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7/30/2019 11 - Moisture Content and Drying Rate Calculations
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MOISTURE CONTENTAND DRYING RATE
CALCULATIONS
SOLIDS
7/30/2019 11 - Moisture Content and Drying Rate Calculations
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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.pdf7/30/2019 11 - Moisture Content and Drying Rate Calculations
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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
7/30/2019 11 - Moisture Content and Drying Rate Calculations
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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.htm7/30/2019 11 - Moisture Content and Drying Rate Calculations
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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
7/30/2019 11 - Moisture Content and Drying Rate Calculations
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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.