Effect of Baking Powder in Wheat Flour Dough on Its Thermal Conduction during

Transcription

1 Food Sci. Technol. Res., 5 (), 7, 009 Effect of Baking Powder in Wheat Flour Dough on Its Thermal Conduction during Heating Tamako mizu and Keiko nagao * Tokyo Kasei University, Faculty of Home Economics, Itabashi-ku, Tokyo 7-860, Japan Received May 7, 008; Accepted January 0, 009 To understand the puffing phenomenon of wheat flour dough, the effect of baking powder (BP) on thermal-physical properties during heating was investigated. The effect of BP on the thermo-physical properties including thermal conductivity, heat capacity, and thermal diffusivity, was evaluated at 0 min after preparing dough samples with or without BP at 0, 0, 60 and 80. The increasing velocity of the temperature in the samples with BP during heating was higher than that in the samples without BP. Thermal conductivity in each sample correlated with the retardation phenomenon irrespective of the presence of BP, while the increasing velocity of the temperature along the x-axis of the samples with BP was higher than that of the samples without BP. Thermal conductivity of the samples irrespective of the presence of BP tended to increase, as the temperature and moisture increased. Thermal diffusivity based on the values of thermal conductivity, heat capacity and density greatly increased with increasing temperature and moisture content of the samples with BP, which is essential for the puffing phenomenon in the baking of bread. Keywords: wheat flour dough, baking powder, puffing phenomenon, thermal conductivity, thermal diffusivity, retardation time Introduction Heating used in cooking plays a significant role in improving digestive efficiency and taste and textural characteristics of food (Nagao et al., 997). Quantitative analysis of thermal conductivity in foods has proven difficult due to constitutional and operational complexities. That is, foods are comprised of thermo-sensitive biological components such as carbohydrates, proteins, lipids, a small amount of vitamins, and minerals. They mainly exist in aqueous complex systems as solutes or dispersed phases in a variety of aqueous media. There are also many methods of heating with different heat transfer media such as boiling, steaming, baking, and frying. We have previously devised a series of food models to address these varying constituents in foods (Nagao and Matsumoto, 999). Food models can be used to characterize the dispersion of a solid phase in a suspending fluid, i.e., a dispersion of mixture of equal amounts of pure cocoa *To whom correspondence should be addressed. nagao@tokyo-kasei.ac.jp powder and soft wheat flour in the form of a solid phase in a suspending fluid consisting of a mixture of water and corn oil. Using these models, moisture content ranging from about 7-50 wt% can be controlled without altering the original shape of the food during preparation. Two different types of heating devices have been reported to measure the increasing temperature in a food along the one-dimensional axis (x axis) up to 0 mm from the heating plane (x = 0) during heating (Nagao and Matsumoto, 00 and 00). The pan broiling method uses one of these devices that can detect changes in temperature in any type of food (solid, paste and even liquid states) during heating in a metal vessel. The other devise directly measures changes in temperature in solid- or semi-solid-type foods during heating using a variety of heat transfer media such as cooking oil in frying, water in boiling, vapor in steaming, and hot air in baking. Using this second method, the relationship between the increasing temperature of a sample and heating time can be explained simply by a retardation phenomenon with a time constant instead of the classical error function for the thermal conduction of food (Nagao and Matsumoto, 00 and 00). This retardation

2 8 phenomenon has been recognized widely for its significant role in thermal conduction in foods, as well as in emulsion systems (Nagao, 00; Fujii and Nagao, 00; Kita and Nagao, 005; Nagao and Kita, 006; Nagao, 007; Mizu and Nagao, 007, 008a and 008b). Heating used in cooking causes components within the food to undergo a variety of phase transitions (Nagao, 00), such as melting of fats, sol transition of hydro gels, thermal denaturalization of proteins, and gelatinization of polysaccharide. Moreover, heating can increase the total volume of the food during cooking, the so-called puffing phenomenon, as in the case of breads, sponge cakes, and pan cakes. Recently, baking powder (BP) has been investigated for its effects on thermal conduction in a series of wheat flour dough. Thermal conductivity, heat capacity and thermal diffusivity of a variety of wheat flour dough with or without BP 0 min after preparation at 0, 0, 60 and 80 have also been compared. The 0-min waiting time following dough preparation corresponded to the steady state at these temperatures. Here, thermal properties of the samples were examined in detail, and the retardation phenomenon occurring during thermal conduction along the x-axis of the samples was analyzed. Experimental Materials A series of wheat flour dough containing different amounts of corn oil (0, 6.,., 0.0,., and to 7.7 wt%) was used in this study (Table ). The samples were prepared with or without BP. The wheat flour was commercially available weak flour (Nisshin Flour Milling Co., Tokyo, Japan). The commercially available corn oil (Ajinomoto Co., Tokyo, Japan) was employed as the liquid phase in combination with water. BP (Aikoku Sangyo Co., Tokyo, Japan) was purchased from a local market. Preparation of the dough samples The combination of pure water and corn oil forms the liquid phase before the addition of wheat flour. Water and corn oil in the liquid phase appeared as an emulsion, most likely due to the role of gluten in the wheat flour on surface activity. Six types of wheat flour dough containing different amounts of corn oil were prepared as follows (Table ). The liquid phase containing a fixed amount of pure water and corn oil was mixed in a bowl, T. mizu & K. Nagao followed by the addition of a fixed amount of wheat flour with or without wt% BP (solid phase). The mixture was kneaded about ninety times by hand and allowed to stand for 0 min at 0, 0, 60 and 80 before analysis. All samples remained in a steady state at each temperature during the waiting time. As BP generates CO in the presence of water even at room temperature, the volume of the samples containing BP was increased slightly during the 0-min waiting time at 0. Thermal conductivity A previously reported device(nagao and Matsumoto, 999) was used to measure thermal conductivity (λ [W m - K - ]) of the samples based on the correlative technique (Matsumoto, 975) using a 5.95-mm thick polycarbonate disk (x p ) as a reference for thermal conductivity λ p (0.0 W m - K - ); this polymer is stable for heating up to about 60. The details of the apparatus and the method for evaluating the value of thermal conductivity of each sample λ S has been described precisely (Nagao and Matsumoto, 999). Briefly, the effective thermal conductivity of the samples λ was evaluated by the correlative method under the stationary heat flux, i.e., a 5 temperature gradient in this study, with thermal conductivity λ p for the polycarbonate disk. The values of λ for a sample are calculated using the following equation: λ = λ p (T H T M ) x s / (T M T L ) x p () where T H, T M and T L are the temperatures at the heating source, at the interface between the polycarbonate and the sample, and at the heat trap, respectively, and x s and x p are the thickness of the sample and the polycarbonate disk, respectively. Heat capacity at constant pressure Cp A water calorimeter was used for measuring heat capacity at constant pressure C p of the samples. The water calorimeter consisted of a 600-ml metallic Dewar flask, an adiabatic box, and two sets of thermocouples for detecting the temperature of the sample (T s ) and water (T w ). When the sample (m s, kg in weight) at a temperature of T s is immersed instantaneously in water (m w ) at a temperature of T w (T s > T w ), an equilibrium (θ) is expected to be obtained by either the temperature after a certain amount of time due to heating from the sample or cooling from the water, according to the following equation: Table. Composition of wheat flour dough. Water (wt%) Liquid phase oil (wt%) Solid phase a) Wheat flour (wt%) Total amount of moisture b) (wt%) a) Solid phase in the model including % baking powder in the wheat flour. b) Total amount of moisture in the model including % water in the wheat flour.

3 Effect of Baking Powder C pw (m w + w) (θ T w ) = C p m s (T s θ) () where C pw is the heat capacity of water at constant pressure and w is the water equivalent of the water calorimeter. The value for C pw has already been determined to be 80 J kg - K - at around room temperature, while w has been evaluated experimentally to be 0.0 kg in a range of temperature from 0 to 80 in this study. Thus, the heat capacity of each sample C p at constant pressure can be calculated as follows. C p = 80 (m w + 0.0) (θ T w ) / m s (T s θ) [J kg - K - ] () Density and rate of volume expansion To evaluate the thermal diffusivity α for the series of samples, the density ρ [kg m - ] of each sample at temperatures of 0, 0, 60 and 80 was measured using a Hubbard-type specific gravity bottle (Daniels et al., 9). As α is generally influenced by the heat expansion of the corresponding matter (Sugiyama, 998; Sugiyama and Shibukawa, 998), the rate of volume expansion K* [K - ] is determined as: K* = ( / v o ) ( v / T) () where v o is the volume of the sample before heating and v is that at temperature T under constant pressure. Thermal conduction during heating Changes in temperature along the one-dimensional axis from the heating plane of all the samples were determined during heating using a pan broiling-type heating device (Fig. ), as described precisely (Nagao and Matsumoto, 00; Nagao, 00). The device consists of a cylindrical brass vessel for holding the sample, a set of thermocouples (Anritsu, type K;.0 mm in diameter) fixed to the brass lid for detecting the temperature at six locations along the one-dimensional axis at 0,, 5, 7, and 0 mm from the bottom of the vessel, and a heating device comprised of a cylindrical thermo-jacket connected to a circulating pump and thermo-regulated bath of silicon oil (Haake, type ). Each sample was heated through the bottom plate of the vessel at 05. Each freshly prepared sample (~ 0 g) was molded to provide a columnar shape of 0 mm in diameter, so that the area of the heating plane at the bottom and the height were 50 mm and about mm, respectively. Each molded sample was placed in the vessel after wrapping the curved surface in an adiabatic sheet, and the lid carrying the set of thermocouples was then placed on the vessel to define the location of each thermocouple along the x-axis of the sample. The vessel was finally placed on the thermo-jacket and heated steadily at 05. For comparison of the changes in temperature, all locations were measured at the same time with the set of thermocouples using a data collector (Anritsu, type AM-700) that recorded the temperature as a function of time during heating. Results and Discussion Heating pattern of the samples Heating patterns obtained for wheat flour dough using the previously reported pan broiling-type device, shown in Fig. (Nagao and Matsumoto, 00, 00 and 005; Nagao, 00), clearly shows a correlation between the heating time and the temperatures at different locations in the sample (0,,, 5, 7, and 0 mm). Figure shows the heating pattern of a sample with 5 wt% moisture using dimensionless temperature ϕ(t), which is defined as ϕ(t) = (T t T o ) / (T T o ) (5) where T o, T t and T mean the temperature at t = 0, t > 0 and t =, respectively. Temperature T was 00 at all locations along the x-axis in each sample. Irrespective of the presence of BP, the heating patterns for all the samples conformed to an exponential equation with the assumption that the retardation phenomenon plays a role in thermal conduction in solidor semi-solid-type food (Nagao and Matsumoto, 00, 00 and 005). That is, the dimensionless temperature of all the samples ϕ(t) at heating time t can be defined as follows: ϕ(t) = exp[ t / τ(x)] (6) where τ(x) is the retardation time in the thermal conduction process at location x in the sample. Retardation time τ(x) in equation 6 corresponds to the time when the temperature ϕ(t) at location x in the sample reaches a value of (= /e). : Lid carrying a set of thermacouples : Sample cell : Sample to be tested : Adiabatic sheet 5 : Heating device 9 Fig.. Schematic diagram of the heating device for detecting temperature along the one-dimensional axis (x-axis).

4 0 T. mizu & K. Nagao Figure clearly shows that the increasing temperature of the sample with BP is higher than that without BP irrespective of the moisture content in the sample. Thus, the dynamic puffing phenomenon of the dough samples may play a role in accelerating thermal conduction. Effect of BP on the thermo-physical properties of wheat flour dough Thermal conductivity Thermal conductivity λ of all the samples was measured 0 min after preparation. The samples with BP at 0 and 0 already began the puffing phenomenon during the 0-min waiting time (Fig. ). While the value λ increases with increasing moisture content for all samples, the presence of BP effectively lowers this value for samples with moisture contents from wt% prepared at 0 and 0. On the other hand, the moisture-dependent λ of each sample with BP at 60 or 80 was quite similar to those without BP (Fig. ). Thermal conductivity of air bubbled gels increases as the amount of air in these gels increases (Sakiyama and Yano, 990, 99 and 999). In the wheat flour dough samples of this study, however, the moisture dependence of their thermal conductivity is not surprising, as thermal conductivity of water is generally higher than that of the other food components. Heat capacity at constant pressure Figure compares the effect of the presence of BP in the series of wheat flour dough samples relative to the heat capacity C p and the moisture content. The value of C p for the samples without BP decreased with increasing temperature, while this temperature dependency of C p for the samples with BP was pronounced between 0 and about 60. Thus, heat capacity appears to be related to the reconstruction of the macroscopic structure (texture) around the temperature of the sample in the presence of BP. Density and the rate of volume expansion The puffing phenomenon due to the presence of BP was clearly exhibited by comparing temperature dependence of density ρ of samples with and without BP (Fig. 5). That is, the occurrence of carbonic gas (CO ) in samples with BP was associated with lower ρ at 0 60 and at increasing moisture content. The rate of volume expansion K increased with increasing temperature and moisture content due to the effect of puffing phenomenon (Table ). Thermal diffusivity An important factor in the heat transport phenomenon is characterized by the thermal diffu-.0.0 Dimensionless temperatureφ(t ) Dimensionless temperatureφ(t ) Heating time [ s ] Heating time [ s ] 600 Fig.. Comparison of the increasing curves of temperature φ(t) detected at 0,,, 5, 7, and 0 mm along the x-axis of flour dough containing 5% moisture Thermal conductivity λ [W m - K - ] Thermal conductivity λ [W m - K - ] Fig.. Relationship between moisture content and thermal conductivity of wheat flour dough with and without baking powder at different temperatures. (n = 5).

5 Effect of Baking Powder Heat capacity C p [kj kg - K - ] Heat capacity C p [kj kg - K - ] Fig.. Relationship between moisture content and heat capacity of wheat flour dough with and without baking powder at different temperatures. (n = 5). The increase in thermal diffusivity was significant at temperatures 0 80 at 0% moisture content... Density ρ [ kg m - ] Density ρ [ kg m - ] Fig. 5. Comparison between effects of moisture content on density of wheat flour dough with and without baking powder at different temperatures. (n = 5; p < 0.00). Table. Effect of moisture content on the expansion rate of wheat flour dough with and without baking powder at different temperatures. Moisture content Temperature [ ] (wt%) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± wheat flour dough a) with BP Moisture content Temperature [ ] (wt%) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± The moisture content was calculated from the moisture of the liquid and solid phases in Table. a) Values in the same row between 0 and 0-60 are significantly different at p < Values in the same column between wt% and.7-. wt% are significantly different at p < 0.00.

6 T. mizu & K. Nagao 6 6 Thermal diffusivity α [m s - ] Thermal diffusivity α [m s - ] Fig. 6. Relationship between moisture content and thermal diffusivity of wheat flour dough with and without baking powder at different temperatures. (n = 5). Table. Reciprocal of retardation time at different locations and moisture content of each sample. Moisture content [/τ (x)] 0 - [s - ] (wt%) 0(mm) (mm) (mm) 5(mm) 7(mm) 0(mm) ± ± ± ± ± ± ± 0..8 ± ± ± ± ± ± ± ± ± ± ± ± 7.6 ± 0.0. ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Moisture content [/τ (x)] 0 - [s - ] (wt%) 0(mm) (mm) (mm) 5(mm) 7(mm) 0(mm) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.00 sivity α in the following equation, α = λ / C p ρ (7) where λ is the thermal conductivity, C p is the heat capacity at constant pressure, and ρ is the density of the sample, respectively. Thus, the value of α is determined based on the sample characteristics. Figure 6 compares the effect of BP with thermal diffusivity α of all samples at different temperatures and moisture contents. The values of α for samples with BP significantly is affected by the moisture content at temperatures higher than 0 (Fig. 6). On the basis of equation 7, α as a significant factor in the cooking process appears to be influenced by thermal conductivity λ, heat capacity C p, and density ρ of the sample. In fact, this study shows that heat capacity and density of samples with BP significantly affected thermal diffusivity (Figs. and 5). Thus, the puffing phenomenon in the samples due to BP may occur from the presence of CO even at temperatures around 0, leading to the decrease in density ρ (Fig. 5). Retardation time of dough samples Equation 6 suggests that the increasing rate of temperature ϕ(t) is dominated by the time constant τ(x) that controls the speed of heating at location x in the food heated, so that the constant τ(x) represents the retardation time. The retardation time can be determined from the experimental results of increasing temperature in the samples during heating, e.g., correlation between the dimensionless temperature ϕ(t) and the heating time t (Fig. ). Thus, the retardation time τ(x) at location x in the sample was evaluated when ϕ(t) is (= /e). Table summarized the reciprocal values of the retardation time /τ(x) evaluated from the experimental results. The results indicate that the presence of BP in the samples accelerates the increasing temperature at each location along the x-axis during heating due to the puffing phenomenon. Correlation between thermal diffusivity and retardation time Thermal diffusivity α plays a significant role in trans-

7 Effect of Baking Powder Reciprocal of the time constant S /τ(ⅹ) [m s ] % 5.0% 9.%.7% 6.% 0.% r = Thermal diffusivity α [m s - ] 0-7 Reciprocal of the time constant S /τ(ⅹ) [m s ] % 5.0% 9.%.7% 6.% 0.% r = Thermal diffusivity α [m s - ] 0-7 ; ; Fig. 7. Correlation between the double logarithmic plots of the reciprocal of the time constant and thermal diffusivity α at 60. (r, correlation coefficient; S is the area of the heating plane ( m ). The amount of moisture in the liquid and solid phases shown in Table (wt%). port of thermal energy and tends to increase with increasing moisture content in foods. The experimental results obtained in this study also indicate that the rate of increasing temperature ϕ(t) of each sample is not only accelerated by an increase in moisture content but also greatly influenced by the presence of BP due to the puffing phenomenon. Plotting α against /τ(x) with double logarithmic coordinates shows a linear relationship for all heating methods and all samples with and without BP (Fig. 7). These support previous reports on a variety of foods using various heating methods (Nagao and Matsumoto, 00 and 005). Therefore, the following empirical equation was obtained: S / τ(x) = k α n (8) where S is the area of the heating plane ( m ), k is the coefficient and n is the power coefficient of thermal diffusivity α. Plotting /τ(x) against α confirmed that the presence of BP in the samples lowers the gradient in the relationship between α and /τ(x). An example of the effect of BP at a fixed location (x = mm) is shown in Fig. 7. Conclusion The puffing phenomenon is widely applied in cooking using a variety of chemicals or ferment fungi, which results in the expansion of the volume of the food during heating. Thus, the effect of the puffing phenomenon on the parameters of thermal transport phenomena was compared between two different types of the wheat flour dough, one with wt% BP and the other without BP. Thermal conduction in the wheat flour dough was adequately characterized by the retardation phenomenon irrespective of the presence of BP; the increasing velocity of the dimensionless temperature ϕ(t) along the x-axis in the samples with BP was higher than that without BP during heating. Thus, higher values in the reciprocal of retardation time /τ(x) were obtained for samples with BP. The physical parameters for wheat flour dough irrespective of the presence of BP, including thermal conductivity λ, heat capacity at constant pressure C p, density ρ and thermal diffusivity α (= λ / C p ρ), were determined experimentally after a 0-min waiting time at different temperatures. The waiting time of 0 min corresponded to a steady state of the dough for the puffing phenomenon due to BP. The effect of the puffing phenomenon was pronounced in the values of thermal diffusivity α, that is, the value of α of the samples with BP increased with increasing temperature and with moisture content. The plot of the thermal diffusivity relative to the reciprocal retardation time /τ(x) on the double logarithmic coordinates was consistent with that obtained in previous studies. Nomenclature C P - heat capacity at constant pressure, kj kg - K λ S - thermal conductivity of sample, W m - K λ P - thermal conductivity of polycarbonate, W m - K x P thickness of polycarbonate, mm x S thickness of sample, mm T H temperature of the heat source, K T M temperature of the interface between the reference and sample, K T L temperature of the heat trap, K T w temperature of water, K T S temperature of the sample, K m w weight of water, kg m S weight of sample, kg θ temperature when T w and T S reached an equilibrium, K

8 ρ density, kg m - m weight of sample at the set temperature, kg V volume of sample at the set temperature, m v volume of sample at constant pressure at temperature T, m v o volume of the sample before heating, m ϕ(t) dimensionless temperature of the sample at heating time t t time, s τ(x) time when temperature ϕ(t) at each location x reaches the value of (= /e, where e is the base of natural logarithm) τ(x) time constant (retardation time) S area of the heating plane, m k coefficient n power coefficient of thermal diffusivity α - α thermal diffusivity, m s References Daniels, F., Mathews, H., and Williams, J. W., (9) Experimental Physical Chemistry, rd Edition, McGraw-Hill, New York, pp.-5. Fujii, S. and Nagao, K. (00), Heat Transfer Characteristics of Food Models Prepared from Wheat Starch, J. Cookery Sci. Jpn., 7,8-9 (in Japanese). Kita, N. and Nagao, K. (005), Role of Pure Cocoa as a Food Model for Heating-Thermal Properties and Amphiphilic Capacity-, J. Home Econ. Jpn., 56, (in Japanese). Matsumoto, S. (975), Subject in Quality Control of Food as the Polyphase Systems in Food Physics: Vol., Ed. by Matsumoto, S. and Yamano, M., Shokuhin Shizai Kenkyukai, Tokyo, pp-6 (in Japanese). Mizu, T. and Nagao, K. (007), Measurement of Thermal Conduction in a Series of Oil-in-Water Emulsions Prepared with Egg Yolk during Heating in a Metal Vessel, J. Home Econ. Jpn., 58, (in Japanese). Mizu, T. and Nagao, K. (008a), An Attempt at Measuring Thermal Conduction in O/W and W/O Emulsions Prepared by Use of Edible type Emulsifiers during Heating, Nippon Shokuhin KagakubKogaku Kaishi, 55, 5- (in Japanese). Mizu, T. and Nagao, K. (008b), Effect of Oil Globule Size in the O/W Edible Emulsions on the Thermal Conduction during Heating Procedure, J. Cookery Sci. Jpn.,, 7- (in Japanese). Nagao, K. (00), Changes in Thermal Conduction and Mechanical Properties of Foodstuffs Accompanying Phase Transitions during heating, J. Home Econ. Jpn., 55, 87-8 (in Japanese). Nagao, K. (007), Occurrence of Macroscopic Changes Foodstuffs Due to the Thermal Conduction during a Variety of Heating Procedures, J. Home Econ. Jpn., 58, 5-55 (in Japanese). T. mizu & K. Nagao Nagao, K. and Fujii, S. (00), Effect of Moisture Content and Temperature on the Mechanical Properties of Food Models for Examining Thermal Conduction, J. Home Econ. Jpn., 55, (in Japanese). Nagao, K. and Fujii, S. (005), Changes in the Macro-and Microscopic States of Starch Granule-in-Water Systems during the Process of Gelatinization, J. Cookery Sci. Jpn., 8, 5-50 (in Japanese). Nagao, K., Hatae, K., Shimada, A. (997).Occurrence of Ruptures on the Surface of Foods during Frying, J. Texture Studies, 8, 7-6. Nagao, K. and Kita, N. (006), Effect of Thermo-Insensitive Ingredients on the Thermal Conduction of Foodstuffs during, J. Home Econ. Jpn., 57, 9-7 (in Japanese). Nagao, K. and Matsumoto, S. (999), Preparation of Food Models for Examining Heat Transfer in Cooking under the Control of Moisture, J. Cookery Sci., Jpn.,, 0-7. Nagao, K. and Matsumoto, S.(00).Thermal Conduction Along by the One-Dimensional Axis in Food-Stuffs during Heating in a Metal Vessel, J. Home Econ. Jpn., 5, -9. Nagao, K. and Matsumoto, S. (00), Detection of the Thermal Conduction Induced Close by the Heating Plane in Food-Stuffs during Different Procedures of Heating, J. Home Econ. Jpn., 5, 6-6. Nagao, K. and Matsumoto, S. (005), Retardation Phenomenon Applied to the Thermal Conduction in Foodstuffs during a Variety of Heating Procedures, Nihon Reoroji Gakkaishi,, Sakiyama, T. and Yano, T., (990), Effects of Air and Water Contents on the Effective Thermal Conductivity of Air impregnated Gels, Agric. Biol. Chem., 5, Sakiyama, T. and Yano, T., (99), Temperature Dependence of the Effective Thermal Conductivity of Food Gels Impregnated with Air Bubbles, J. Chem. Eng. Jpn., 7, Sakiyama, T., Akutsu, M., Miyawaki, O., Yano, T., (999), Effective Thermal Diffusivity of Food Gels Impregnated with Air Bubbles, J. Food Eng., 9, -8. Sugiyama, K., (998), Estimation Method of Baking Condition of Cake for Oven Baking Rate of Expansion and moisture Evaporation of Cake during Baking, Annual report on the Iijima Memorial Foundation for the Promotion of Food Science and Technology, 998, 7- (in Japanese). Sugiyama, K., Shibukawa, S. (998), Estimating Method of Heating Conditions for Pan Frying, 9 th Jpn. Sym. on Thermophys. Prop., 9-97 (in Japanese). Sugiyama, K., Shibukawa, S. (000), Estimating Method of Heating Conditions of Cake Thermophysical properties during Baking of Different Cake Batters, th Jpn. Sym. on Thermophys. Prop., (in Japanese).