IKDUSTRIAL AKD EKGIKEERING CHEMISTRY
4'78
Equation 3
1s
rewritten in terns of over-all resistance: (19)
Differentiating (18) and ccnbining w t h (19):
The two integrals on the left of this equation are integrated graphica,lly, following a similar procedure to that employed in solving Equation 17. hTOhIEKCLATURE
a
=
sp. area of interface, sq. ft./cu. ft. active tower volume
A = cross-sectional area of tower, sq. ft. B = a constant c = concentration of liquor, lb. SOn/cu. ft. G = gas velocity, lb./min./sq. ft.
Vol. 25, No. 4
G' = inert gas velocity, ib./min./sq. it. H = solubility coefficient = c,/p, k = absorption coefficient, lb./min./sq. ft./(lb./cu. ft.) L = liquor velocit,y, lb./min./sq. ft. L' = water velocity, lb./min.jsq. ft. 1 = height of active tower, ft. p = pressure of sulfur dioxide, mm. of Hg P = total pressure of gas, mm. of Hg ?'G = gas film resistance (lb./min./cu. ft./mm. Hg)-l rL = liquid film resistance [lb./rnin./cu. ft./(lb./cu. ft.)]-' RG = over-all diffusional resistance (lb./min./cu. ft./mm. of Hg)-* RL = over-all diffusional resistance [Ib./min./cu. ft./(lh./cu. ft.)]-1 s = ep. gr. of liquor 1' = active (packed) volume of tower, cu. it. W = weight of sulfur dioxide, lb. 2 = liquor concentration, lb. SOz/lb. H20 y = gas concentration, lb. SOz/lb. inert gas b = time, min. Subscripts: o, at bottom of tower; ', at top of tower; at equilibrium.
LITERaTURE CITED ISD. ESG. CHEM.,16, 1224
(1) Haslam, Hershey, and Kean,
(1924). ( 2 ) Lewis and Whitman, I b i d . , 16, 1215 (1924). (3) Mass. Inst. Tech,, School of Chem. Eng. Practice. Unpublished Repts. (4) S h e r w o o d , . I s ~ .ESG. CHmf.,17, 745 (1925). ( 5 ) Kalker, Lewis, and Slc;ldams, "Principles of Chemical Engineering," 2nd ed., p. 680, McGraw-Hill, 1927. RECEIVEDNovember 18, 1932. Presented before t h e meeting of the American Institute of Chemical Engineers, Washington, D . C., December 6 t o 9, 1932.
Heat Flow through Bakery Products I. Time-Temperature Relationships Existing during t h e Baking of Bread LAWRENCE E. STOUT. ~ K DFREDDROSTEN, Washington University, St. Louis, &io.
T
Time-temperature relationships during the mental data in their study for b r e a d h a s become a baking of bread indicate that the baking operafion four k i n d s O f b r e a d a t o v e n temperatures of 230" C. highly specialized indusmay be divided into three general periods. S u m e r o u s other investigat r y , y e t it i s o n e w h i c h is First, there is a rapid rise in temperature Within tors have studied the baking of governed by empirical standards. the loaf. T h i s is followed by a progressipe debread, but t h e i r r e p o r t s seem Oven temperatures and time of subject to criticism as follows: baking are fixed by experience crease in rate of temperature rise which, in turn, B a l l a n d (1) used maximumand the Only test for "baked" precedes the third or final period of consfant temperature thermometers and load of bread is the physical aptemperature. During the Jirst two periods the f o u n d a recorded temperature pearance of the crust. From an rate of rise in femperature varies with the applied of 101" to 102" C. His work engineering standpoint it A T but during the third period the AT has no shows no time-temperature redoubtful that such control of the lationships. G i r a r d ( 2 ) theobaking operation can take care of effect upon the constant temperature registered. the possible variations in condirized concerning t h e w o r k of This third period must be at least 9 minutes long Balland but added no experitions that are likely to arise from lo insure a done loaf of bread. m e n t a l d a t a . M a l l e t t (3) time to time. It would seem that studied the baking of bread using a critical study of the baking of bread might disclose some time-temperature relationship that alum baking powders. Read (6) determined the temperatures attained, the rate of temperature change, and the points would insure a properly baked loaf as a finished product. The literature contains few complete experimental data of change for bread baked one hour in a n oven at 173" C. on the time-temperature relationships during the baking of These last-mentioned baking conditions do not conform to a loaf of bread under ccmmercial temperature conditions. usual oven temperatures, and the thermometers were inserted As previously mentioned, Platt (6) stated that the done loaf when the bread mas put into the oi-en. This means that t h e of bread attained a temperature of 100" C. Tenny ('7) dis- loaf was punctured just before baking and possibly does not cusses the cooling cf bread in a recently published article and represent a normal loaf of bread. Moreover, Read states gives cooling curves to show the time-temperature relation- that the literature contains nothing on the subject. ships existing when bread cools. These readings were obtained b y inserting a thermcmeter within the loaf of bread BAKISG TESTS immediately after its withdraval frcm the oven. He names The experimental attack on this problem consisted of 210' F. (98.9" C.) as the initial ccoling temperature. Keumann a n d Ealecker (4) approach completeness of experi- baking a large number of loaves of bread under controlled HE commercial baking of
'
April, 1933
INDUSTRIAL AND ENGINEERISG
experimental conditions and measuring the tiine-temperature relationships involved. The mix or formula was rigorously maintained as follows: Flour, 100 parts by weight; yeast, 1.56 parts by weight; salt, same; milk powder, same; malt,, same; water, 50 parts by weight. One and one-half pounds of dough nere allowed to rise for a period of 50 minutes at room temperature. It was then punched, allowed to stand 15 m i n u t e s (again at room temperature), and /oo m a d e up. T h e pan used was a standard individual type, 9 X 4 >: 3 i n c h e s (22.8 X 10.2 X 7.6 cm.). 30 Thermometers or thermccouples were i n s e r t e d at various places within the BO loaf at this time to eliminate the danger of "knocking down" the loaf. The b u l b of the thermometer 70 used to indicate the done point TTas p l a c e d in the . I exact center of the loaf, at an a n g l e s u c h t h a t t h e opposite end of the ther$ mometer rested upon the top side of one end of the pan. $50 ip After the proof had reached 80 per cent (of the b a k e d v o l u m e ) , the b r e a d was 40 baked at a constant oven t e m p e r a t u r e in a twoburner modified household o v e n t h a t had been fitted 3 1 7 with a suitable steam injector to give a good crust to the loaf of bread.
--.
$
8
4
/2
/6 20
29
The only e x p e r i m e n FIGURE 1. TIME-TEMPER.%TURE tal c o n d i t i o n that was CURVES FOR BREADB A K E D I N varied in this study rvas F.4ST OVEri the t e m p e r a t u r e of the oven. Preliminary trials indicated that the bread was not done until the temperature within the load had remained constant for a considerable period of time. It seemed advisable to determine whether this t'emperature was a constant, regardless of the oven temperature or whether the form of the curve in this region waslaltered by varying the applied differential temperahre. Gnufe5
TABLEI .
TIME-TEYPEKITCRE D \ T i F3R IS FASTOVES ,
TIME 41iTi
2 45
L ~ A V EBS~ K E D
c. 30 63 84 90 93 95 96 98 99 99 100 100 101 101 101 101 101 101 101 101 101
c'. 25 44
80 89 91 93 95 96 Si 98 99 100 101 101 101 101 101 101 101 101 101 101
The oven temperatures were varied from 200" to 250" C. The results obtained from ovens a t temperatures of 240" to 250" C. are typical of those for an oyen too hot to yield the best rewltc. The data listed in Table I are plotted in Figure 1.
429
These data indicate a rapid rise in temperature a t firat, then a gradual slowing down, and finally a long zone of no temperature change. The runs listed are those used to produce a done loaf. The operator was an experienced baker whose judgment was considered final in regard to the condition of the bread. Shorter baking times gave loads of bread incompletely baked inside. In each case the oven temperatures were too high to produce a good bake. The outside or crust began to burn before the inside of the loaf was conipletely baked. To go t o t h e other extreme, bread w a s b a k e d with oven temperat u r e s of 200" t o 210" C. The same g e n e r a l t y p e of curve w a s n o t e d , but the p i t c h was less steep. Marked defects were evident in each loaf baked. The crust of the loaf was too hard by the time the i n s i d e of the loaf was baked. The data in Table 11, shown graphically i n F i g u r e 2, are t y p i c a l of this temperature range. Experiments showed that, when o v e n temperatures of 205" and 210°C. T e r e u s e d , the inFIGURE 2. T I M E - T E M P E R I T U R E qide was not done CURIESFOR B R E 4 D B.~KED IV SLOW o\ E\ until the temperature had remained a t 100" C. for 9 minutes. With a n oven temperature of 200" C. the lag occurred a t 99" C., but after 12 minutes the loaf teqted done on the inqide. TABLE11. 'LIME-TEMPERITURE DATAF O R BAKEDIS SLOWOVEX T E S i P . ISIDE
TEMP.1.NSIDE L O ~ nFI T H Or IlS iT: 2.500 c. ?40° C 245' C.
c.
CHEXTISTRY
TIME JI1n.
0 2 4 5 6
7 8 9 10 11 12 13
c. c.
2100
23 25 33 40 56 71
ii
82 85 88 90
ie
15 16
17 18 19 20 21 22
23 24 25 26
27 2s 29 30 31 32
99 99 99
R-. R
100 100 100 100 100 100 100
out
LO.4YEs
L O ~ WFI T H O V E NAT:
c. c.
2050
22 24 29 36 44 58
68 76 82 85 88
R.. O
92 94 96 9i 98 98 99 99 99 99 QQ 100 100 100 100 100 100 100 100 Out
... ...
2000
c
c. 20 21 23 -.
26 30 36 53 68 77 83 87 4n 92 94 95 96 97 98 98 98 98 98 98 99 99 99 99 99 99 99 99 99 99 Out
_ I
1 >X I) I1 S'l' II 1 A I ,
430
A X 1)
E N G 1 N E 13 II I N G C I1E hf IS T I{ Y
Table 111, illustrated in Figiirc 3, sliows tlie time-temperature relationships which exist witliin a loaf of bread during baking in a n oven of moderate temperature. These data differ little from those previously given; the general shape of the cnrves is the same, differilig only as to pitch. EXD& nients a g a i n s h o w e d t h a t a m i n i m u m of 0 minutes a t 100" C. was ncceasary to prodnee n d o n e loaf of brcarl. pio s e r i o u s trouble resulted if this time were extended to 12 minutes. Ta.ken as a w h o l e , these d a t a w a r r a n t certain generalizations. In the first place, the oven temperature sfiould be such that a constant temperature of 100" C. c a n b e maintained within thc loaf of bread for 9 to 12 m i n u t e s before the c r u s t is b u r n e d or becomes too hard. Yllorter periods of bakiiig do not yield done loaves of bread. These Pi?"u/e.. finding5 a u g m e n t the FIGURE 3. T~XE-TEMIPEHATURR CURVESFOR B n ~ mBAKEDfly r c s u l t s of previorrs MODERATE OVEN workers who reported maximum temneratures attained. To state only this figure is, a t best, misleading to the layman. It is true that no h i g h temperature need be attained, hut tile iIlside of the loaf of bread must have reached that temperatureat least 9 minutes before the loaf can be declared done. Moreover, the lag in the temperature curve a t this point-in some cases lasting as long as 12 minutes-makes it difficult to picture tho loaf as being in other than a state of equilibrium. Finally, the general experimental results fit in with our known laws of flow of heat. Higher differentialtemperatures increase the rate of heat flow, giving curves of steeper pitch. However, in each case, the temperature relationships indicate a point where some definite endothermic reaction occurs. At this point the magnitude of the differential temperature seems to exert little effect upon the time-temperature relationships within the system.
TANLE
1x1.
VOI.
'rIMB-TEMPEEATUIm D A T A TOR IN hfODE2LbTE OVES
B.4KED TiAll;
xin 0 2 4
5
6 7
TEMP.INSIDS 1,nrr 2
w 0
c.
c.
?7 32 60 80 83
c.
0
27
33 50
0s
77 83 87
9
87 89 90
111 11
o2
12
sa
oa
95 96 87
95 90 97 98
x
13 14
I:,
OX
16
9!1 99 91
17 18 IS
a0 21
22 23 24 25 26 27 28 29 30
0') 100 100 100 I00 100
100
Out
...
... ...
...
WITX
c.
2~
89
*a
99
99
99 99 100
100 100 100 100 100 io0
Out
... ... ...
25, No. 4
LOAVES
OVFWAT:
215' C
" C. 28 20 40 58 09
78 82 85
88 90 92 '33 94
95 90
97 98 99
99 95
100 100
ion
100 100 100 100 101 Out
Co;ucLnsIO.Ys 1. The time-temperature curves for brer rrinc! bi :ing show a fast rise for tile first 10 minutes, a slow rise for-the next 10 minutes, and a practically constant temperature for the last 9 to 12 minutes of the baking cycle. 2. Under the experimental conditions listed, the inside temperature of a loaf of bread during baking does not exceed 100" to 101" c. 3. Under the experimental conditions listed, this temperature must have been maintained for a t least a period of 9 minutes to Droduee a done loaf of bread. ACKNOWLEDGMENT The authors are indebted to Charles 1,. Faust, University of Minnesota, for verifying certain of the references listed in this Paper. LITERATUHE CITBD (1) Balland, Compl. rend., 117. 519 (1893). (a) Girard, Zhid., 117, 684 (18V8). (3) Mallctt, Chem. Nnus. 1888, 1515-16. (4) Noumann and Saleoker. 17. ges. Gelmidew., 1.41-3 (1909). ( 5 ) Platt. Cered Chom.. 7, 1 (1930). (6) Road, Zowa A d . Sd..37, 231 (1930). (7) Tenny, B a k e d Helper, 57, 324 (1932). Rscrrvsu A w w t 20, 1932. Prssantsd before the Division of Induatrial and Engineering Chemistry st the 84th Meeting of the American Cbemioal Suoiety, Denvsr. Colo.. August 22 to 2%. 1932.
AIIWL~ ON
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