Determination of Heat and Mass Transfer Coefficients Associated of Convective Drying of Calcium Carbonate / Water Slurry
Sophie Lee Landau, Emmy Kuo, Joseph Stern Professor Brazinsky Spring 2015
Abstract n rmfie!d rmfie!d "ray #ryer $as used to separate a mi%ture of &a!&ium &ar'onate and $ater 'y &on(e&ti(e drying) "he heat h eat and mass transfer &oeffi&ients asso&iated $ith the pro&ess $ere &a!&u!ated using t$o methods* a gi(en e+uation &orre!ated $ith the heat transfer &oeffi&ient and empiri&a! data regarding humidity 'y using the moisture &ontent of the &a!&ium &ar'onate s!urry) "hese $ere done o(er three tria!s at different temperature settings) or the first method, the a(erage heat transfer &oeffi&ient $as &a!&u!ated to 'e 2-)1- . 0)/5 m2K, and the a(erage mass transfer &oeffi&ient $as 5)05E05 . -)32E05 kgm2s) or the se&ond method, the a(erage heat transfer &oeffi&ient $as 4)35E03 . 6)42E03 m2K) "he a(erage mass transfer &oeffi&ient $as 0)02 . 0)01 kgm2s) "he differen&e in magnitudes 'et$een the t$o methods indi&ates a !a&k of a&&ura&y in either or 'oth of the &a!&u!ation methods, a!though their pre&ision &an 'e a&&epted due to the re!ati(e!y sma!! standard de(iations asso&iated $ith the &oeffi&ients) 7t is re&ommended that a ne$ psy&hrometer 'e o'tained so as to impro(e the a&&ura&y of the humidity data attained)
Table of Contents Abstract ..................................................................................1 List of Tables .............................................................................3 List of Figures ...........................................................................4 Nomenclature ............................................................................5
Theory.................................................................................6 Experimental........................................................................8 Results...............................................................................10
List of Tables "a'!e 1
4
"a'!e 2
10
"a'!e 3
11
"a'!e 6
18
List of Figures igure 1
13
igure 2
/
igure 3
15
igure -
16
igure 5
18
Nomenclature 9 &ross se&tiona! area of the pan : 9 &onstant ;1-)5< h 9 heat transfer &oeffi&ient ;m2K< = 9 humidity of air ;kg of =2>kg of air< =s 9 humidity of saturated air ;kg of = 2>kg of air< ? 9 gas mass (e!o&ity ;kg;m2s<< k 9 mass transfer &oeffi&ient λ 9 !atent heat of (aporization ;Jkg ;= ><< 2
@ 9 m 9 mass of paste A 9 mo!ar mass of air P 9 pressure of the air ;atm< ρ 9 density of air "9 temperature ;< "g 9 temperature of the air stream ;:< "s 9 temperature of the !i+uid surfa&e ;:< "red 9 redu&ed temperature "&rit 9 &riti&a! temperature of $ater v 9 air (e!o&ity ;ms<
Theory #rying is the pro&ess of remo(ing a !i+uid so!(ent ' y e(aporation) "he so!(ent is ordinari!y $ater, and is usua!!y separated from a so!id andor !i+uid) >ften, heat and a massseparating agent are used to de&rease the time re+uired to &omp!ete the drying pro&ess) 7n &on(e&ti(e drying, hot gas is passed o(er the mi%ture to speed up heat and mass transfer) #rying is most $ide!y used and re&ognized in the food and pa&kaging industries) Aar'!e dust, a 'yprodu&t from the mar'!e pro&essing industries, is often &ontained in the $aste s!urries from mar'!e pro&essing p!ants) 7t &an ' e used as a ra$ materia! in produ&tion pro&esses $ithin the paper, ru''er, and tire industries) 7n order for the &a!&ium &ar'onate to 'e suita'!e for reuse, it must first 'e re&o(ered from the s!urry $aste) emo(ing the mar'!e dust from $ater is a so!id!i+uid separation that &an 'e performed 'y &on(e&ti(e drying $ith hot air) 7n this e%periment, &a!&ium &ar'onate $as separated from $ater using the pro&ess of &on(e&ti(e drying) "he heat and mass transfer &oeffi&ients asso&iated $ith the drying pro&ess &an 'e determined) "he pro&ess of drying o&&urs in phasesC in the first, a !ayer of !i+uid rests on the top of the surfa&e of the mi%ture) De%t, the $ater in the s!urry must mo(e through the s!urry 'efore e(aporating at the surfa&e of the mi%ture) 7n theory, during this stage, the rate of drying is &onstant) ina!!y, on!y mar'!e dust is !eft in the pan and the pro&ess of drying is &omp!ete) "he rate of heat transfer from the f!o$ing hot air to the so!id fo!!o$s the e+uation*
q =hA ( T g−T s ) T g $here A is the surfa&e area a(ai!a'!e for &on(e&tion, is the temperature of the hot air,
T s
is the temperature of the surfa&e, and the heat transfer &oeffi&ient,
fo!!o$s the e+uation
h =(constant ) G
is effe&ti(e!y a mass transfer re!ation*
q =kAλ ( H s − H )
h
,
0.8
) "his heat transfer &an a!so 'e e+uated to $hat
7n this e+uation,
k is the mass transfer &oeffi&ient, and λ is $aters !atent heat of
(aporization) E+uating the t$o, e!iminating area, and so!(ing for the mass transfer &oeffi&ient, k =h
T g −T λ ( H s− H )
"he redu&ed temperature is defined as
T ¿ =
T ( K ) T crit ( K ) ) "his &an 'e used to
&a!&u!ate the !atent heat of (aporization of $ater, using the fo!!o$ing re!ation* λ =52053000∗( 1−T ¿ )
2
0.3199− 0.212 T ¿ + 0.25795T ¿
&a!&u!ated using the idea! gas !a$,
empiri&a!!y determined air (e!o&ity,
ρ=
v
. "he density of air, ρ , &an then 'e
PM RT , and &an 'e used in &onFun&tion $ith the
, to determine the gas mass (e!o&ity,
G= ρv
)
!ternati(e!y, the moisture &ontent of the &a!&ium &ar'onate mi%ture &an 'e used to determine the heat and mass transfer &oeffi&ients) "he moisture &ontent of the s!urry is the ratio 'et$een the mass of the $ater and the mass of the dry paste) ssuming a &onstant rate of drying, the rate of $ater e(aporation &an 'e e%pressed using the fo!!o$ing e+uation*
dw q hA ( T g −T s ) = = =kA ( H s− H ) $here dt λ λ
dw / dt is the rate of $ater e(aporation)
"he heat and mass transfer &oeffi&ients &an then 'e &a!&u!ated using the re!ations* dw ∗ λ dt h= A ( T g −T s )
dw ∗1 dt k = A ( H s− H )
7n this e%periment,
dw / dt
$as found a&&ording to dis&retized time inter(a!s)
"he heat and mass transfer &oeffi&ients asso&iated $ith the pro&ess of &on(e&ti(e drying &an thus 'e &a!&u!ated using the gas mass (e!o&ity, and using the moisture &ontent of the pan) 7n the first method, the heat transfer &oeffi&ient fo!!o$s dire&t!y from a gi(en e+uation, and the mass transfer &oeffi&ient is &a!&u!ated a&&ording!y) 7n the se&ond, ho$e(er, the &oeffi&ients are &a!&u!ated upon the assumption that the pro&ess is operating at a &onstant rate of drying)
Experimental n rmfie!d "ray #ryer $as used to dry a &a!&ium &ar'onate paste at three of its temperature &ontro! settings* 6, 8, and /) "he 'ooster atta&hed to the dryer $as set to ma%imum and the airf!o$ &ontro!!er $as set at /) "he dry $as preheated for ten minutes prior to the start of the e%periment) tray &ontaining the paste $as suspended on a $ire mesh drying ra&k atta&hed to an e!e&tri&a! 'a!an&e) "he air stream (e!o&ity $as measured using an anemometer) $et and dry 'u!' thermometer $as used to measure the upstream and do$nstream temperatures) n 7 thermometer $as used to measure the surfa&e temperature) or ea&h of the three tria!s, 500 g of so!id &a!&ium &ar'onate $as mi%ed in a tray $ith appro%imate!y 155 g of $ater in order to o'tain a &a!&ium &ar'onate paste) "he $eights of the &a!&ium &ar'onate, $ater, and the tray $ere re&orded) "he tray &ontaining the paste $as p!a&ed on the drying ra&k) "he $eight of the pan, air stream temperatures, surfa&e temperature, and air (e!o&ity $ere re&orded at ea&h time point) or the first hour of data &o!!e&tion, measurements $ere taken e(ery fi(e minutes) fter the first hour, measurements $ere taken e(ery ten minutes, and after t$o hours, measurements $ere taken e(ery fifteen minutes) "he $eight of the dry paste $as re&orded) "hroughout the data &o!!e&tion, the $et 'u!' had to 'e re$et $ith a pipet 'et$een ea&h measurement 'e&ause it dehydrated +ui&k!y) ;n image of the setup is sho$n 'e!o$ in igure 2)<
igure 2* rmfie!d "ray #ryer
Results "he drying of the mar'!e dust and $ater mi%ture $as measured 'y monitoring se(era! (aria'!es throughout the drying pro&ess) "hese (aria'!es $ere* the surfa&e temperature of the mar'!e paste, the air speed (e!o&ity of the fan, the $et and dry 'u!' temperatures upstream and do$nstream the paste and fina!!y the mass of the paste) "hese (aria'!es are sho$n in ta'!es 1, 2 and 3, for the three e%periments done)
Tim e
Mass (g)
Air Veloc (m/s)
Upstrea m Temp (deg F) Wet
Downstream Temp (deg F) Dr Wet y
Dry
Internal temp (deg F)
0:00
982
0.73
88
90
90
91
77.9
0:09
975
1.99
95
99
101
104
84.5
0:15
968
2.07
104
10
111
113
97.9
8 0:23
956
2.11
115
116
116
116
106.1
0:33
937
2.02
104
110
110
114
110
0:46
915
2.04
101
10
108
113
113.1
9 0:57
896
2.11
100
113
113
117
111.3
1:09
877
2.08
100
110
108
114
110.6
1:23
857
2.02
100
110
115
120
110.8
1:39
846
2.12
100
110
115
118
114.2
1:49
843
2.05
116
118
116
118
114.3
Time
0*00 0*05 0*10 0*15 0*20 0*25 0*30
Weigt of !an "g# 106/ 1055 1052 10-1038 1032 1020
$%str& Wet 'ulb "degF# 84 84 /3 40 48 10/ 8-
$%str& Dry 'ulb "degF# 10/ 110 1111112 111 104
Do(nstr& Wet 'ulb "degF# 8/ 8/ /0 /6 42 108-
Do(nstr& Dry 'ulb "degF# 106 104 110 111 104 104 10/
Surfac e "degF# 40 108)0 108)1 106)6 105)/ 105)/ 102)4
Air )elocity "m/s# 1)14 1)46 1)46 2)00 2)02)06 2)0/
0*35 1014 82 110 82 10/ 108)6 0*-0 1013 8112 83 110 105)0 0*-5 1000 8113 82 110 105)0 0*50 441 83 112 82 111 106)6 0*55 4/8113 83 111 108)1 1*00 484 8113 8111 10/)5 1*10 46/ 85 116 8111 10/)5 1*20 4-/ 8/ 116 8112 105)4 1*30 436 /0 113 84 113 104)6 1*-0 4384 118/ 113 104)1 1*50 426 /0 113 84 112 110)6 1*55 426 /1 115 /0 113 104)8 2*05 42/1 111 /0 111 104)1 2*15 423 46 115 42 11104)6 2*25 422 83 10/ 8108 10/)6 "a'!e 1* irst drying e%periment done on the first $eek, performed at the ma% speed setting of 10 and a temperature setting of /)
1)/4 1)4/ 2)06 2)06 2)00 2)05 1)48 2)06 2)11 1)4/ 2)04 2)04 2)10 2)02 2)03
Time
Weigt $%str& $%str& Do(nstr& Do(nstr& Surfac Air of !an Wet 'ulb Dry 'ulb Wet 'ulb Dry 'ulb e )elocity "g# "degF# "degF# "degF# "degF# "degF# "m/s# 0*00 1068 /5 111 /5 104 106)/ 2)10*05 1063 // 112 /2 104 108)6 2)11 0*10 1055 45 110 42 110 106)3 2)08 0*15 10-/ 44 112 48 110 10-)6 2)05 0*20 10-3 88 110 86 10/ 108)2)12 0*25 1038/ 111 88 104 10-)6 2)06 0*30 102/ /0 110 8/ 110 105)0 2)13 0*35 1022 8/ 104 88 108 102)3 2)13 0*-0 10184 104 88 10/ 10-)2)0/ 0*-5 1012 /1 110 84 10/ 10-)3 2)05 0*50 100/2 110 /1 10/ 10-)2 2)02 0*55 445 /8 104 /3 108 103)3 2)06 1*00 4/5 83 10/ 82 108 105)0 2)03 1*10 46/ 82 10/ 81 105 105)2 2)03 1*20 451 82 10/ 81 108 102)2 2)10 1*30 434 8104 82 108 10-)2 2)11 1*-0 433 85 10/ 8106 105)8 2)01*50 424 84 104 86 10/ 10-)0 2)05 2*00 4284 10/ 88 108 105)1 2)08 2*15 422 /10/ 84 106 105)2)05 2*30 421 /0 106 /0 106 10-)4 2)10 "a'!e 2* Se&ond drying e%periment done on the se&ond $eek, performed at the ma% speed setting of 10 and a temperature setting of 6)
Time
Weigt $%str& $%str& Do(nstr& Do(nstr& Surfac of !an Wet 'ulb Dry 'ulb Wet 'ulb Dry 'ulb e "g# "degF# "degF# "degF# "degF# "degF# 0*00 1086 40 108 /5 102 44)0 0*05 1081 41 10/ // 106 106)0 0*10 1068 /2 110 /0 108 108)0*15 1060 86 110 85 10/ 10-)6 0*20 1052 85 111 85 110 105)6 0*25 10-3 86 112 85 110 106)0*30 10386 113 8110 106)8 0*35 102/ 88 113 86 111 108)/ 0*-0 1021 86 113 85 111 105)/ 0*-5 1015 86 112 85 104 108)0*50 10088 113 8110 106)4 0*55 1000 86 112 86 111 106)3 1*00 44/0 115 88 110 10/)1 1*10 483 84 111 8/ 104 108)1*20 46/ /2 112 /0 110 108)3 1*30 451 /6 111 /3 104 105)2 1*-0 4-0 44 111 4104 108)0 1*50 433 8/ 110 86 108 106)8 2*00 425 /0 111 84 110 104)5 2*15 414 84 110 8/ 10/ 106)6 2*30 418 /3 112 /1 111 110)/ "a'!e 3* "hird drying e%periment done on the fina! $eek, performed at the ma% speed setting of 10 and a temperature setting of 8)
Air )elocity "m/s# 1)4/ 2)05 2)12 2)03 2)15 2)12 2)12 2)12 2)11 2)11 2)12 2)08 2)06 2)10 2)1/ 2)0/ 2)11 2)12)03 2)0/ 2)06
Gsing these re&orded measurements, it $as then possi'!e to find the mass (e!o&ity of the air stream during &onta&t $ith the drying pan as $e!! as the heat transfer &oeffi&ient of the air and paste) "his $as done using the formu!a* G= ρv "he density of the air,
ρ=
ρ
, $as found using the perfe&t gas !a$*
PM RT
pressure of 1 atmosphere $as used as $e!! as a mo!ar mass of 2/)48 kgmo!) 7n order to find the mass (e!o&ity of the air during &onta&t $ith the paste, the a(erage of the dry 'u!' temperatures upstream and do$nstream of the drying ra&k $as used) "he fo!!o$ing &orre!ation $as then used to find the heat transfer &oeffi&ient* 0.8 h =C ∗G $here : is e+ua! to 1-)5)
n e%amp!e &a!&u!ation up to the heat transfer &oeffi&ient is gi(en 'e!o$* (1 atm ) 28.97 kg kmol PM kg ρ= = = .93 3 3 RT m .08206 atm∗m 107 K kmol∗ K
(
)
(
G= ρv =.93
)
kg m
m s
∗1.19 = 1.1
3
kg 2
m s
h =C ∗G =14.5∗( 1.1 ) =15.71 0.8
.8
W 2
m K
"he a(erage heat transfer &oeffi&ients o(er time for ea&h e%periment using this method are gi(en in "a'!e 6) Gsing this heat transfer &oeffi&ient, it is then possi'!e to determine the mass transfer &oeffi&ient of the $ater !ea(ing the paste and e( aporating into the air) "his $as done using the fo!!o$ing &orre!ation* kλ ( H s− H ) =h ( T g− T s ) $hi&h &an 'e rearranged to so!(e for k* T g −T s k =h λ ( H s− H ) "he a(erage temperature of the dry 'u!' temperatures $ere used for "g) "he saturated humidity data as a fun&tion of temperature $as o'tained from Perry’s Chemical Engineering Handbook, 8th Edition) "his data $as interpo!ated to find the humidity at the $et and dry 'u!' temperatures, $hi&h &orresponded to =S and = respe&ti(e!y) "he empiri&a! humidity data $as then estimated 'y a !inear 'est fit* H =0.0009 T −0.0492 "his fit is sho$n in igure 1)
Saturation Humidit 0.05 0.05 0.04
f(x) = 0x - 0.05 R² = 0.98
0.04 0.03 Saturation umi!ity
0.03 0.02 0.02 0.01 0.01 0 60
70
80
90
100
110
Temperature (F)
igure 1) Linear fit of empiri&a! data of humidity (s) temperature, data o'tained from Perrys hand'ook)
λ $as found using an empiri&a! &ur(e fit 'y the fun&tion* λ =52053000∗( 1−T ¿ )
2
0.3199− 0.212 T ¿ + 0.25795 T ¿
here "red is the redu&ed temperature of the dry 'u!', $here "red is gi(en 'y* T ( ° K ) T ¿ = T crit ( ° K ) >n&e these (a!ues $ere found, the mass transfer &oeffi&ient k &ou!d then 'e foundC an e%amp!e &a!&u!ation is done 'e!o$* T ( K ) 299 T ¿ = = =.462 T crit ( K ) 647 λ =52053000∗( 1−.462 )
0.3199
− 0.212 ( .462) + 0.25795 (.462 )
2
= 4.38∗1 0 ( / kg ( H !)) 7
2
H " =0.0009 (107 )−0.0492 =.0481 H = 0.0009 ( 78.5 )− 0.0492 =.0222 k =h
T g −T s λ ( H s− H )
=( 15.71 )
−305.4 =1.31∗10− kg / m s ( .0481−.0222 )
314.8
∗
4.38 1 0
7
4
2
"his method of finding the mass and heat transfer &oeffi&ients, to distinguish from an a!ternate method emp!oyed !ater is kno$n as the Hgas mass (e!o&ity method)I "he a(erage mass transfer &oeffi&ients for ea&h e%periment &an 'e seen on "a'!e 6) graph of the mass transfer rate (arying (ersus the moisture &ontent in the $et so!id $as dra$n to o'ser(e a possi'!e !ink 'et$een the rate of drying (ersus the remaining $ater $ithin the paste) "he moisture &ontent $as determined 'y taking the &urrent mass of the pan, and su'tra&ting the mass of the pan and initia! &a!&ium &ar'onate to determine the mass of $ater remaining in the pan) "he mass of the $ater $as then di(ided 'y the tota! mass of the $ater and &a!&ium &ar'onate to determine the moisture &ontent) "his graph is sho$n as igure 3) "he mass and heat transfer of the paste &an a!so 'e measured as a deri(ati(e dm dt , and &an 'e estimated 'y determining the mass !ost 'et$een time inter(a!s,
#m #t ) "his method is &a!!ed the moisture o(er time method) "he heat transfer &oeffi&ient &an then 'e found a&&ording to the fo!!o$ing formu!a* #m hA (T g−T s ) = $hi&h is rearranged to find h* #t λ #m ∗ λ #t h= A ( T g −T s ) !! (a!ues are a!ready kno$n, is the area of the pan, $hi&h is e+ua! to )0502 m2, thus it is simp!e to &a!&u!ate h* ( 1.075−1.061 ) kg #m ∗4.38∗107 ∗ λ kg ( 300− 0 ) s #t h= = 2 A ( T g −T s ) .0502 m ( 314.8 −305.4 ) K 4
2
h =2.94∗10 W / m K Simi!ar!y, the mass transfer &oeffi&ient &an a!so 'e found using the fo!!o$ing formu!a* ( 1.075−1.061 ) kg #m ∗1 ∗1 ( 300− 0 ) s #t k = = A ( H s− H ) .0502 m 2 ( .0504−.0222 )
k =.0331
kg 2
m s
igure -, again &ompares the mass transfer &oeffi&ient (ersus the moisture &ontent of the paste using this ne$ method)
"ryin# Rate $s. %oisture &ontent usin# 'as %ass eloity 0.0004
0.0003
0.0002
!"# 1 !"# 2
%ass trans*er rate (+#,m-/s)
!"# 3 0.0001
0.0000 0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
"ryin# Rate $s. %oisture &ontent usin# 'as %ass eloity 0.0004
0.0003
0.0002
!"# 1 !"# 2
%ass trans*er rate (+#,m-/s)
!"# 3 0.0001
0.0000 0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
-0.0001 %oisture &ontent
igure 3) Gsing the gas mass (e!o&ity method, graph of the drying rate, represented as the mass transfer rate of $ater from the paste to the air, (ersus the remaining moisture &ontent of the $ater)
"ryin# Rate $ersus %oisture &ontent sin# %oisture $er Time 0.1200
0.1000
0.0800 !"# 1 %ass Trans*er &oe2ient (+#, m-/s)
0.0600
!"# 2 !"# 3
0.0400
0.0200
"ryin# Rate $ersus %oisture &ontent sin# %oisture $er Time 0.1200
0.1000
0.0800 !"# 1 %ass Trans*er &oe2ient (+#, m-/s)
0.0600
!"# 2 !"# 3
0.0400
0.0200
0.0000 0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
%oisture &ontent
igure -) Gsing the moisture o(er time method, graph of the drying rate, represented as the mass transfer rate of $ater from the paste to the air, (ersus the remaining moisture &ontent of the $ater)
or a (isua!ization of the drying pro&ess, the moisture &ontent of the paste &ompared to the time the test &ontinued $as a!so graphed) "his is sho$n in igure 5)
%oisture &ontent $ersus Time 0.35 0.30 0.25 0.20 !a 1 !a 2 'oi&tur% ont%nt ( * +at%r,* dr a&t%) 0.15 0.10 0.05
!a 3
or a (isua!ization of the drying pro&ess, the moisture &ontent of the paste &ompared to the time the test &ontinued $as a!so graphed) "his is sho$n in igure 5)
%oisture &ontent $ersus Time 0.35 0.30 0.25 0.20 !a 1 !a 2 'oi&tur% ont%nt ( * +at%r,* dr a&t%) 0.15
!a 3
0.10 0.05 0.00 0
2000 4000 6000 8000 10000 $im% (&)
igure 5) Aoisture :ontent of the paste o(er time) n a(erage &omparison of the e%periments is sho$n in "a'!e 6, to pro(ide a summary of the tota! e%periment)
"a'!e 6) "ota! heat and mass transfer &oeffi&ients for ea& h e%periment as $e!! as their standard de(iations)
Discussion
"$o main methods $ere emp!oyed to determine the heat transfer &oeffi&ient) "he first $as the gas mass (e!o&ity method) "his uti!ized the &orre!ation of* 0.8 h =C ∗G to determine the heat transfer &oeffi&ient) Bui!ding upon this, it $as assumed that the drying &ake $as at e+ui!i'rium and thus the heat transferred to the surfa&e $as e+ui(a!ent to the heat used to (aporize the $ater $ithin the paste) "his made it possi'!e to d etermine the mass transfer &oeffi&ient 'y e+uating the heat re+uired*
kλ ( H s− H ) =h ( T g− T s ) "his &orre!ation re!ies on se(era! other fa&tors) "he first fa&tor is the determination of the saturated humidity of the air at the measured temperatures) "his $as &a!&u!ated 'y fitting a !inear &ur(e to empiri&a! data found in Perrys =and'ook of :hemi&a! Engineering) !inear &ur(e $as used 'e&ause it $as deemed a&&urate enough for the purpose of this e%periment and had a de&ent &orre!ation to the data, $ith an 2 (a!ue of 0)4/) "his fun&tion is a!so re!iant on the determination of λ , the !atent heat of (aporization of =2>) "his $as determined 'y using the empiri&a! re!ationship des&ri'ed in the esu!ts se&tion) Gti!izing a!! of these (a!ues as $e!! as the surfa&e temperature and heat transfer &oeffi&ient found pre(ious!y, the mass transfer &oeffi&ient $as a'!e to 'e determined) 7n order to 'etter (isua!ize the mass transfer o(er time, the mass transfer &oeffi&ient $as graphed (ersus the moisture &ontent $ithin the paste ;igure 3<) =o$e(er, the graph yie!ded e%treme!y &onfusing resu!ts, $hi&h offer !itt!e e!u&idation of the stages of drying) 7t $as e%pe&ted that there $ou!d 'e t$o (isi'!e and distin&t stages of drying) 7t $as e%pe&ted that there $ou!d 'e a &onstant rate period, $here the rate of mass transfer $ou!d 'e high yet &onstant, due to a &onstant !i+uid fi!m a'o(e the so!id) "his $ou!d e(entua!!y !ead to a de&rease in mass transfer, as the !i+uid fi!m disappears, !eading to the ne%t stage &a!!ed the Hfa!!ing rate periodI) =o$e(er it is diffi&u!t to see a &!ear distin&tion 'et$een the stages) "his is most!y due to the e%treme!y os&i!!atory nature of the rate o(er the moisture &ontent) E%amining igure 3, it is determined that the most !ike!y s$it&h of the stages o&&urs at a appro%imate moisture &ontent of )05, sin&e there is a de&rease that e(entua!!y !eads to a mass transfer rate of 0) "here are se(era! reasons for the diffi&u!ty in the stages that $i!! 'e dis&ussed after the des&ription of the ne%t method) "he ne%t method uti!ized the mass !ost o(er time to determine the rate of $ater e(aporation) "he a(erage s!ope in mass o(er time $as uti!ized to find the rate &oeffi&ients) #m hA (T g−T s ) #t
=
λ
#m =kA ( H s− H ) # t
"heoreti&a!!y, this method shou!d &ontain !ess error for the mass transfer &oeffi&ient than the first method) "his is 'e&ause the mass transfer &oeffi&ient does not re!y upon the heat transfer &oeffi&ient as $e!! as the !atent heat of (aporization, un!ike the first method) "his resu!ts in !ess propagation of error as $e!! and !ess rooms for mistakes) Simi!ar!y, the mass transfer &oeffi&ient $as graphed against the moisture &ontent ;igure -<) Gnsurprising!y, the trends of the tests $ere simi!ar to the first method) =o$e(er, &omparing igure - and igure 3, there is a maFor differen&e 'et$een the mass transfer rates, the se&ond method gi(es a mass transfer rate 100% more than the first method) Gnfortunate!y, this is not e%p!aina'!e from the &a!&u!ations and remains in&on&!usi(e as to the reasoning 'ehind the in&onsisten&ies 'et$een the methods) "he error of the system pro(ed to 'e +uite !arge) E%amining the a(erage mass transfer &oeffi&ients in "a'!e 6, the standard de(iation $as on the same magnitude if not greater than the a(erage itse!f) "his suggests that there is a $ide spread of the mass transfer &oeffi&ient) "here is one maFor issue that o&&urred that introdu&ed error into the system) "he most &u!pa'!e sour&e of error $as the psy&hrometer, or more spe&ifi&a!!y the $et 'u!' thermometer) #ue to !oss of the $i&k, the $et 'u!' $ou!d not stay &onsistent!y $et) #ue to this, the $et 'u!' needed to 'e $et at &ertain inter(a!s $hen it 'egan to dry) "his &aused maFor s$ings in the $et 'u!' temperature) "his &aused the $et 'u!' temperature to ha(e range of 80100 ) "his e%p!ains the os&i!!atory nature of the mass transfer rate) s the $et 'u!' dried, the temperature rose, in&reasing the =, the air saturation of the e+uation, &onse+uent!y in&reasing the mass transfer &oeffi&ient) "his is true for 'oth methods, as they 'oth use the $et 'u!' temperature in their &a!&u!ations) s the 'u!' dried &onstant!y throughout the run and $ater $as reapp!ied, this &aused the e%treme!y os&i!!atory nature of the mass transfer &oeffi&ient) igure 5, the graph of the moisture &ontent o(er time seems to support the &on&!usion that the os&i!!atory nature is due to the $et 'u!' instead of a property of the drying pro&ess) "he moisture &ontent seems to suggest a re!ati(e!y &onstant rate of drying u nti! a time of 5000 se&onds, at $hi&h the rate starts to de&rease) >ther sour&es of error in&!ude potentia! &a!&ium &ar'onate !oss during the mi%ing pro&ess and in&onsisten&y in the $etness of the &ake 'et$een e%periments) =o$e(er, these are sma!! errors that are not e%pe&ted to ha(e as !arge an effe&t as the $et 'u!' temperature)
*ecommendations
7t is re&ommended that a ne$ psy&hrometer 'e o'tained, that &an &onsistent!y ensure a $et 'u!', or if not the $et 'u!' shou!d 'e re$et after e(ery measurement, to ensure &onsistent $etness and to pre(ent the os&i!!atory nature o'tained in this e%periment)
*eferences
1M Perry’s Chemical Engineering Handbook , /th Edition >n!ineM 2M #rying :hE 1-2 :hemi&a! Engineering La'oratory Pa&ket, Spring 2015
