Measurement of Thermal Conductivity of Cured Tobacco Material

Transcription

1 Food Sci. Technol. Res., 14 (), , 8 Measurement of Thermal Conductivity of Cured Tobacco Material Takayoshi kuroia 1*, Norio araki and Yukio nakanishi 3 1 Japan Tobacco Inc., --1 Toranomon, Minato-ku, Tokyo 15-84, Japan Intellectual Property Bank Corp., Shua Toranomon # Bldg., Toranomon, Minato-ku, Tokyo 15-1, Japan Tobacco Science Research Center, Japan Tobacco Inc., 6- Umegaoka, Aoba-ku, Yokohama, Kanagaa 7-851, Japan Received February 8, 7; Accepted November 7, 7 A novel method has been developed to measure the thermal conductivity of leaf-like material (tobacco) in the perpendicular direction to its surface over broad ranges of temperature and moisture ith the aim of designing primary processes in the tobacco industry. Reduction in the time a sample is exposed to high temperature and humidity is a decisive factor because tobacco easily changes its nature under these conditions. A closed sample chamber ith minimum volume permitted thermal conductivity measurements under these conditions ithout any significant deterioration in the sample. This method could also be applied to other et materials that deteriorate easily. The thermal conductivity increased ith both temperature and moisture and as regressed into to simple equations. It should become possible to estimate the heat transfer rate at desired temperatures and moistures hen more extensive data become available. Consequently, a method for the measurement of the thermal conductivity of tobacco, hich is one of the crucial factors in the rational design of primary processes, has been established. Keyords: tobacco, specific heat, transport phenomena, thermal conductivity *To hom correspondence should be addressed. takayoshi.kuroia@ims.jti.co.jp Introduction In the tobacco industry, the moisture of tobacco in cigarettes is extremely important because it determines the firmness and taste of cigarettes. In the cigarette manufacturing process, cured tobacco leaves (ra material) are moistened before being cut into shreds because they are too brittle to be cut as they are. Thereafter, the tobacco shreds have to be dried to the desired moisture of the end products. The tobacco is heated in either process to facilitate ater migration, and a precise control of temperature is necessary since excessive heating spoils the taste of tobacco through the vaporization of tobacco constituents. Therefore, knoledge of the thermal conductivity of tobacco is crucial for the rational design of the primary processes. In the primary process, the moisture and temperature of the tobacco ranges from.1 to.4 kg/kg and from 3 to 35 K, respectively. Consequently, the thermal conductivity must be available over extensive moisture and temperature ranges. Furthermore, in recent times there has been a demand for a reduction in the process time so as to permit improvements in productivity, and, inevitably, knoledge of conductivity at higher temperatures, even close to 373 K, has become desired. Thus far, hoever, it has been considered to be virtually impossible to measure the thermal conductivity of tobacco under conditions of high temperature and moisture, because tobacco ends up changing its nature before reaching the equilibrium for the ater adsorption. In addition to the extremely slo migration rate of ater (Kuroia and Nakanishi, 3), since the change in moisture corresponding to a certain prescribed change in relative humidity increases ith increasing moisture, it takes longer and longer for the ater to reach the adsorption equilibrium at high moistures. The deterioration of tobacco is accelerated at high temperature because the deterioration is mainly caused by chemical reactions, e.g., the Maillard reaction, hich occurs during the roasting in the primary process (Li et al., 3). In addition to taking care to prevent deterioration, care must also be taken hen the application of the thermal conductivity to the process design is considered. That is, the thermal conductivity should be an intrinsic property of tobacco itself; it should not depend on the bulk density of the packed bed of tobacco. Since the bulk density of tobacco ranges idely and tobacco is not normally regarded as a

2 Heat Conduction Measurement packed bed in the primary process, such as hen it is in a rotary drum mixer, the calculation of the conductivity of the packed bed from the conductivity of tobacco ould be more rational than the direct measurement of the tobacco in a packed bed itself. In addition, since tobacco shred is merely cut material of a dried leaf, its anisotropy must be considered hen the thermal conductivity is measured; namely, the conductivity of tobacco in the perpendicular direction to the tobacco surface is considered to be of primary importance, because the tobacco leaf is very thin. The thermal conductivity of tobacco has been reported by several authors. Hoever, it as found to be difficult to use the reported thermal conductivities in the primary process design. There has been no study on the dependence of the thermal conductivity of tobacco on temperature. In all previous studies, measurements ere performed at room temperature and the anisotropy of the tobacco material as not considered. For example, Locklair et al. (1957) measured moisture dependency of the thermal diffusivity of shredded tobacco, and Samfield and Brock (1958) calculated the thermal conductivity from the thermal diffusivity. Hoever, their measurements ere performed on a packed bed at room temperature, and, as a result, neither the temperature dependency nor the anisotropy of tobacco as considered. These defects are found in all of the folloing studies: Sykes and Johnson (1973), reporting the bulk thermal conductivity of tobacco shreds during freeze-drying; Muramatsu et al. (1979), ho measured dependency of the thermal conductivity of shredded tobacco on the bulk density of the packed bed at room temperature in order to investigate the combustion of cigarettes; Childs et al. (1983), ho measured the thermal conductivity of a packed bed of tobacco lamina for the design of a arehouse cooling system; Casada and Walton (1989), ho determined the thermal conductivity of baled tobacco leaves hen considering a ay of stacking them. The purpose of this study as to develop a novel method to measure the thermal conductivity in the perpendicular direction to the tobacco surface over broad ranges of temperature and moisture. The formulation of the thermal conductivity as a function of temperature and moisture as also attempted. Materials and Methods Materials A typical variety of tobacco, flue-cured tobacco, as selected as the experimental material. Flue-cured tobacco drives its name from the unique curing process used to produce lemon-colored cured leaves ith high sugar content, and curing is the process for drying the freshly harvested tobacco ith fully controlled temperature and moisture schedules (Peedin, 1999). The thickness, standard deviation Table 1. Thickness and density of flue-cured tobacco. Thickness, l [m] Standard Deviation of Thickness, σ [m] Apparent Density, ρ d [kg/m 3 ] True Density, ρ t [kg/m 3 ] of thickness, apparent density and true density of the tobacco are shon in Table 1. Design schemes of method Our primary aim is to measure the thermal conductivity of tobacco in extensive temperature and moisture ranges ithout deterioration. Deterioration as observed hen a tobacco sample as exposed to high temperature, such as 363 K, for several hours; namely, the sample became dark bron, emitted a roasted smell, and the leaves adhered to each other hen they ere piled. Since the sample must be in equilibrium hen it is prepared for an experiment, the time required for the sample to reach thermal and ater adsorption equilibrium needs to be reduced in order to avoid such deterioration, especially at high temperatures and humidity. Hoever, it is particularly difficult to achieve ater adsorption equilibrium over a short time. That is, even though the moisture of sample can be adjusted to the desired value at room temperature in a ay hich avoids deterioration of the sample, the adsorption equilibrium needs to be re-established hen the sample is heated to the measuring temperature; nonetheless, it needs a long time to reach this ne adsorption equilibrium because of the extremely slo migration rate of ater (Kuroia and Nakanishi, 3). Accordingly, in order to minimize fluctuations of the ater adsorption amount, a closed sample chamber as designed, in hich there is virtually no room except that for the gas contained in the voids inside the tobacco sample itself. Moreover, in order to enhance the efficiency of heating by reducing the quantity of heat and the thermal transfer length, the sample size as minimized as far as possible hile ensuring that the accuracy of the measurements as not affected. Additionally, oil as used as heating medium instead of air in order to improve the thermal transfer rate, because oil has far greater thermal conductivity (.16 W/m K) and specific heat per unit volume (~1 6 J/m 3 K) than air (.3 W/m K and ~1 3 J/m 3 K, respectively). A second requirement is that the measured property should be the conductivity of tobacco itself in the perpendicular direction to its surface. Unfortunately, it as difficult to measure the thermal conductivity of a sheet of tobacco in the perpendicular direction because the tobacco is very thin; furthermore, the dispersion in the thickness of tobacco is too large, as shon in Table 1. Consequently, it as determined to measure the thermal conductivity of a tobacco block, namely a pile of circularly cut tobacco leaves. A schematic draing of the sample block configuration is shon in Fig.

3 16 4 l Thermal flux R 1. If tobacco leaves are piled on a plate heater, the measured thermal conductivity should be along the perpendicular direction to the tobacco surface as long as the edge effect could be neglected. Hoever, it as found that irregularity of the leaf surface had to be evened out before measurement. Therefore, the pile of tobacco leaves as compressed until the height per sheet of tobacco became equal to the average thickness of the tobacco leaf in the environmental chamber adjusted at 95 K and 6 % RH (Relative Humidity), here the tobacco leaf is relatively soft. Subsequent to this treatment, the moisture of the tobacco block as adjusted to a given value by changing the conditions in the environmental chamber. Sample Dimension The height of the sample block as determined as follos: 1) When n sheets of tobacco leaf ere sampled, the 95 % confidence limits concerning the difference beteen sample mean and population mean are specified by e / n (1) L Plate heater Temperature distribution Circularly cut tobacco leaves Fig. 1. Schematic draing of sample block configuration. (Snedecor, 1937); ) given that error ithin 1 % ould be alloable in vie of the fact that tobacco is a natural plant material, it as decided that the temperature could be measured at the top and bottom of the block comprising sheets of the tobacco leaf according to Eq. (1), ith the thickness of the tobacco leaf and the standard deviation given in Table 1; 3) given that the hole height of the sample must be tice the height of the temperature measuring point so as to satisfy the assumption of a semi-infinite sample (hich as necessary for calculation), it as eventually decided to use 4 sheets in the tobacco block. (The appropriateness of this assumption ill be described later in a typical result of the measurements.) The size (diameter) of each circularly cut tobacco leaf as chosen so as to permit the assumption that the heat transfer in the tobacco block is one-dimensional along the perpendicular direction to the tobacco surface (Fig. 1). The diameter of the sample block as determined by numerical calculations using the folloing equation employing a thermal diffusivity of 1 x 1-7 m /s and the approximate temperature rise of the heater plate (the first equation in Eq. (4)), hich ere obtained at the exploratory experiments at room temperature: T t T z T r 1 rt r, () T r at r, T T at r R, (3) T 5 t 6 at z, T T at z 4l, (4) T T at t. (5) The calculated result for a sample ith a diameter of mm at t = 9 s revealed that the possible error in temperature at the location of 1 mm outards from the center of the sample as ithin 3 % of the temperature in the case of a sample ith infinite diameter (R ). Therefore, a sample diameter of mm as chosen. To summarize, a pile of 4 sheets of tobacco leaf cut in circles ith diameters of mm as used in these experiments. Apparatus The experimental apparatus is shon in Fig.. The sheets of tobacco ere cut in circles ith diameters of mm. Forty sheets of the tobacco leaf ere laid on top of each other on a circular heater plate (; positive temperature coefficient heater; Kurabe Industrial Co., Ltd., Hamamatsu, Japan) at 95 K and 6 % RH. Three thermocouples (4) ere set at the center of the sample (3) so that the intervals from the heat source ere, 1 and sheets of tobacco, respectively. (The thermocouple at the top of the mm mm 7 T. Kuroia et al. Fig.. Schematic draing of experimental apparatus [1. closed sample chamber. plate heater. 3. sample. 4. thermocouples (positions I, II, III). 5. data logger. 6. constant voltage poer supply. 7. heat insulator. 8. thermal conductor. 9. spacer. 1. O-ring. 11. plug. 1. oil bath.]. 1 6

4 Heat Conduction Measurement sheets of tobacco as used to validate the measured values, as ill be described later.) The diameter of the thermocouple as.5 mm and it as so fine that its heat capacity could be neglected. The sample as compressed in the sample chamber (1) for one night to average out the thickness of the tobacco. Thereafter, the moisture of the sample as adjusted to a given value in the environmental chamber for a eek. After the sample chamber had been hermetically sealed, the sample temperature as adjusted by completely immersing it in an oil bath (1). After the sample reached the desired temperature, hich as indicated by the measurements from the three thermocouples, electric poer as supplied to the heat source using a constant voltage poer supply (6), and then the temperatures ere recorded for 9 s at 1-s intervals by use of a data logger (5). The amount of the poer supplied as determined so that the temperature increment ould be ithin 1 K during the measurement. As mentioned earlier, the closed sample chamber as designed in such a ay that there as virtually no room except for the voids inside the tobacco sample itself. Therefore, the moisture of tobacco could hardly change in the chamber even though the temperature as increased. In fact, hen the sample in equilibrium at 95 K and 8 % RH as heated to 373 K, it as expected that the moisture of the sample ould be reduced by only.69 kg/kg, according to the folloing estimation. 1) The volume of voids as calculated from the apparent and the true densities in Table 1; the volume of the interspace beteen the chamber all and the spacer (9) as added to it; the total void fraction in the chamber as estimated to be.67. ) The moisture in the tobacco as calculated from the sample volume packed into the chamber and the adsorption isotherm reported by Kuroia and Nakanishi (3) at 95 K and 8 % RH, in hich they measured the migration rate of ater in the to major types of tobacco including the one used here; the amount of moisture in the voids as calculated using the ideal gas equation at 95 K and 8 % RH. 3) The moisture at 373 K as calculated by a trial-and-error method using the adsorption isotherm and the ideal gas equation under the condition that the total amount of moisture in the chamber as constant. Although the pressure in the chamber increases ith temperature, the effect as considered to be negligible because the change in thermal conductivity of solids ith pressure is usually very small. As expected, every sample used in this study reached thermal and adsorption equilibrium ithin 15 min, and the measurements ere certainly carried out before any deterioration occurred in the tobacco sample. Thermal Conductivity As mentioned earlier, the thermal 17 conduction obtained by this method as considered to be one-dimensional. Furthermore, the change in temperature during the measurement as sufficiently small that any physical property of the sample could be treated as constant. Therefore, the thermal diffusion equation became T t T z, k C p z. (6) The initial condition and the boundary conditions ere T T at t, (7) t T T, (8) bot bot here subscript bot denotes the position of loer temperature measuring point, that is, either of the positions of point I and II. In this case, the solution of Eq. (6) as T t T n l t T bot exp n l 4t d 3 t (Carsla and Jaeger, 1959), here T(t) is the temperature at z = z bot + n l and n is the number of the layers. The thermal diffusivity as calculated by the parameter-fitting method using the above expressions. Due to concerns that errors could arise due to the thermal resistance resulting from the contact beteen the leaves composing the sample block, the validity of the thermal conductivity obtained by this method as verified by changing the top and the bottom positions: A typical result is shon in Fig. 3, here the keys Point I, II and III indicate Temperature Rise T z T [K] Point I Point II Point III I II II III I III Top α I II = 1.7x1-7 Time t [s] (9) α II III = 1.3x1-7 α I III = 1.5x Fig. 3. Typical temperature rises at respective temperature measuring points (T = 313 K; m =.155 kg/kg; α = m /s).

5 18 the rise in temperature measured at temperature measuring points I, II and III in Fig., respectively. The curves expressed by the keys I II, II III and I III in Fig. 3 sho the results of the calculation in the cases of the combinations of the respective positions of the temperature measuring points. The curve expressed by the key Top in Fig. 3 represents the temperature rise at the very top of the sample, hich as calculated from the Eq. (9) as n = 4. It can be seen that the assumption of the semi-infinite sample is appropriate because the calculated temperature rise at Top is very small. Additionally, since the differences beteen the thermal diffusivities calculated from the above-mentioned combinations in several preliminary experiments ere ithin 15 %, it as concluded that there as essentially no thermal resistance beteen the leaves in the series of experiments. Therefore, the thermal diffusivity based on the temperature measurements at Points I and III as adopted as a representative value. Since the density and specific heat of et tobacco are represented as ρ d (1 + m ) and Eq. (11), hich ill be described in the next section, respectively, the thermal conductivity as calculated using the folloing expression: k C 1 m p d 6.31 m 7.35 T 34.5 m 434. (1) Specific heat In order to calculate the thermal conductivity from the thermal diffusivity, the specific heat of the tobacco as measured in advance by use of a differential scanning calorimeter (DSC; DSC-6A, Shimadzu Inc., Kyoto, Japan) ith the samples encapsulated in closed pans. The measurements ere performed from 33 K to 353 K at a constant heating rate of 5 K/min. The moisture and temperature dependencies of the specific heat of tobacco are shon in Figs. 4 [a] and [b], respectively. The specific heat increases almost linearly ith moisture at every temperature. The linear change ith moisture suggests that the specific heat of tobacco is composed of the sum of those of dry tobacco, the adsorbed ater, and the air in the voids. In fact, the subtraction of the contributions of ater and air from the specific heat at a certain temperature made it almost constant. Likeise, it can be seen in Fig. 4 [b] that the specific heat also increases almost linearly ith temperature. Therefore, a linear regression as performed. The straight lines in Figs. 4 [a] and [b] are the results of the regression from the measured values, ith the assumption that both the specific heats of dry tobacco and moisture linearly depend on temperature and that the specific heat of et tobacco linearly depends on moisture, and can be expressed as the folloing: C 6.31 m 7.35 T 34.5 m 434. (11) P T. Kuroia et al. As seen in the figures, it as found that the linear equation sufficiently represents the specific heat of tobacco in practical use. The thermal conductivities above 353 K ere calculated using the specific heat obtained by the extrapolation of Eq. (11), as Muramatsu et al. (1979) reported that the specific heat of tobacco linearly depends on the temperature in the range of K. Results and Discussion Verification of the method In order to verify the appropriateness of the method for the measurement of thermal conductivity, a comparison beteen the proposed method Specific Heat C P x 1-3 [J/kg K] K 343 K [a] [a] Specific Heat C P x 1-3 [J/kg K] kg/kg.49 kg/kg.39 kg/kg 3.5 [b] [b] Moisture m [kg (Water) /kg (Dry Material) ] Temperature T [K] Fig. 4. Specific heat ([a]: moisture dependency, [b]: temperature dependency).

6 Heat Conduction Measurement and existing methods as performed at room temperature, here there is no concern about sample deterioration. The methods used for comparison ere Kemtherm (QTM-D3, Kyoto Electronics Manufacturing Co., Ltd., Kyoto, Japan) and KD (KD, Decagon Devices, Inc., Nelson Court, NE, USA). Kemtherm is a kind of heat ire method, that is, the heat ire is put beteen a sample and an insulator hose thermal conductivity is knon; electric poer is supplied to the ire heater and then the thermal conductivity is determined by the temperature increment and the output of the ire heater. This method needs a mm 3 rectangular parallelepiped sample as the minimum dimension for the sample ith a thermal conductivity equivalent to the tobacco. KD is also a variety of heat ire method, that is, the needle sensor, hich includes a heater and a thermistor, is inserted into a sample; a constant electric poer is supplied to the heater and then the thermal conductivity is determined by the temperature increment of the needle. All measurements ere performed in an environmental chamber to maintain constant sample temperature and moisture. In order to prevent sample deterioration, the measurements ere performed at room temperature, 95 K. As for measurements by Kemtherm, the sample as a pile of 46 sheets of tobacco leaf cut into.5-m squares, hile the sample of KD as a poder that as ground from tobacco leaf. The thermal conductivities obtained by these methods are shon in Fig. 5. The thermal conductivities from KD measurements ere smaller than other conductivities because the packed density of the sample composed of poder as inevitably loer than the other samples; that is, the measurements ere performed ith a sample of kg/m3 hile other measurements ere performed ith samples of 515 kg/m3. Since it is impossible for the tobacco poder to fill the sample container ith the same structure as tobacco leaf, and it is knon that the thermal conductivity of the tobacco filler in the packed bed depends on the density of the bed (Muramatsu et al., 1979), KD as considered to be inadequate for measurement of the thermal diffusivity. In contrast, the results from Kemtherm and the proposed method ere quite consistent, and this demonstrates the appropriateness of the proposed method. Thermal conductivity The moisture and temperature dependencies of the thermal conductivity of the tobacco are shon in Figs. 6 and 7, respectively. It should be noted that the proposed method allos the thermal conductivity to be Thermal Conductivity k [W/m K] K 333 K 353 K 373 K Calculated by Eq. (1) Calculated by Eq. (13) Moisture m [kg (Water) /kg (Dry Material) ] Fig. 6. Moisture dependency of thermal conductivity..14 Thermal Conductivity k [W/m K] Proposed method Kemtherm KD Moisture m [kg (Water) /kg (Dry Material) ] Fig. 5. Thermal conductivities obtained by various measuring methods (95 K). Thermal Conductivity k [W/m K] kg/kg.14 kg/kg.43 kg/kg.31 kg/kg.343 kg/kg Calculated by Eq. (13) Calculated by Eq. (1) Temperature T [K] Fig. 7. Temperature dependency of thermal conductivity.

7 13 measured at high temperatures up to 373 K. The moisture dependency of the thermal conductivity of tobacco is rather complicated; namely, the conductivity linearly increases ith moisture until a moisture content of about.4 kg/kg (ignoring a small peak-like change around moisture of.1 kg/kg) and then shos a steeper increase above this level. An attempt to determine the thermal conductivity of tobacco tissue itself, hich must be independent of moisture, as made by the application of the porous model (Kunii, 1961) to the thermal conductivity of tobacco. The constant thermal conductivity of tobacco tissue itself, hoever, could not be obtained. The complexity of the development of ater adsorption on plant material such as tobacco seems not to allo the ordinary model to be adopted; that is, it is speculated that the adsorbed ater does not contribute much to the thermal conductivity at lo moisture because it distributes in the cell all in isolation, but facilitates the thermal conduction beyond a certain threshold of moisture because the adsorbed ater on the individual cells begin to connect together. Hoever, the data as too limited in quantity to dra any further conclusions about characterization of the thermal conductivity of tobacco. Further data accumulation ill allo more detailed analysis and discussion. Incidentally, a measurement over 373 K (at 393 K) as also attempted. Hoever, it as concluded that the measurements became inconsistent, because the thermal conductivity at 393 K drastically decreased and fell to the same level as that at 333 K. This decrease as considered to stem from the loss of supplied heat due to ater evaporation, because the saturated vapor pressure of ater increases exponentially ith temperature. The regression of the thermal conductivity to a function of temperature and moisture as attempted for the application of the conductivity to the practical design of the primary processes. The temperature dependency of the thermal conductivity distinctly changes at a moisture of.4 kg/kg, as can be seen in Fig. 7. The thermal conductivity gradually increased ith temperature at relatively lo moistures; hoever, it began to sho a steeper increase above a moisture of about.4 kg/kg. Therefore, the thermal conductivity might be fitted to a quadratic curve separately above and belo the moisture of.4 kg/kg. Vieed in this light, the data shon in Fig. 6 seem to allo the moisture dependence of the thermal conductivity to be roughly approximated by the combination of straight lines crossed at this ater content (.4 kg/kg). As a result, the coefficient of each term in the regression equation, hich is described by a poer series of temperature, ould be expressed as a linear function of moisture. The curves in Figs. 6 and 7 sho the results of the regression described by the folloing expressions: k m T.86 m.63t 14 m.98, k m T.14 m. T 4 m m.4, (1) m 3.5,.4. (13) The lines in Fig. 6 ere simple combinations of the above regression equations at those respective temperatures. It as concluded that these regression equations sufficiently expressed the measured thermal conductivities. It should become possible to estimate the heat transfer rate at desired temperatures and moistures hen more extensive data becomes available. Conclusion A novel method as developed to measure the thermal conductivity of leaf-like material in the perpendicular direction to its surface over broad ranges of temperature and moisture. The folloing schemes ere adopted for achieving the measurement ithout deterioration of the plant material: 1) minimization of the room in the sample chamber to prevent moisture from vaporizing, hich should lead to reduction of the time required for ater adsorption; ) minimization of the dimensions of the sample in order to reduce the amount of heat required to raise temperatures of both the sample and the chamber; and 3) employment of an oil bath for the enhancement of heat transfer. Overall, these schemes enabled the time required to reach temperature and moisture equilibrium to be greatly reduced. Consequently, measurements of thermal conductivities at higher temperatures and moistures than ever before could be carried out. This method should be applicable to other et materials that deteriorate easily. The measured thermal conductivity increased ith both temperature and moisture and as regressed into to simple equations. It should become possible to estimate the heat transfer rate at desired temperatures and moistures hen more extensive data become available. Consequently, a method for the measurement of the thermal conductivity of tobacco, hich is one of the crucial factors in the rational design of the primary processes in the tobacco industry, has been successfully established. Nomenclature C P e L k specific heat, J/kg K error in distance beteen temperature measuring points, m thermal conductivity, W/m K T. Kuroia et al.

8 Heat Conduction Measurement l thickness of tobacco leaf, m L length scale, m m n r R t T T z moisture, kg (ater)/kg (dry material) number of tobacco sheets laid beteen temperature measuring points radial coordinate, m radius of tobacco sample, m time, s absolute temperature, K initial temperature, K spatial coordinate, m <Greek letters> α thermal diffusivity, m /s ρ density of et material, kg/m 3 ρ d apparent density of dry material, kg/m 3 ρ t true density of dry material, kg/m 3 σ standard deviation of thickness of tobacco leaf, m References Carsla, H.S. and Jaeger, J.C. (1959). Conduction of Heat in Solids, Oxford University Press, London. Casada, M.E. and Walton, L.R. (1989). Thermal conductivity of baled burley tobacco, Transactions of the ASAE, 3(3), Childs, D.P., Fletcher, L.W. and Beard, J.T. (1983). Cooling tobacco in arehouse during the inter to kill cigarette beetles, Part I: 131 Relevant physical properties of stored tobacco, Tobacco Science, 7, Kunii, D. (1961). Conduction of heat in particle matter, Kagaku Kogaku, 5(1), (in Japanese). Kuroia, T. and Nakanishi, Y. (3). Measurement of migration rate of ater in cured tobacco material, Food Sci. Technol. Res., 9(3), Locklair, E.E., Galloay, W.D. and Samfield, M. (1957). The thermal diffusivity of tobacco. Tobacco Science, 1, 8-3. Muramatsu, M., Umemura, S. and Okada, T. (1979). Studies on natural smoldering of cigarettes III. Determination of the thermal properties of tobacco shreds packed in columns, Beitrage Zur Tabakforschung International, 1(1), Li, P., Wu, M. and Xie, J. (3). Changes in levels of amino acids and basic components in burley tobacco produced by roasting, Beitrage Zur Tabakforschung International, (7), Peedin, C.F., Flue-cured tobacco, In Tobacco Production, Chemistry and Technology, ed. Davis, D and Nielsen, M. (1999), Blackell Science, London, pp Samfield, M. and Brock, B.A. (1958). The bulk thermal conductivity of tobacco, Tobacco Science,, Snedecor, G.W. (1937). Statistical Methods, Ioa State Univ. Press, Ames, Ioa. Sykes, L.M. and Johnson, W.H. (1973). Bulk thermal conductivity of cured bright tobacco shreds during freeze drying, Tobacco Science, 17,