296 Bulletin UASVM Agriculture, 66 (2)/2009
Print ISSN 1843-5246; Electronic ISSN 1843-5386
The Theoretical Preliminary of the Mathematical Modeling in the Bread Baking
Adriana-Paula DAVID1, N. BURNETE2, Al. NAGHIU1
1 University of Agriculture Science and Veterinary Medicine, 3-5 Mãnãstur Street, 400372 Cluj- Napoca, Romania, e-mail: dayadavid2003@yahoo.com
2 Technical University of Cluj-Napoca, Romania
Abstract. The industrial practice in bread making is to bake bread in an oven that is controlled at a constant temperature. Due to the oven structure, the bread effectively experiences four major temperature zones. On the other hand, temperature in each zone is the dominating factor on the baking mechanisms including gelatinisation, enzymatic reaction and browning reaction, therefore the final bread quality. This research aims to establish an optimal temperature profile for white-sandwich bread to achieve the best product quality. Experiments were conducted by a multi-level partial factorial design, where dough was baked in a process with 4 equally divided zones. Mathematical models were established to describe the effects of tin temperature and baking time in bread quality attributes
Keywords: bread baking; modelling; optimisation; temperature.
INTRODUCTION
In the bread making, baking is a important step in which the raw dough piece is transformed into a porous, light, digestible and flavourful product, under the influence of heat.
With the requisite quality attributes in the bread production presumes a carefully controlled baking process. The key influence on final product quality includes the rate and amount of heat application, the humidity level in the baking chamber and baking time. During baking, the most apparent interactions are: crust formation, volume expansion, inactivation of yeast and enzymatic activities, protein coagulation and partial gelatinisation of starch in the dough [2].
A typical baking process can be divided into 3 stages:
- The first stage takes one-fourth of a total baking time of 26 min. The temperature of outer crumb increases at an average rate of 4 - 7 °C per minute to 60 °C. An increase in temperature enhances enzymatic activity and yeast growth resulting in oven rise. The volume increases by one-third of the original. Furthermore, surface skin loses elasticity, thickens and begins to appear brown in colour.
- In the second stage the crumb temperature increases at a rate of 5,5 °C per minute to 98 – 99 °C before remaining constant. At this temperature, all reactions are maximized velocity, including moisture evaporation, starch gelatinisation, and protein coagulation.
Dough becomes crumb in structure from outer to inner portions by penetrating heat. A typical browning crust can be observed when crust temperature ar 150°C.
- Finally, the volatilisation of organic substances is designated as the bake-out-loss.
This is because crust colour is actually developed by Maillard reaction at around 150–205 °C This period also takes one-fourth of the total baking time [3].
The common industrial practice is to bake bread in an oven that is controlled at a constant temperature. On the other hand, temperature in each zone is the dominating factor on the baking mechanisms including gelatinisation, enzymatic reaction and browning reaction,
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therefore the final bread quality. This paper aims to establish to describe the effect of baking temperature and time on the bread quality attributes including crust colour, crumb temperature and weight loss. The temperature profile and baking time are then optimised to minimise weight loss, using the models developed.
The experiment was designed by a 35 partial factorial. The five independent variables were temperatures in zone 1, zone 2, zone 3, and zone 4, and baking time. The dependent variables included weight loss, top crust colour, side crust colour, bottom crust colour, average crust colour, and crumb temperature. The total baking time was equally distributed to the four zones during baking.
Bread: Dough was prepared in batches. Six pieces of dough were made in each batch, composing for 1 kg final bread dought: of 595 g flour, 18 g yeast, 12 g salt, 12 g fat, and 363 g water. They were placed in an array of moulds and baked in an oven under one set of designated conditions.
Oven was set up at different conditions covering tin temperature from 180 to 210 °C, airflow velocity from 0 to 1.8 m/s, and baking time from 22 to 30 min. To simulate the four spatial zones in an industrial oven, during each experiment, four stages of the oven conditions were set up sequentially and the baking time for each stage was the same.
Temperature was monitored during baking as shown in fig. 1, tin temperature was measured on the lid, side and bottom of the mould, and crumb temperature was measured at 53 mm from the lid.
Fig. 1. Measuring positions for top (1), side (2), bottom (3) and internal (4) temperatures during baking.
Moisture loss was calculated by the weight difference between the dough and bread.
Crust colour is an important attribute of bread, contributing to consumer preference. It is produced by chemical reactions including Maillard reaction and caramelisation. Bread crust is measured by a CR-310 colorimeter with L–a–b system. The response was expressed as the lightness of crust colour. The acceptable top and side of bread is in the table 1. It is worth to note that the darker the colour, the lower the corresponding value.
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Tab. 1 Value of crust colours
Parameters Scale [points] Colorimeter value
Top crust colour 50 – 60 50 – 60
Side crust colour 60 – 72 60 – 72
Bottom crust colour 54 – 62 54 – 62
Average crust colour 53 – 65 53 – 65
Fig. 2. Measuring positions for crust colour. A: top, B: side, C: bottom. Average crust colour=(A+B+C)/3.
During each experiment, oven conditions were set up to generate different tin temperature profiles including top, side and bottom temperatures. Typical temperature profiles are shown in fig. 3.
The profiles were generated by adjusting the oven temperature settings. In addition, with the same adjustment of the oven settings temperature, different airflow velocity would produce different tin temperature profiles because of its effect on heat transfer. The average value of the measured temperatures in each zone was then calculated, which was used as a modelling parameter later. Tab. 2 shows several temperature profiles with the corresponding oven conditions.
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Fig. 3 Typical temperature profiles. (1) bottom temperature, (2) top temperature, (3) side temperature, (4) averaged bottom temperature, (5) averaged top temperature, (6) averaged side temperature.
Tab. 1.
Examples of oven conditions and temperature profiles Example Zone Baking time
[min]
Temperature [ oC]
Air velocity [m/s]
Temperature average [ oC] T/S/B
I 1 6 180 0 105/80/101
2 6 180 0 123/113/136
3 6 180 0 151/141/164
4 6 180 0 164/155/174
II 2 6,5 195 0,8/0,4 143/115/142
3 6,5 195 0,8/0,4 160/149/172
4 6,5 195 0,8/0,4 170/158/179
5 6,5 195 0,8/0,4 175/163/182
III 1 6,0 210 1,8/1,6 147/130/154
2 6,0 180 0 156/143/168
3 6,0 210 1,8/1,6 162/154/172
4 6,0 180 0 176/168/187
IV 1 7 210 1,8/1,6 168/137/165
2 7 210 1,8/1,6 187/170/188
3 7 210 1,8/1,6 194/177/192
4 7 210 1,8/1,6 199/183/196
V 1 7 180 0 125/96/109
2 7 210 1,8/1,6 152/148/158
3 7 210 1,8/1,6 162/155/163
4 7 180 0 170/161/168
It was observed that the side tin temperature was always lower than the top and bottom tin temperatures. This is because of the physical shape of the moulds. There was a small gap between any two neighboring moulds, which affected the circulation of hot air and therefore
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created a relatively cold spot. The bottom tin temperature was generally the highest because the distance between the moulds and the bottom heating element/convective fan was shorter than the distance between the moulds and the top heating element/convective fan. However normally the top and bottom temperatures were not significantly different. This is because that the lid was pre-heated before being placed on the moulds, as a result, the initial top tin temperature was high.
Different tin temperature profiles produced various crumb temperature profiles, which resulted in different rates of mass transfer and thermal reactions including browning reaction, gelatinisation and enzymatic reaction, therefore the variations in bread quality.
REFERENCES
1. Auerman, L. J. (1977). Technologie der Brotherstellung. , VEB Fachbuchverlag, Leipzig.
2. Pyler E. J. (1988). Baking science & technology, Vol. II (3rd ed.), Sosland Publishing Company, Merriam.
3. Swortfiguer M. J. (1968). Dough absorption and moisture retention in bread. Baker Digest 42 4 (1968), pp. 42–44.
