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Forced draft tray dryer
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INTRODUCTION

 

Drying of solids is considered to occur in two stages , a constant rate period followed by a falling rate period. In the constant rate period the rate of drying corresponds to the removal of water from the surface of solid. The falling rate period corresponds to the removal of water from the interior of the solid.The rate in either case is dependent on :

1.Flow rate of air

2. Solid characteristics

3. Tray material.

 

 

 

Drying can be described in terms of gas mass transfer and heat mass transfer co-efficients.

Rate of drying is given by :

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»N«/mi»«mi mathvariant=¨bold¨»C«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»K«/mi»«mi mathvariant=¨bold¨»y«/mi»«/msub»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»Y«/mi»«mrow»«mi mathvariant=¨bold¨»S«/mi»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨bold¨»Y«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mi mathvariant=¨bold¨»q«/mi»«msub»«mi mathvariant=¨bold¨»§#955;«/mi»«mi mathvariant=¨bold¨»S«/mi»«/msub»«/mfrac»«/math».................................................1

 

Where Q is the total heat supplied by the gas stream to the solid and is given by :

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»q«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mrow»«mi mathvariant=¨bold¨»g«/mi»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»)«/mo»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»r«/mi»«/msub»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mrow»«mi mathvariant=¨bold¨»r«/mi»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»)«/mo»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mrow»«mi mathvariant=¨bold¨»g«/mi»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»)«/mo»«/math».....................................2

 

Total heat supplied = Convective heat + Radiation heat + Conduction heat

Where hc , hr , hk are the heat transfer co-efficient for convection , radiation , and conduction respectively.

These co -efficients are given by :

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»14«/mn»«mo».«/mo»«mn»6«/mn»«msup»«mi mathvariant=¨bold¨»G«/mi»«mrow»«mn»0«/mn»«mo».«/mo»«mn»8«/mn»«/mrow»«/msup»«/math»...................................................3

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»r«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨bold¨»§#949;§#963;«/mi»«mfrac»«mrow»«mo»(«/mo»«msup»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»r«/mi»«/msub»«mn»4«/mn»«/msup»«mo»-«/mo»«mo»§nbsp;«/mo»«msup»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mn»4«/mn»«/msup»«mo»)«/mo»«/mrow»«mrow»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»r«/mi»«/msub»«mo»-«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»)«/mo»«/mrow»«/mfrac»«/math».......................................4

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mn»1«/mn»«mfenced»«mrow»«mfrac»«mn»1«/mn»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«/mfrac»«mfrac»«mi mathvariant=¨bold¨»A«/mi»«msub»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»U«/mi»«/msub»«/mfrac»«mo»+«/mo»«mfrac»«msub»«mi mathvariant=¨bold¨»Z«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»K«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msub»«/mfrac»«mfrac»«mi mathvariant=¨bold¨»A«/mi»«msub»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»U«/mi»«/msub»«/mfrac»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»Z«/mi»«mi mathvariant=¨bold¨»S«/mi»«/msub»«mfrac»«mi mathvariant=¨bold¨»K«/mi»«msub»«mi mathvariant=¨bold¨»K«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msub»«/mfrac»«mfrac»«mi mathvariant=¨bold¨»A«/mi»«msub»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»U«/mi»«/msub»«/mfrac»«/mrow»«/mfenced»«/mfrac»«/math»...........................................5

 

Putting the value gives

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«mrow»«msub»«mi mathvariant=¨bold¨»K«/mi»«mi mathvariant=¨bold¨»y«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»C«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mfenced»«mfrac»«mrow»«mi mathvariant=¨bold¨»S«/mi»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨»P«/mi»«mi mathvariant=¨bold¨»r«/mi»«/mrow»«/mfrac»«/mfenced»«mrow»«mn»0«/mn»«mo».«/mo»«mn»567«/mn»«/mrow»«/msup»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mi mathvariant=¨bold¨»Le«/mi»«mrow»«mn»0«/mn»«mo».«/mo»«mn»567«/mn»«/mrow»«/msup»«/math»..........................................6

 

Ratio of (hc/ky) = Lewis number (Le) and is given by

 

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»Y«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨bold¨»Y«/mi»«mo»)«/mo»«msub»«mi mathvariant=¨bold¨»§#955;«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«/mrow»«mfrac»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»K«/mi»«mi mathvariant=¨bold¨»y«/mi»«/msub»«/mfrac»«/mfrac»«mo»=«/mo»«mfenced»«mrow»«mn»1«/mn»«mo»+«/mo»«mfrac»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«/mfrac»«/mrow»«/mfenced»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»g«/mi»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mfrac»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»r«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»c«/mi»«/msub»«/mfrac»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»r«/mi»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»s«/mi»«/msub»«mo»)«/mo»«/math».......................................7

 

Cs is the specific heat of saturated gas at Ts

For an air water system Le is approximately equal to 1

Equations (3) and (7) yields hc and ky respectively.

Simultaneously iterative solutions of eqn. (6) with saturation humidity curve provides the the solid surface temperature ,Ts and the corresponding value of humidity Ys.

Knowing Ys eqn. (1) is used to find out the drying rate Nc.

 

      NOMENCLATURE:

A : Drying surface area, m2

AU : Non drying surface area of drying solid , m2

Am : Average solid surface area , m2

CS : Saturated specific heat of air, J/kg0C

G : Mass velocity of gas, kg/m2-sec

N : Drying rate

NC : Constant drying rate , kg/m^2-sec

S : Mass of dry solid

Tg : Absolute temperature of gas (dry bulb),K

Zm : Metal thickness

Tr : Absolute temperature of radiating surface ,K

Ts : Absolute temperature of solid surface ,K

 

 

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