MOISTURE CONTENT MOISTURE CONTENT AND DRYING RATE AND DRYING RATE

CALCULATIONSCALCULATIONSSOLIDS SOLIDS

MOISTURE CONTENT RELATIONSHIPS

MOISTURE/SOLID EQUILIBRIUM RELATIONSHIPS

FIGURES 9.4-1 AND 9.4-2 FOR SEVERAL TYPES OF SYSTEMS

DEFINED ON THE BASIS OF RELATIVE HUMIDITY AT A SPECIFIC TEMPERATURE

EQUILIBRIUM AMOUNT OF MOISTURE TENDS TO DECREASE WITH INCREASING TEMPERATURE

MOISTURE CONTENT MOISTURE CONTENT VARIABLESVARIABLES

BASED ON THE MASS OF MOISTURE RELATIVE TO THE MASS BONE DRY SOLID

)(

.

%100@

)25.9(

15.9

*

*

MoistureSurface

XXBoundAboveContentMoistureX

MoistureUnbound

HwithSaturationContentMoistureX

XXContentMoistureFreeX

ContentMoisturemEquilibriuX

BDSSolidDryMass

LiquidMassX

BtU

RB

t

t

DRYING RATE CURVES

DEPEND ON WHETHER HEAT OR MASS TRANSFER CONTROLS• FREE MOISTURE VS. TIME• DRYING RATE VS. MOISTURE CONTENT

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

DRYING REGIMESDRYING REGIMES CONSTANT RATE - NO LIMIT TO MASS

TRANSFER IN SOLID PHASE • SURFACE MOISTURE• TRANSFER NEAR SURFACE

FALLING RATE –MOISTURE FLUX THROUGH THE SOLID IS HINDERED

• CRITICAL POINTS OCCUR BETWEEN CONSTANT RATE AND FALLING RATE WITH A CHANGE IN THE FALLING RATE DRYING MECHANISM

DRYING MODELSDRYING MODELS RATES FROM EMPIRICAL DATA

CONSTANT RATE DRYING• CONTROLLED BY HEAT TRANSFER TO

VAPORIZE THE MOISTURE OR MASS TRANSFER

)35.9(

tA

XLR S

76.9)(

HHMkTTh

R WByW

WC

HEAT TRANSFER HEAT TRANSFER CORRELATIONSCORRELATIONS

TO PREDICT CONSTANT RATE DRYINGTO PREDICT CONSTANT RATE DRYING

RADIATION CAN ALSO BE A FACTORRADIATION CAN ALSO BE A FACTOR

)106.9(37.017.1

:

)96.9(0128.00204.0

:

37.02

37.02

8.02

8.02

GRft

BTUhG

Km

Wh

SURFACETOLARPERPENDICU

GRft

BTUhG

Km

Wh

SURFACETOPARALLEL

FACTORS THAT FACTORS THAT AFFECT h

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

FOR SURFACE MOISTUREFOR SURFACE MOISTURE MATERIALS SURFACE FINISH OR ANY MATERIALS SURFACE FINISH OR ANY

CONDITION THAT STIMULATES CONDITION THAT STIMULATES TURBULENCETURBULENCE• J. E. SUGARMAN & T. J. VITALE, J. E. SUGARMAN & T. J. VITALE, OBSERVATIONS ON THE OBSERVATIONS ON THE

DRYING OF PAPER: FIVE DRYING METHODS AND THE DRYING DRYING OF PAPER: FIVE DRYING METHODS AND THE DRYING PROCESSPROCESS Journal of the American Institute for Journal of the American Institute for ConservationConservation ,, 1992, Volume 31, Number 2, Article 3 (pp. 175 1992, Volume 31, Number 2, Article 3 (pp. 175 to 197) to 197) http://www.jstor.org/stable/3179491?seq=1

CONSTANT RATE DRYING TIMECONSTANT RATE DRYING TIME

DRYING TIME CAN BE CALCULATED BY INTEGRATING (9.5.-3)• LOWER VALUE OF X > XC (CRITICAL

POINT)

1

22

X

X CC

SR XXWHERE

R

dX

A

Lt

C

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 < XC

16.9)(

1

2

X

X

SF XR

dX

A

Lt

FALLING RATE DRYING NUMERICAL CALCULATION FOR NUMERICAL CALCULATION FOR

COMPLEX SYSTEMS COMPLEX SYSTEMS • SEE EXAMPLE (9.7-1) FOR NUMERICAL SEE EXAMPLE (9.7-1) FOR NUMERICAL

INTEGRATIONINTEGRATION SIMPLIFICATIONS FOR LINEAR SIMPLIFICATIONS FOR LINEAR

RELATIONSHIPS: R(X) = aX + bRELATIONSHIPS: R(X) = aX + b

FOR b = 0, LINEAR THRU ORIGINFOR b = 0, LINEAR THRU ORIGIN

)47.9(ln)(

)(

2

1

21

21

21

21

R

R

RRA

XXLtSO

XX

RRa S

F

)87.9(lnln22

X

X

AR

XL

R

R

AR

XLtSOaXR C

C

CSC

C

CSF

FALLING RATE EXAMPLEFALLING RATE EXAMPLE

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

FALLING RATE EXAMPLEFALLING RATE EXAMPLE

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