBULENCE

J. E. SUGARMAN & T. J. VITALE, OBSERVATIONS ON THEDRYING OF PAPER: FIVE DRYING METHODS AND THE DRYINGPROCESS Journal of the American Institute for Conservation , 1992, Volume 31, Number 2, Article 3 (pp.175 to 197) http://www.jstor.org/stable/3179491?seq=1
http://www.energysolutionscenter.org/GasIRPaper/Learn%20About/Paper_Drying.htmhttp://www.jstor.org/stable/3179491?seq=1http://www.jstor.org/stable/3179491?seq=1http://www.energysolutionscenter.org/GasIRPaper/Learn%20About/Paper_Drying.htm


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CONSTANT RATE DRYING TIME

DRYING TIME CAN BE CALCULATEDBY INTEGRATING (9.5.-3)

LOWER VALUE OF X > X C (CRITICALPOINT)

1

22

X

X C C

S R X X WHERE RdX

A L

t C


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FALLING RATE DRYING

CONTROLLED BY GAS PHASE MASS TRANSFER FROM

SOLID OR HEAT TRANSFER INTO THE SOLID

TO VAPORIZE THE MOISTURE. GENERAL FORM OF THE EQUATION:

X1 < X C

16.9)(

1

2

X

X

S F

X R

dX

A

L t


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FALLING RATE DRYINGNUMERICAL CALCULATION FOR

COMPLEX SYSTEMS SEE EXAMPLE (9.7-1) FOR NUMERICAL

INTEGRATION

SIMPLIFICATIONS FOR LINEARRELATIONSHIPS: R(X) = aX + b

FOR b = 0, LINEAR THRU ORIGIN

)47.9(ln)(

)(

2

1

21

21

21

21

R R

R R A X X L

t SO X X R R

a S F

)87.9(lnln22 X

X

AR

X L

R

R

AR

X Lt SOaX R C

C

C S C

C

C S F


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FALLING RATE EXAMPLE

Shibata, H.; Iwao,Y., Vacuum Dryingof Sintered Spheresof Glass Beads,Ind. Eng. Chem.Res.; 1999; 38(9);3535-3542


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FALLING RATE EXAMPLE

Carmen Rossello, Jaime Canellas, Susana Simal, Angel Berna, Simple mathematical modelto predict the drying rates of potatoes, J. Agric. Food Chem .; 1992; 40(12); 2374-2378.

11 - Moisture Content and Drying Rate Calculations

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