Numerical Study on Heat Transfer and Release Characteristics of Key Components in Electrically Heated Tobacco Products

,


Introduction
With the increasing awareness of the health risks associated with smoking, new tobacco products are being marketed as less toxic alternatives to traditional cigarettes in order to lower emissions of toxicants and reduce harm [1,2].Among them, the electrically heated tobacco product is a new type of tobacco product emerging rapidly in the tobacco industry in recent years [3], accounting for 42.7% of the global market share of new tobacco products in 2021.
An electric heating sheet or heating needle is typically used to heat the tobacco substrate to temperatures sufcient to release water and volatile organic compounds such as nicotine, without initiating a self-sustaining smoldering combustion process [4].As the heating temperature (below 500 °C, mostly 350 °C) is lower than the combustion temperature of traditional cigarettes (600 °C-900 °C), it can efectively reduce the harmful components produced by pyrolysis and thermal synthesis of tobacco at high temperatures [5,6].
Generally, the electrically heated tobacco product is composed of a tobacco section, a hollow section, and a flter section [7,8].Diferent types of wrapping paper are used to securely bond and afx each individual section.Among them, the tobacco section is the core area that determines the quality of the product.Te heat and mass transfer characteristics in the tobacco section are directly related to its internal temperature distribution and the release process of key components.Various factors, such as the initial component ratio in the tobacco substrate, the tobacco fller mass, and the temperature profle of the heater, will signifcantly afect the taste of the aerosol.Tere are studies on the pyrolysis process and release characteristics of water, glycerol, and nicotine in tobacco materials under the condition of a fxed heating temperature or continuous heating processes.It is found that at low temperatures, free water and some loosely bound water are frst released.As heat is gradually transferred into the tobacco substrate, the temperature continues to rise, leading to the subsequent release of nicotine and glycerol.Glycerol undergoes minimal pyrolysis during heating, with the majority transferring to the gas phase at temperatures between 150 °C and 250 °C [9].Nicotine is transferred into the gas phase by vaporization, and the release rate reaches its peak value in the range of 160∼200 °C [10].Water, glycerol, and nicotine account for more than 80% of the aerosol mass [11][12][13].At temperatures exceeding 200 °C, other low-molecular-weight gases (such as CO, CO 2, and ammonia), aldehydes, ketones, and other primary pyrolysis products are released [14], and all these gas-phase components form and aggregate in the pores of porous tobacco media.Zheng et al. [15] test the aerosol components and the release characteristics of the aerosol former, nicotine, and other substances at 11 equidistant temperature points in the range of 200∼470 °C.Te results reveal that within the temperature range of 260 °C to 320 °C, the glycerol content in the aerosol increased signifcantly as the heating temperature rose.Gómez-Siurana et al. [16] fnd that only water and CO 2 are released from tobacco materials under 150 °C through real-time data of the Fourier transform infrared spectrum.In addition, a series of investigations have been conducted to explore the thermophysical properties of tobacco [17][18][19] and the reaction kinetic mechanism of volatile release [20][21][22][23][24], which contribute to a better understanding of the heat and mass transfer processes inside the electrically heated tobacco products.
For the design of a suitable component ratio in the tobacco substrate and the temperature profle of the heating element, it often costs a lot to adopt experimental means for parameter adjustments.With the rapid advancement of computer technology, numerical simulation methods have been extensively used to study the law of heat and mass transfer [25,26].Te tobacco section of the electrically heated tobacco product is mainly flled with cut tobacco or tobacco sheets, which can be considered as porous media characterized by a tobacco substrate and void space.Based on the theory of porous media, several studies [27][28][29] have established foundational heat transfer models for the tobacco section of the electrically heated tobacco product, which are capable of predicting the temperature distribution within the gas-phase domain under static heating conditions and during dynamic pufng, but do not take the release of components into consideration.Nordlund and Kuczaj [30] establish a relatively complete mathematical model for the entire electrically heated tobacco product, which includes the heat and mass transfer processes of gas-phase components in anisotropic porous media, as well as the transient volume and mass changes in multicomponent aerosols, but the changes in thermal properties and density of the tobacco substrate during heating are not considered.Wang et al. [31] experimentally derive the relationship between the volume-averaged temperature of the tobacco section and the release of key components, employing a simplifed lumped parameter method, which treats the electrically heated tobacco product as a single point.However, as the model assumes a uniform distribution of temperature and key component concentrations throughout the tobacco section, it fails to provide a three-dimensional temperature distribution and detailed insight into the heat transfer process within the tobacco section.Current numerical models are still in the early stages of development.
To sum up, existing experimental results have provided valuable insights into the thermodynamic behavior of tobacco materials under various conditions; however, they have not yet been able to yield sufcient guidance for practical applications.However, most numerical simulations fail to correlate heat transfer with component release.Terefore, based on the existing models' foundation, a coupled numerical model of gas fow, heat transfer, and the release of key components in the electrically heated tobacco product is established in this study, which exhibits improvements primarily in the following aspects: frstly, it helps reveal the internal heat and mass transfer characteristics in the porous media of tobacco; secondly, it accounts for changes in the thermal properties of tobacco and the permeability of flamentous porous media during the heating process; and lastly, the accuracy of the model is validated through experiments, including temperature monitoring at multiple measurement points and determination of residual contents in the tobacco substrate after each puf, which allows for a better match with actual conditions.Te efects of the initial component ratio, the tobacco fller mass, the dimensions of the tobacco section, and the temperature profle of the heater on temperature distribution and the release characteristics of key components within the tobacco section are investigated under dynamic pufng conditions.Te commercial software Fluent is used to solve the coupled model through user-defned functions (UDFs).Te results are helpful in further understanding the release mechanisms of water, glycerol, and nicotine and can provide suggestions for the design and optimization of electrically heated tobacco products.

Numerical Modelling
2.1.Physical Model.Te electrically heated tobacco product studied in this paper is mainly composed of a tobacco section, a hollow section, and a flter section.Te diameter of the EHTP is 7.8 mm, and the length of the tobacco section is 13.5 mm.Te diameter of the heating needle is 2.15 mm, the head is conical, and its length is 2 mm.Te total depth of insertion is 13.8 mm.In the numerical simulation, the heat transfer process, component release through phase transition, and chemical reactions in the tobacco section are mainly focused.Terefore, the infuence of ventilation holes can be ignored.A two-dimensional axisymmetric model, as shown in Figure 1, is established to reach a faster calculation speed.
In the numerical simulation, the following assumptions are adopted to simplify the solution: (1) As the stacking of tobacco shreds is characterized by randomness and disorder, it is technically hard to obtain their anisotropic thermal properties.Terefore, based on the macroscopic solution method in the feld of porous media, the tobacco substrate in the EHTP is considered as a uniform porous medium with uniform thermal properties in all directions.(2) As only a small fraction of tobacco near the heater surface undergoes mild pyrolysis reactions during heating, the impact of tobacco pyrolysis on heat transfer is considered minimal in the tobacco substrate.Additionally, the thermal expansion of the tobacco substrate is typically negligible within the temperature range of the heating process.Terefore, it can be assumed that the density of the tobacco substrate does not change during heating.(3) Te heat transfer process and component release caused by temperature rise in the tobacco section are mainly focused, ignoring the detailed evolution including the condensation and interception of gasphase components in the hollow section and the flter section.(4) Based on ideal heating conditions, the potential local temperature diferences on the surface of the heater are neglected.Besides, compared to thermal conduction, the contribution of thermal radiation to heat transfer is considered to be relatively minor and can be ignored.
It is important to highlight that assumption (1), which treats the tobacco substrate in the EHTP as uniform and isotropic porous media rather than considering its actual anisotropic thermal properties, could potentially result in errors in heat transfer and thereby afect the temperature distribution within the tobacco section.However, it is worth noting that mathematical models based on the assumption of isotropic porous media have been shown to yield satisfactory results [27][28][29].Te close match between numerical and experimental results indicates that when the most relevant physical and chemical processes are considered in the numerical model, the predictive errors of the model are maintained within an acceptable range.However, although the actual stacking pattern of tobacco shreds may exhibit anisotropic characteristics, it is reasonable to treat the tobacco substrate as isotropic on a macroscopic scale due to the random distribution of tobacco shreds.Tis perspective is particularly applicable when focusing on the overall heating efect rather than specifc local details, which aligns with the focus of this study.

Governing Equations.
During the operation of the electrically heated tobacco product, the gas and solid phases cannot reach the thermal equilibrium state within the short duration of each puf.Terefore, with the assumption of a local thermal imbalance between phases, a solid zone that is spatially coincident with the porous fuid zone is defned.In this case, the conservation equations for energy are solved separately for the fuid and solid zones, and each variable is treated as intrinsic to its respective domain [32].Te governing equations of the mathematical model are as follows.
Te energy equation for the gas phase is as follows: ( Te energy equation for the solid phase is as follows: where t is time, s; ϕ is the porosity of porous media; ρ g is the gas-phase density, kg/m 3 ; ρ s is the solid-phase density, kg/ m 3 ; E g is the total gas-phase energy, J/kg; E s is the total solidphase energy, J/kg; v is the gas-phase velocity, m/s; p is the local pressure, Pa; k g is the gas-phase thermal conductivity, W/(m•K); k s is the solid-phase thermal conductivity, W/ (m•K); h i is the enthalpy of gas-phase component i, J/kg; J i is the difusion fux of gas-phase component i, Kg/(m 3 •s); τ is the stress tensor, Pa; S h g is the gas-phase enthalpy source term, S h s is the solid-phase enthalpy source term, W/m 3 ; S h s �  k (− ΔH k )(zρ k /zt), W/m 3 ; h gs is the heat transfer coefcient for the fuid/solid interface, W/(m 2 •K); A gs is the interfacial area density, m − 1 ; T g is the gas-phase temperature, K; and T s is the solid-phase temperature, K.
Te momentum equation for the gas phase is as follows: International Journal of Chemical Engineering where B f is the body force, N/m 3 ; S i is the source term of porous media, , where μ is the dynamic viscosity of the gas phase, kg/(m•s); α is the permeability of porous media, m 2 ; and C 2 is the inertial resistance factor.
Te component transport equation is as follows: where Y i is the mass fraction of component i in the gas phase, Y i � ρ i /ρ g , ρ i is the density of component i in the gas phase, kg/m 3 ; and D i is the difusion coefcient of component i in the gas phase, m 2 /s, which is computed by the Chapman-Enskog formula using kinetic theory [33].
Te mass conservation equation is as follows: where S s⟶g ρ is the mass transfer source term of gas-solid two phases, which can be obtained by accumulating the amount of component i released at each moment: where m s is the tobacco fller mass, kg; S s⟶g Y i is the mass of component i released per unit mass of tobacco at each moment, mg/mg; and V is the volume of the entire domain of the tobacco section, m 3 .
According to the combustion reaction of traditional cigarettes [34,35], the release rates of the three key components of water, glycerol, and nicotine in our model are calculated by the Arrhenius kinetic parameters.To standardize integral expressions, all release processes are quantitatively described by the frst-order Arrhenius formula.Te activation energy and pre-exponential factors can be obtained by ftting the thermogravimetric curve of tobacco substrates [20] (see Section 3.1 for the values of the kinetic parameters).
where k i is the chemical reaction rate, 1/s; S * Y i is the maximum mass of component i that can be released under infnite time and high pyrolysis intensity, mg/mg; A i is the pre-exponential factor, 1/s; E i is the chemical reaction activation energy, kJ/mol; and R is the universal gas constant, 8.314 J/(mol•K).

Boundary and Initial Conditions.
Te boundary and initial conditions in the simulation, along with their associated parameters, are listed in Table 1.At the outlet of the flter section, the Health Canada Intense (HCI) pufng protocol (55 mL, 2 s sinusoidal pufs every 30 s) for 8 pufs is specifed, and the frst puf starts at 15 s after heating.For mass fraction boundary conditions, the release rates of the three key components within the tobacco domain are calculated by the Arrhenius kinetic parameters and are loaded into governing equations as a source term by the userdefned functions (UDFs).Zero difusive fux is specifed for species boundary conditions at the walls.Te operating pressure is set at a constant value of 101325 Pa.

Numerical Method.
Te mixed aerosol emitted from the electrically heated tobacco product includes air, water, glycerol, and nicotine, as well as other constituents.Te compressibility efects of air, water, glycerol, and nicotine components, as well as the gas mixtures, are treated by employing the ideal gas law.Te specifc heat capacity of air, water, glycerol, and nicotine components adopts a polynomial function of temperature, with the properties of air obtained from Zhang et al. [36] and properties of water, glycerol, and nicotine components referenced from Data Handbook of Chemistry and Chemical Engineering [37] and the CAMEO Chemicals database [38].Te thermal   1) and ( 2) 1), ( 3), (4), and ( 5) International Journal of Chemical Engineering conductivity and viscosity of each component are calculated according to the kinetic theory [39], which is updated and dependent on temperature.Te initial values of these properties for the simulation are listed in Table 2. Other parameters, including the density, initial porosity, and permeability of tobacco, as well as the equivalent diameter of tobacco shreds, are obtained through experimental measurements.Meanwhile, changes in the thermophysical properties of the tobacco accumulation body under diferent component contents and heating temperatures are considered in this study (see Appendix for details).
Te numerical simulations are performed with ANSYS Fluent 19.0 software.Te source terms are loaded into governing equations by the user-defned functions (UDFs).Te governing equations are discretized by the fnite volume method and linearized and solved by the implicit mode.Te second-order upwind scheme is used for the discretization of all terms.Te pressure-velocity coupling is implemented through the SIMPLEC algorithm.Te second-order implicit time integration scheme is employed in terms of time discretization.Te time step is set to 0.05 s, and the convergence criteria of globally scaled residuals are set to 10 − 3 for all variables.Te Courant number remains below 1 throughout the simulation, which ensures the stability of the numerical solution.

Grid Independence Analysis.
To evaluate the grid independence of the computational domain, six diferent grid schemes (9963, 16324, 23982, 41681, 57589, and 99486) are tested.A hybrid mesh setup, incorporating both triangular and quadrilateral elements, is utilized for discretization.Te temperatures of three monitoring lines in the tobacco section at the maximum fow rate of the last puf are selected for comparison.It can be seen from Figure 3 that the temperatures of the models with 9963 and 41681 grids difer signifcantly from those of other models, and there is no further improvement in calculation accuracy when the number of grids exceeds 57589.Te puf-by-puf release amounts of the three key components including water, glycerol, and nicotine are shown in Figure 4.It can be observed that diferent grid schemes result in some variations in the release amounts of components, but the maximum discrepancy is less than 3.29%.Based on the predictive performance of diferent grid schemes on both temperatures and release amounts of the three key components, the model with grid number 57589 is selected to discretize the computational domain in this study.

Experimental Determination of Chemical Composition of
Tobacco.Before pufng, the determination of the initial contents of water, glycerol, and nicotine in the tobacco substrate is conducted using gas chromatography according to CORESTA recommended method no.57 [40], no.60 [41], and no.62 [42], respectively.Te water content is determined by extraction in a methanol solution containing isopropanol as an internal standard, followed by gas chromatographic (GC) analysis with thermal conductivity detection (TCD).Te glycerol is determined by extraction in a methanol solution containing 1,3-butanediol as an internal standard, followed by gas chromatographic (GC) analysis with fame ionization detection (FID).Te nicotine content is determined by liquid/liquid extraction into an organic solvent containing an internal standard, followed by gas chromatographic (GC) analysis with fame ionization detection (FID).To ensure an adequate amount of the target components for the analytical indicators of water, glycerol, and nicotine, fve EHTP sticks (with wrapping paper) are placed together in a 50 mL centrifuge tube.Teir mass is measured and recorded, followed by the addition of the appropriate volume of extraction solvent, and then, the mixture is agitated in preparation for gas chromatographic analysis.Tree parallel experiments are conducted for each component, and the results are reported as weight percent (wt%).Accordingly, the initial contents are determined as 11.38 wt% for water, 16.48 wt% for glycerol, and 1.13 wt% for nicotine in the tobacco substrate.

6
International Journal of Chemical Engineering

Pyrolysis Experiment in a Tube
Furnace.Based on the combustion reaction of traditional cigarettes [34,35], the release rates of water, glycerol, and nicotine components in our model are quantitatively calculated using the Arrhenius formula.To unify the integral expressions, all release processes are simplifed to frst-order reactions.To obtain the release characteristics of water, glycerol, and nicotine in the tobacco substrate under diferent temperature conditions, a tobacco pyrolysis experiment is carried out in a tube furnace to calibrate the reaction kinetic parameters for the tobacco substrate in the studied EHTP.Five identical EHTP samples, each flled with 200 mg of tobacco, are used in the experiment.Fifteen pufs are taken according to the HCI pufng protocol (55 mL, 2 s sinusoidal pufs every 30 s).Te release amounts of the three key components are measured at seven equidistant temperature points from 50 °C to 350 °C.
According to the pyrolysis experimental results (pyrolysis temperature: 50∼350 °C; pyrolysis time: 1 minute; analysis temperature: 250 °C; analysis time: 5 minutes), water is continuously released during the heating process, exhibiting two release peaks below 160 °C and another release peak above 225 °C, which can be approximately divided into three release International Journal of Chemical Engineering processes.Correspondingly, for glycerol and nicotine, a primary phase transition occurs at temperatures above 100 °C, accompanied by a secondary phase transition over a broad temperature range, which can be approximately divided into two release processes.Te reaction kinetic parameters for the tobacco substrate in the studied EHTP are then calibrated and ftted to obtain the release rates of water, glycerol, and nicotine that could closely match the experimental curves, as shown in Figure 5. Results of the ftted reaction kinetic parameters for the tobacco substrate in the studied EHTP are listed in Table 3.

3.3.1.
Validation of the Temperature.Due to the limited geometric dimensions of the electrically heated tobacco product, it is impractical to directly measure the internal temperature within the tobacco section of the product.In this regard, a self-designed and constructed scale-up experimental device is developed.Te schematic diagram and detailed geometric parameters of the device are presented in Figure 6 and Table 4, respectively.Te experiment is conducted under room temperature conditions at 27 °C.Te experimental device regulates the fow rate by adjusting the glass rotor fow meter (k) connected to the external vacuum pump (l), thus simulating the pufng process of electrically heated tobacco products.A DC-regulated power supply (j) provides electrical energy (at an applied voltage of 50 V) to the heater (d).A paperless recorder (a) equipped with the K-type armored microfne thermocouple (b) is utilized to collect real-time temperature data, including the surface temperature of the heater at measurement point ①, the internal temperatures at measurement points ②∼⑤ within the  International Journal of Chemical Engineering tobacco substrate, the aerosol temperature at measurement point ⑥, and the ambient air temperature.Te error within the measurement range of the thermocouple is ≤0.05%, and the temperature acquisition frequency is 10 Hz.In addition, the thermostat (i) regulates the surface temperature of the heater by controlling the on-of operation of the circuit based on the deviation between the measured temperature and the target temperature setting value.
Te temperature simulation results of the numerical model are validated by comparing them with the measured temperatures at measurement points ①∼⑥.Four repetitions of the experiments are conducted at each temperature measurement point, and the maximum standard deviation value is less than 1.0 °C.During the experiment, the temperature is recorded for 400 seconds under the heating condition with a constant fow rate of 6.6 L/min.Te comparison between the average measured temperatures and the simulation results is presented in Figure 7.It can be observed that the measured temperature decreases signifcantly in the radial direction across the porous media of tobacco.After 400 seconds, the measured temperature at 0.25R decreases by 48% compared with the surface temperature of the heater.Te simulation results demonstrate that the temperature rise pattern within the porous media of the tobacco accumulation body exhibits a good ft with the measured results, with a maximum deviation of less than 15%.Te comparative results at 0.25R from the surface of the heater show a relatively greater diference, which may be attributed to the fact that the numerical model is based on the assumption of isotropy in porous media, while the tobacco shreds in the tube furnace are manually flled, leading to potential regions of nonuniform stacking that exhibits anisotropic heat conduction.In addition, the observed fuctuations in experimentally measured temperatures may be attributed to unavoidable fuctuations in the positioning of the thermocouple probe, thereby resulting in slight instability in temperature measurements, while a uniform fow ③ measurement point at a distance of R from the surface of the heater (on the inner wall surface of the sleeve); ④ measurement point at a distance of 0.25R from the surface of the heater; ⑤ measurement point at a distance of 0.75R from the surface of the heater; ⑥ measurement point(s) for the temperature of the aerosol.Te letter "R" represents the distance between the inner surface of the sleeve and the surface of the heater, which is 15.6 mm.Note.(1) "a" denotes the hollow section of 3.50 mm diameter in Figure 1, "b" denotes the hollow section of 5.20 mm diameter in Figure 1.
(2) Te scale-up experiment is only conducted on the tobacco section of the prototype tobacco product under equivalent criteria conditions (scaled-up by a factor of 4). 10 International Journal of Chemical Engineering velocity is specifed at the outlet of the numerical model; thus, the simulated temperature curves do not show signifcant fuctuations.

Validation of the Residual Content in the Tobacco
Substrate.Te reaction kinetic simulation results are validated by comparing them with the experimental values of the residual contents of water, glycerol, and nicotine in the tobacco substrate.During the experiments, fve sets of EHTP sticks each were mounted and fxed onto the corresponding puf channels of the X500E rotary smoking machine.Te smoking machine is then set to execute the HCI pufng protocol (55 mL, 2 s sinusoidal pufs every 30 s) for each EHTP stick, with the number of pufs starting from n � 1, n � 2, ..., and up to n � 8.After each pufng protocol ends, the EHTP sticks are immediately removed from the smoking machine and placed together in a 50 mL centrifuge tube.Teir mass is weighed and recorded, followed by the addition of the appropriate volume of extraction solvent, and then, the mixture is agitated in preparation for gas chromatographic analysis to determine the residual content of water, glycerol, and nicotine in the tobacco substrate.Tree parallel experiments are conducted for each component, and the relative deviation (RD%) between the results is less than 10%, which ensures the reliability and consistency of the obtained data.Before the frst puf starts, the initial amounts of water, glycerol, and nicotine in the tobacco substrate are measured to be 35.98 ± 0.89 mg, 52.09 ± 1.79 mg, and 3.62 ± 0.05 mg, respectively.Accordingly, the initial conditions of the simulation are set to be consistent with the mean values of the abovementioned experimental results.Te comparison between the numerical simulation results and the measured values is listed in Table 5. Te average prediction errors for the residual amounts of water, glycerol, and nicotine in the tobacco substrate during pufng are 7.13%, 14.90%, and 15.81%, respectively.In general, the model exhibits good predictive performance.Te simulation error for nicotine residuals is primarily observed during the 3rd to 5th pufs.Tis is because the residual amount is tested after a specifc number of pufs.Terefore, the results are susceptible to the cumulative efects of experimental and measurement errors.Additionally, the total amount of nicotine in the tobacco substrate is relatively small, which tends to magnify the overall error in the comparison of the experimental and simulated values.

Te Initial Component Ratio.
To investigate the infuence of diferent amounts of water and glycerol on the overall heat transfer efect within the tobacco section and the release characteristics of the three key components, fve diferent initial component ratios are set: (1) 5% water content and 12% glycerol content; (2) 5% water content and 22% glycerol content; (3) 10% water content and 12% glycerol content; (4) 10% water content and 17% glycerol content; and (5) 15% water content and 12% glycerol content."%" here refers to "weight percent" (wt%).It should be noted that there exists a natural equilibrium correlation between water and glycerol contents in the tobacco substrate of the EHTP, as glycerol acts as a humectant and will equilibrate the water content of the substrate [9].In this regard, the main objective of this section is focused on conducting a quantitative analysis of the infuence of the relative content between water and glycerol.Additionally, as nicotine is a substance naturally contained in tobacco leaves, a consistent nicotine content of 1.13%, which is determined through experimental testing, is set in the simulation.
Te puf-by-puf release amount and release efciency of the three key components corresponding to the fve initial component ratio conditions are shown in Figure 8.In all fve working conditions, the water release efciency is approximately 90%.Te higher the water content, the lower the release efciency, and the larger the variance values during individual pufs, which indicates poorer puf-by-puf release uniformity.Tis is because the water and glycerol contents will afect the thermal conductivity of the tobacco section, thereby afecting the heat transfer process.Figure 9 illustrates the changes in thermal conductivity of the tobacco section with diferent water and glycerol contents, corresponding to working conditions 2, 4, and 5, respectively, at representative time points (t � 0, t � 50 s, t � 100 s, and t � 200 s) during heating.Te time points are listed below each image, and the water and glycerol contents are labeled above each column.For working condition 2 (5% water content and 22% glycerol content) with lower water content, International Journal of Chemical Engineering since most of the water has been released in the frst 50 s, the infuence of water content is less in the later stage of heating.Terefore, the distribution of thermal conductivity is relatively uniform.Te stratifcation of thermal conductivity along the radial direction is obvious under working condition 5 (15% water content and 12% glycerol content) where the water content is similar to the glycerol content.As the water and glycerol components are completely released near the surface of the heater, the thermal conductivity of this area is signifcantly lower.Meanwhile, the peripheral area of the tobacco section has a lower temperature.As a result, the distribution of thermal conductivity forms a band between the surface of the heater and the periphery.
It can also be seen in Figure 8 that an increase in the initial content of both water and glycerol can signifcantly enhance their release amounts.At the same glycerol content, a lower water content in the tobacco substrate results in higher glycerol release efciency.As the water content decreases from 15% to 10%, the glycerol release efciency increases from 22.93% to 24.37%, but excessively low water content will make the aerosol dry [43].Te impact of different water and glycerol contents on the release of nicotine is more pronounced in the 3rd to 5th pufs, and when the water content is slightly lower than the glycerol content (as in working condition 3 in the simulation), the release efciency and puf-by-puf release uniformity of nicotine are relatively better.

Te Tobacco Filler Mass.
For tobacco substrate with an initial water content of 11.38%, glycerol content of 16.48%, and nicotine content of 1.13%, fve groups of tobacco fller mass (220 mg, 280 mg, 320 mg, 360 mg, and 410 mg) are simulated to explore their impacts on heat transfer and the release characteristics of the three key components.
Te volume fraction of tobacco in six temperature ranges from room temperature to 350 °C is shown in Figure 10.Te periodic changes in volume fraction over time can be attributed to changes in the temperature distribution within the tobacco section.Due to the rapid cooling efect of the periodic pufng airfow, the forced convective heat transfer between the incoming airfow and heated tobacco leads to a decrease in the overall average temperature of the tobacco section, which is represented by periodic sharp peaks in the volume fraction within the low-temperature ranges.Besides, it can be observed that the pufng airfow has a more signifcant impact on tobacco in the temperature ranges of 100∼150 °C and below 100 °C.Tis is attributed to the higher volume fractions of tobacco in these two temperature ranges.Moreover, tobacco above 250 °C tends to accumulate near the surface of the heater, where the airfow velocity is lower.As a result, the volume fraction of tobacco in the hightemperature range is less afected by the pufng airfow.
Comparing the fve fller mass conditions, it turns out that with the increase in fller mass, the volume fraction of tobacco in the high-temperature regions gradually increases and the overall average temperature of the tobacco section is relatively higher, with the simulation results of 123.90 °C, 127.57°C, 130.82 °C, 133.83 °C, and 138.31 °C, respectively, at the end of the pufng protocol.From the perspective of heat transfer, this is because as the fller mass increases, the porosity of the porous media of tobacco decreases.Although the increase in tobacco fller mass also leads to an overall rise in the specifc heat capacity, the impact of porosity on the increase in thermal conductivity is more signifcant.As a consequence, based on the assumption of porous media with uniform thermal properties in all directions, heat is transferred faster along the radial direction.As the fller mass increases from 220 mg to 410 mg, the volume fraction of tobacco decreases from 32.55% to 5.31% at temperatures below 100 °C, increases from 38.10% to 55.92% in the temperature range of 100∼150 °C, and increases from 25.28% to 34.14% in the temperature range of 150∼200 °C during the entire pufng protocol, which helps promote the release of the three key components.
Te puf-by-puf release amount and release efciency of the three key components corresponding to the fve fller mass conditions are shown in Figure 11.Overall, increasing the tobacco fller mass could enhance the puf-by-puf release amount and release efciency of water, glycerol, and nicotine.For every 10 mg increase in the tobacco fller mass, the release amounts of water, glycerol, and nicotine increase by 5.99%, 13.43%, and 10.77%, respectively.Tis is attributed to the increase in the initial content of each component and the rise in the overall temperature within the tobacco section.As the tobacco fller mass increases from 320 mg to 360 mg, the increase in the release amounts of glycerol and nicotine is the most signifcant.However, the puf-by-puf release uniformity deteriorates with the increase in fller mass.Moreover, excessively high fller mass (410 mg) would International Journal of Chemical Engineering also lead to increased resistance during pufng.Within the range of the studied fller masses (ranging from 220 mg to 410 mg), the maximum resistance during pufng increases from 1853 Pa to 8591 Pa.Terefore, it can be concluded that both excessive and insufcient tobacco fller masses will lead to a less satisfactory aerosol taste.

Te Diameter and Length of the Tobacco Section.
To investigate the impact of the diameter and length of the tobacco section on temperature distribution and the release characteristics of the three key components, the diameter and length of the prototype EHTP (V7.8 × 13.5 mm) are modifed ("V7.8 × 13.5 mm" denotes the dimensions of the EHTP's tobacco section, where "V7.8" represents its diameter and "13.5 mm" represents its length.Te naming principles for the other working conditions are the same).Four diferent tobacco section dimensions (V6.8 × 13.5 mm, V8.8 × 13.5 mm, V7.8 × 11.5 mm, and V7.8 × 15.5 mm) with the same tobacco fller mass of 320 mg are simulated, respectively.
As the nonequilibrium model of porous media solves the energy equations separately for the gas phase and solid phase, the temperature distribution in both the gas-phase and solid-phase domains can be obtained.Te temperature distribution in these two domains at the third puf (t � 106 s) is shown in Figure 12.In the radial outward direction from the heater's surface, there is a stratifed temperature distribution for both the gas and solid phases in the tobacco section, with temperatures gradually decreasing from the International Journal of Chemical Engineering 13 heater's surface toward the periphery.By reducing the diameter of the tobacco section to 6.8 mm, the majority of temperatures within the tobacco substrate are in the range of 100∼200 °C.According to the volume fraction temperature range statistics, there is an increase in the volume fraction of tobacco from 8.89% to 13.57% within the temperature range of 200 °C to 250 °C, which is benefcial for the release of the three key components and facilitates the efcient utilization of tobacco.Reducing the length of the tobacco section to 11.5 mm, the low-temperature regions directly above the tip and adjacent to the acetate wall of the hollow section are eliminated.Terefore, it is concluded that reducing the diameter or length of the tobacco section is equivalent to removing tobacco that does reach the temperature required for the initial release of components.As a result, the overall temperature of the tobacco section increases, and the temperature distribution is more uniform.However, extending the length of the tobacco section to 15.5 mm will result in insufcient heating of the peripheral tobacco near the tip of the heater and its adjacent area.Once widening the diameter of the tobacco section, the heat transfer range in the radial direction is expanded.Te temperature in the widened area is about 68∼89 °C, which does not reach the peak release temperatures of the three key components.Additionally, extending either the diameter or the length will increase the volume of the tobacco section.International Journal of Chemical Engineering Under the same tobacco fller mass condition, it is equivalent to increasing the porosity of the porous media of tobacco, which results in a decrease in the overall thermal conductivity of the tobacco section and hinders the heat transfer process.
Te puf-by-puf release amount and release efciency of the three key components corresponding to diferent dimensions of the EHTP's tobacco section are shown in Figure 13.Reducing the diameter of the tobacco section to 6.8 mm, a notable increase is observed in the release amounts of components, especially for glycerol and nicotine.Correspondingly, reducing the length of the tobacco section to 11.5 mm increases the release efciency of water and glycerol by 4.22% and 10.90%, respectively.However, it should be noted that the accelerated heat transfer process in these two working conditions leads to a more pronounced diference in the release amounts between the frst three pufs and the last three pufs, which has a negative efect on the pufby-puf release uniformity.Extending the diameter or length based on the prototype dimension of the EHTP's tobacco section by 2 mm results in a decrease in the component release efciency, ranging from 7.97% to 29.89%.As previously mentioned, this is attributed to the increase in the volume fraction of tobacco below 100 °C, and these lowtemperature regions fail to meet the conditions required for the initial release of glycerol and nicotine.
To sum up, with other conditions held constant, extending both the diameter or length of the EHTP's tobacco section will result in a decrease in the release efciency of components and may lead to underutilization of tobacco materials.Conversely, reducing the diameter or length of the tobacco section could efectively increase the average temperature of the tobacco section and promote component release.However, excessively small dimensions of the  International Journal of Chemical Engineering tobacco section will result in the nonuniform release of components in each puf, thereby afecting the pufng experience.Moreover, changes in the diameter of the tobacco section have a more pronounced impact than changes in its length, as changes in diameter will result in a more signifcant change in the volume of the tobacco section.

4.4.
Te Temperature Profle of the Heater.Te design of the temperature profle refects the heating characteristics of the heater and directly infuences the heat transfer process within the tobacco section of the EHTP.To qualitatively explore the infuence of the heating mode on the internal heat transfer and the release characteristics of the three key components within the tobacco section, three diferent timedependent temperature profles of the heater are studied and compared.Among them, temperature profle (A) represents the temporal temperature change in the heater in the current EHTP, which is derived from experimentally measured data of the heater's surface temperature.On the basis of temperature profle (A), two additional temperature profles, (B) and (C), are designed, as shown in Figure 14.Temperature profle (B) exhibits an average temperature and temperature change trend that are essentially consistent with those of temperature profle (A).However, it is specifcally designed to facilitate the release of components by canceling the initial 5-second heating phase of the current EHTP, thus initiating heating immediately upon product activation.Additionally, a stepped temperature rise is introduced after 170 seconds to further increase the temperature of the tobacco section and explore its potential efect on promoting the release of components during the last few pufs.Te temperature profle (C) is designed to investigate the impact of heating rate on component release by employing a continuous progressive heating mode.In this mode, the surface temperature of the heater gradually rises to 304.95 °C during 150 seconds and then remains constant.With the above three temperature profles, simulations are conducted for the EHTP with a tobacco section dimension of V7.8 × 13.5 mm and the tobacco fller mass of 320 mg.
Te puf-by-puf release amount and release efciency of the three key components corresponding to the three temperature profles are shown in Figure 15.Te results indicate that by adopting the temperature profle (B), the release amounts of the three components in the frst two pufs increase signifcantly, as well as the release efciency.Te increase in glycerol release is the most obvious, with an increase in the amount ranging from 0.06 to 2.39 mg per puf in comparison with the working condition adopting the temperature profle (A).However, it also leads to a lower residual component content in the last three pufs, and the designed "stepped temperature rise" is insufcient to compensate for the reduced release amounts of components.As a result, there is a signifcant diference in the total release amounts between the early and late stages of pufs.Te heating temperature of profle (C) rises slowly in the frst 70 seconds; therefore, the release process of components is the slowest, as it is directly associated with the rate of heat transfer.It can be observed that water is predominantly released between the 2nd and 4th pufs, while the release peak of glycerol occurs at the 6th puf, which contributes to regulating the uniformity of component content in the aerosol to some extent.Compared with the temperature profle (A), the release efciency of water, glycerol, and nicotine in this case is slightly increased by 1.35%, 2.60%, and 2.63%, respectively.

Conclusions
In this study, a coupled mathematical model of gas fow, heat transfer, and the release of key components in an electrically heated tobacco product is established.Te release rates of water, glycerol, and nicotine are quantitatively described by the frst-order Arrhenius function.Te infuences of several important parameters, including the initial component ratio, the tobacco fller mass, the diameter and length of the EHTP's tobacco section, and the temperature profle of the heater, are studied using CFD simulation.Te major conclusions are listed as follows: (1) Increasing the initial water and glycerol content in the tobacco substrate can increase the total release amounts, but the higher the water content, the lower the release efciency of the key components and the poorer the puf-by-puf release uniformity.(2) Increasing the mass of the tobacco fller can increase the thermal conductivity and average temperature of the tobacco section.For every 10 mg increase in the tobacco fller mass, the release amounts of water, glycerol, and nicotine increase by 5.99%, 13.43%, and 10.77%, respectively.(3) Based on the prototype EHTP with a tobacco section dimension of V7.8 × 13.5 mm, a reduction in either the diameter or length of the tobacco section could help increase its overall average temperature, which, in turn, would promote the release of key components.However, it would also have a negative efect on the puf-by-puf release uniformity.Extending the length or diameter of the tobacco section will hinder the heat transfer process and lead to a decrease in the component release efciency.(4) A slower heating rate matched with longer preheating times enables the complementary release of water and glycerol components, which helps regulate the uniformity of component content in the aerosol to some extent.

Appendix
According to Krupiczka et al. [44], the approximate solution of the thermal conductivity model of the stacked porous media is as follows: where k e is the efective thermal conductivity, W/(m•K); k g is the thermal conductivity of gas, W/(m•K); k s is the thermal conductivity of wet tobacco material, W/(m•K); and ϕ is the porosity of the tobacco accumulation body.Te values of a, b, and c are constants and can be obtained by ftting the experimental data.Te thermal property of wet tobacco material is mainly afected by the inner skeleton of tobacco and water and glycerol contents in the pores.Assuming that the two liquid components and tobacco particles are randomly distributed, the spatial random distribution model of Tavman et al. [45] can be used to calculate the thermal conductivity of the tobacco substrate: where k w is the thermal conductivity of liquid water, W/(m•K); V w is the volume fraction of liquid water in tobacco particles; k gly is the thermal conductivity of liquid glycerol, W/(m•K); k b is the thermal conductivity of the solid skeleton, and for homogeneous solids, it can be considered to have a linear relationship with temperature, k b � k b0 (1 + dT), W/(m•K); k b0 is the thermal conductivity of solid particles at 0 °C under atmospheric pressure, W/(m•K); and d is a constant.Te Hot Disk TPS 2500 S instrument is used to test the thermal properties, including the thermal conductivity and volumetric heat capacity of the tobacco sheets with fve diferent components at 20∼300 °C.Air atmosphere is used at room temperature, and helium atmosphere is used at high temperature.Tree parallel experiments are conducted for each working condition.Te experimental results are presented in Table 6.Based on the measured values, by ftting the functions of equations ( 1) and ( 2), the results of each coefcient are obtained in Table 7.
Furthermore, the thermal properties of the tobacco accumulation body with four diferent fller densities and fve diferent water contents are measured at room temperature.Tree parallel experiments are conducted for each working condition.Te experimental results are presented in Table 8.
Within the investigated range of temperature and water content, the comparison of the thermal conductivity predicted by the thermal conductivity model with the experimental values is presented in Table 9, with an average deviation of 6.72% and a maximum deviation of 15.86%.Terefore, the thermal conductivity model exhibits excellent predictive accuracy over the range of temperatures investigated in this study.

Nomenclature
A gs : Interfacial area density (m − 1 ) A i : Pre-exponential factor in the Arrhenius formula (s − 1 ) B f : Body force (N•m − 3 ) C 2 : Inertial resistance factor D i : Difusion coefcient of gas-phase component i (m 2 •s − 1 ) E g : Gas-phase energy (J•kg − 1 ) E i : Chemical reaction activation energy (kJ•mol − 1 ) E s : Solid-phase energy (J•kg − 1 ) g: Gas phase h: Enthalpy (J•kg − 1 ) h gs : Heat transfer coefcient for the fuid/solid interface (W•m − 2 •K − 1 ) h i : Enthalpy of gas-phase component i (J•kg − 1 ) ΔH k : Energy absorbed per unit mass of component k during phase transition (J•kg − 1 ) i: A specifc component in the gas phase J i : Difusion fux of gas-phase component i (kg•m − 3 •s − 1 ) k: A specifc component in the solid phase k g : Gas-phase thermal conductivity (W•m − 1 Gas-phase temperature (K) T s : Solid-phase temperature (K) V: Volume of the entire domain of the tobacco section (m 3 ) Y i : Mass fraction of component i in the gas phase v: Gas-phase velocity (m•s − 1 ) α: Permeability of porous media (m 2 ) ϕ: Porosity of porous media τ: Stress tensor (Pa) μ: Dynamic viscosity of the gas phase (kg•m − 1 •s − 1 ) ρ: Density (kg•m − 3 ) ρ g : Gas-phase density (kg•m − 3 ) ρ i : Density of component i in the gas phase (kg•m − 3 ) ρ k : Density of component k in the solid phase (kg•m − 3 ) ρ s : Solid-phase density (kg•m − 3 ).

Figure 1 :
Figure 1: Schematic diagram of the two-dimensional axisymmetric model of the electrically heated tobacco product.

Figure 2 :
Figure 2: Time-varying temperature of the heating element surface.

Table 2 :Figure 3 :
Figure 3: Comparison between the temperatures of (a) line 1, (b) line 2, and (c) line 3 at the maximum fow rate of the last puf (t � 226 s) with diferent grid numbers.

Figure 6 :
Figure 6: Schematic diagram of the scale-up experimental device: (a) temperature recorder; (b) thermocouple; (c) electronic balance; (d) heater; (e) sleeve; (f ) quartz tube; (g) Cambridge flter; (h) wires; (i) thermostat; (j) power supply; (k) glass rotor fow meter; (l) vacuum pump; ① measurement point on the surface of the heater; ② measurement point at a distance of 0.5R from the surface of the heater;③ measurement point at a distance of R from the surface of the heater (on the inner wall surface of the sleeve); ④ measurement point at a distance of 0.25R from the surface of the heater; ⑤ measurement point at a distance of 0.75R from the surface of the heater; ⑥ measurement point(s) for the temperature of the aerosol.Te letter "R" represents the distance between the inner surface of the sleeve and the surface of the heater, which is 15.6 mm.

Figure 7 :
Figure7: Comparison between the measured temperatures of the scale-up experimental device and the simulation results ("aerosol" refers to the aerosol temperature; 0.25R refers to the internal temperature within the tobacco substrate at a distance of 0.25R from the surface of the heater.Te naming principles for the other points are the same).

Figure 8 :
Figure8: Puf-by-puf release amount and release efciency of (a) water, (b) glycerol, and (c) nicotine corresponding to diferent initial component ratio conditions ("W5%, G12%" refers to 5% water content and 12% glycerol content in the tobacco substrate.Te naming principles for the other working conditions are the same).

Figure 11 :Figure 12 :
Figure 11: Puf-by-puf release amount and release efciency of (a) water, (b) glycerol, and (c) nicotine corresponding to diferent tobacco fller mass conditions ("220 mg" refers to the working condition with a tobacco fller mass of 220 mg.Te naming principles for the other working conditions are the same).

Table 1 :
Overview of boundary and initial conditions in the simulation.
s in equations (

Table 3 :
Results of the ftted reaction kinetic parameters for the studied tobacco substrate.
Note.(1) "Water 1" denotes the frst phase transition that promotes the release of water, and "Water 2" denotes the secondary phase transition.Te naming principle for other numbered reactions is the same; (2) the maximum release rate � the maximum mass of component that can be released during the release process/the total mass of tobacco.

Table 4 :
Geometric parameters of the scale-up experimental device and prototype EHTP stick.

Table 5 :
Model validation of the residual contents in the tobacco substrate.

Table 6 :
Experimental results of the thermal properties of tobacco sheets at diferent temperatures.

Table 7 :
Parameter ftting results of the thermal conductivity model.

Table 8 :
Experimental results of the thermal properties of tobacco accumulation body.

Table 9 :
Termal conductivity calculated by the thermal conductivity model and its deviation from the experimental values.