Study of nasal heating function based on 40 cases of nasal cavity model

Abstract

The geometric structure of the nasal cavity has a certain influence on the heating function. In this paper, a study with a larger sample will be conducted to investigate the differences in the heat transfer function of the nasal cavity on the breathing airflow.

Nasal CT images from 40 healthy volunteers were obtained to establish 40 computational models for numerically simulating the heating function of the nasal cavity. These 40 nasal models were classified into four categories based on surface area-to-volume ratio, mean airway width, nostril size, and Intake direction. And the impact of four indicators on heating function was compared. Results: In terms of overall nasal heating function, the correlation coefficient r between surface area to volume ratio and nasal heating function was 0.639. The correlation coefficient r between average airway width and nasal heating function was − 0.572. For the anterior region of the nasal cavity heating, the correlation coefficient r of nostril size was − 0.452. There is no obvious correlation between the intake direction and the heating function, but the intake direction will affect the direction of the air flow and indirectly affect the overall heating function. Conclusion: In the overall nasal heating process, the parameters influencing heating effectiveness, in descending order, are surface area-to-volume ratio, mean airway width, nostril size, and Intake Angle size.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-45098-9.

Introduction

As a crucial organ in the human body, the nasal cavity performs an essential physiological function of adequately conditioning the inhaled air, thereby enhancing the efficiency of gas exchange within the alveolar capillaries. The heating capability of the nasal cavity is intimately tied to an individual’s daily life^1,2. If the nasal warming function is poor, it may lead to insufficient heating of the inhaled air. When the airflow reaches the pharynx or lungs at a suboptimal temperature, it can cause irritation in these areas and potentially contribute to respiratory conditions. Therefore, conditioning the temperature of inhaled air is one of the primary functions of the nasal cavity in protecting the lower airways. Extensive research on the nasal heating function has validated that the anterior region of the nasal cavity serves as the primary site for heat exchange during inspiration^3–7. Na et al. suggested that, assuming a steady flow rate of 250 mL/s, the heat recovery during expiration is approximately one-third of the heat supplied during inspiration⁸. Lindemann et al. measured the mucosal temperature during breathing and believed that the nasal volume and blood temperature along the nasal airway were related to the mucosal temperature, so they considered the nasal volume and blood temperature along the nasal airway to be the most important predictors of the regulation of nasal heating function^8,9. Chung S et al. further discovered that during inspiration, there are notable changes in epithelial surface temperature and surface heat flux, whereas during expiration, these changes and their magnitudes diminish significantly¹⁰.Borojeni et al.¹¹ hold that the normal range of the average unilateral thermal flux from the nostril to the posterior nasal aperture is 94 ± 29 to 281 ± 58 W/m2. Sullivan C D et al.¹² confirmed that the average nasal thermal flux > 50 W/m2 can predict the nasal congestion symptom score. Meanwhile, Kimbell et al.¹³ conducted CFD simulations on patients with nasal airway obstruction before and after surgery, and also found that airflow and thermal flux can be objective assessment indicators for nasal airway obstruction conditions.

Differences in the structure of the nasal cavity will also affect the heating function of the nasal cavity. For example, Garcia et al. established a case of atrophic nose and four healthy human noses, and compared their calculated results of heat transfer to study the difference in heating function between pathological nasal cavity and normal nasal cavity¹⁴. Lindemann J et al. established three nasal cavity models with different positions of nasal septum perforation and one nasal cavity model without nasal septum perforation, and compared the heating function of inspiration. Numerical simulation showed that the heating effect of nasal cavity on air was reduced due to the influence of nasal septum perforation. and the perforation model at the Limen nasi had the greatest impact on the heating function of the nasal cavity. This not only shows the importance of the heating function of the anterior area of the nasal cavity, but also shows that the structure of the nasal cavity can affect the heating function¹⁵.

Some structural geometric features also affect the heating function of the nasal cavity. For example, Sara Vahaji et al. compared the heat transfer of the nasal cavity between a human and a monkey, and found that the surface area to volume ratio of the nasal cavity of the monkey was smaller than that of the human nasal cavity, and the heat transfer effect of the monkey was more effective¹⁶. Phuong N L et al. established nasal cavity models of two human cases and found that the model with greater nasal intake speed at the same flow rate had greater convection heat transfer coefficient¹⁷. Xiao Q et al.¹⁸ found through a comparison before and after nasal congestion relief in 10 healthy subjects that nasal congestion relief would reduce blood flow in the turbinate, thereby expanding the airway cavity. After nasal congestion was relieved, the amount of heat absorbed from the inhaled air would be reduced.

In this paper, the imaging data of a large sample of human nasal cavity were collected, and 40 human nasal cavity models were established to study the influence of different nasal structures on the heat transfer function of respiratory airflow. The large data were used to solve the data bias caused by the differences in human nasal cavity, and the results were more universal and practical. Forty nasal cavity models were classified into four categories according to the ratio of surface area to volume, average airway width, nostril size and inlet direction, and their effects on heating capacity were compared. A correlation model between wall heat flux and four geometric parameters was established. Through comparative analysis of parameter correlations, a multiple linear regression equation was further developed to quantify the influence degree of each parameter on the heat flux.

Materials and numerical simulation methods

Construction of nasal cavity model

For the establishment of the model, healthy adult volunteers aged 18–55 years were recruited, and people with nasal and paranasal sinus diseases such as allergic rhinitis and nasal surgery patients were excluded. Nasal endoscopy showed no deviation or mild deviation of nasal septum, mucosal edema, turbinate hypertrophy, nasal obstruction and snoring symptoms. The sample included 40 volunteers, including 25 males and 15 females, with an average age of (31.5 ± 7.4) years. The patients were asked about medical history, underwent endoscopy and nasal resistance testing. After 30 min of quiet rest, the volunteers underwent spiral CT scan of the upper airway. Written informed consent was provided to the subjects to inform them of the purpose and process of the study, and their cooperation was obtained. The study protocol was approved by the Ethics Committee of Dalian University of Technology (DUTVEM20230912-02).

Using Mimics 21.0 to extract the obtained nasal CT data, and then using Geomagic Warp 2021 to smooth and reconstruct the geometric structure of the nasal airway and exclude the bilateral maxillary sinus cavities. The model was divided into grids, using tetrahedral elements. After the verification of grid independence, the entire nasal airway structure was divided into approximately 2 million elements and 1.2 million nodes. The governing equations include: continuity equation, N-S equation and energy equation.

The governing equations include: continuity equation, N-S equation and energy equation¹⁹.

continuity equation:

1-1

N-S equation:

1-2

In Eqs. (1–1) and (1–2), u is the velocity vector, P is the fluid pressure, ρ is the fluid density, and µ(T) is the dynamic viscosity Eq. (1–3) .

Energy equation:

1-3

Where T is the space temperature field, is the specific heat, k is the heat conduction coefficient, and S is the source term. In this study, the influence of the source term is not considered. The physical parameters of the air are as shown in Table 1 below.

Table 1.

Physical Parameters of Air.

				S
1.225 kg/m3	1.8135 × 10− 5N·s/m2	1.0059 kJ/(kg/J)	0.0268 W(m·℃)	0

Boundary condition setting

Ansys Fluent 2022 software can be used to numerically analyze the nasal heating function during breathing. Due to the relatively low airflow rate set in this study, the respiratory flow was considered incompressible and laminar. The boundary conditions for the numerical simulation of the nasal cavity model were primarily defined based on the normal human nasal volumetric flow rate, ambient pressure, and ambient temperature^20,21. :

1. The nasal airway wall was set as no slip and no penetration condition, that is, V = 0 m/s;

2. The front nostril is connected with the outside world, and is set as the relative pressure of the pressure inlet P = 0 Pa;

3. Set the ventilation volume at the velocity inlet to 200 ml/s and the corresponding tidal volume to 500 ml;

4. During the exhalation, the nasopharynx was set as the outlet of air velocity. The temperature is set to 36.5 ℃;

5. The nasal cavity wall surface is set as four parts as shown in Fig. 1, which respectively represent the Limen nasi, inferior turbinate head, the head of the middle turbinate and the nasopharynx. The temperatures of the Limen nasi, the head of the inferior turbinate, the head of the middle turbinate and the nasopharynx during exhalation are set at 33.7℃, 33.93℃, 35.31℃ and 36.26℃ respectively; while during inhalation, they are set at 33.58℃, 33.74, 35.19℃ and 36.14℃ respectively²²;

Fig. 1.

Map of the Four Regions of the Nasal Cavity.

This study does not take into account the calculation of latent heat and humidity, flow to ordinary air as the medium, and simplified as incompressible Newtonian fluid.

Results

40 cases of nasal cavity model of different location of the heating condition

After the nasal cavity model of 40 cases was established, the minimum coronal cross-sectional area and its hydraulic diameter were measured for each nasal cavity model, and the nasal resistance of each cavity was determined based on the pressure difference across the nasal passage, as presented in Table 2.

Table 2.

Geometric measurements and nasal resistance for each nasal model.

No.	MCA	Hd	NR	No.	MCA	Hd	NR
1	80.7	5.6	60.7	21	74.2	7.5	75.7
2	81.1	6.2	79.2	22	70.5	6.4	82.7
3	79.6	7.7	70.0	23	68.9	7.1	51.6
4	50.4	5.9	69.3	24	70.3	7.7	54.9
5	119.5	9.0	26.3	25	86.7	9.1	22.7
6	106.9	7.7	55.1	26	80.5	8.5	26.5
7	78.0	6.4	48.5	27	70.8	7.3	46.5
8	70.5	7.6	45.5	28	88.9	8.5	50.5
9	98.7	9.1	69.8	29	40.2	5.9	26.6
10	67.5	7.1	44.0	30	68.2	8.4	81.5
11	64.0	7.1	22.9	31	35.4	5.5	26.6
12	71.8	7.2	29.0	32	34.5	4.9	27.7
13	91.5	8.7	14.2	33	64.0	8.0	22.8
14	82.1	8.4	12.5	34	51.4	6.8	15.2
15	56.2	5.8	25.5	35	45.4	5.8	88.0
16	86.0	8.9	33.4	36	56.4	5.9	99.8
17	98.1	8.6	43.0	37	57.5	6.4	50.7
18	69.8	7.2	47.2	38	58.1	6.4	48.9
19	67.1	6.1	42.0	39	41.1	4.7	39.3
20	62.4	7.1	30.6	40	45.6	5.0	42.2

MCA: minimum coronal cross-sectional area (mm²).

Hd: hydraulic diameter (mm).

NR: nasal resistance (pa/L/s).

The temperature of Limen nasi, anterior end of inferior nasal concha, anterior end of middle nasal concha, middle end of middle nasal concha and nasopharynx were counted. The average value and standard deviation of different positions during exhalation of 40 cases were drawn as shown in Fig. 2a, showing that the temperature difference between Limen nasi and nasopharynx was not large. The average and standard deviation of temperature at different positions during inspiration in 40 cases were drawn as shown in Fig. 2b. It can be seen that the front end of the nasal cavity is the main heating area during inspiration, which is consistent with the existing conclusions^3–7.

Fig. 2.

(a) the mean and standard deviation of temperature at different locations during exhalation in 40 cases, (b) the mean and standard deviation of temperature at different locations during inspiration in 40 cases, (c)A case of nasal section cloud map and measurement sites on streamlines, (d) 12 cases of different temperature distribution in a streamline of the nasal cavity.

Compared with the temperature changes on different streamlines during inspiratory process, six planes were intercepted on the nasal cavity, starting with the inferior meatus, set at 0 mm, and each plane was separated by 10 mm. The point on a streamline of the middle meatus and the inferior meatus in each section was selected as the nasal temperature measurement point, as shown in Fig. 2c. The temperature values of 12 different nasal cavities on the streamline of the middle meatus and the inferior meatus were selected for comparison, as shown in Fig. 2d. It was found that the inferior nasal meatus was 1–2 degrees Celsius higher than the middle nasal meatus in the same section, indicating that the middle nasal meatus bears more heating work.

The classification of 40 cases of nasal cavity model and heating conditions

According to the study of Yu Shen et al.²⁰, nasal airway structural parameters such as airway surface area, volume and length of nasal passage have a certain influence on nasal heating. The following will be grouped according to several geometric features to study the influence on nasal airflow heating function. The principle of grouping is explained in detail in the supplementary materials, as shown in Figure S1.

The first kind of geometric features: The surface-to-volume ratio of the nasal cavity directly affects the heating efficiency of the nasal cavity, and is sorted according to the ratio of surface area (S) to volume (V)and grouped according to the standard normal distribution.

Second geometric feature: the width of nasal airway is an important factor of nasal heating. 40 cases of nasal cavity were classified according to the mean width of airway. The average width was defined by taking the Limen nasi, the anterior end of the inferior concha, the anterior end of the middle concha and the nasopharynx as the measurement section, as shown in Fig. 3a. The upper, middle and lower values of the left and right nasal airways in each section were taken for average calculation as the representative value of the section, and then the representative values of several sections were calculated on average to obtain the average airway width. The average airway width was ranked and divided into groups according to the ratio of 1∶1.

Fig. 3.

(a) Average airway width diagram of a model cross-section, (b) intake direction diagram, (c) nasal section position diagram.

Third geometric feature: The size of the nostril directly affects the air intake speed, and the air intake speed will affect the front heating ability of the nasal cavity. Consequently, 40 nasal cavities were sorted in ascending order based on the size of their nostrils, and subsequently grouped in accordance with the standard normal distribution.

The fourth geometric feature: the different intake direction of air flow will directly affect the path of air flow. As shown in Fig. 3b, the Angle between the intake direction and the nasal base direction is taken as the Angle of the intake direction, sorted according to the Angle of the intake direction, and grouped according to the ratio of about 1:1.

The above is the group of 40 cases of nasal cavity, which is drawn into a table as shown in the Table 3 below.

Table 3.

Nasal group of 40 cases.

Geometric feature definition	The first geometric feature			The second geometric feature		The third geometric feature			The fourth geometric feature
	Surface-volume ratio			Mean airway width		Nostril area size			Intake Angle
Grouping Method	standard normal distribution			The ratio is roughly 1:1		standard normal distribution			The ratio is roughly 1:1
Group name	a1	a2	a3	b1	b2	c1	c2	c3	d1	d2
Count of Scores	6	28	6	20	20	6	28	6	20	20
Group Definition	less than 0.565	between 0.565 and 0.878	greater than 0.878	less than 1.8 mm	greater than 1.8 mm	less than 40mm2	between 40 and 111mm2	greater than 111mm2	greater than 60°	less than 60°

In the Limen nasi by taking seven ZX plane surface, capture the first plane in Limen nasi is set to 0 mm, each plane interval of 10 mm, as shown in Fig. 3c, The heating function of each nasal cavity was analyzed by the size of the average surface value.

The values of all sections of the nasal cavity in group a1 were calculated, and then the values of each section in Group a1 were averaged as the representative values of group a1. Similarly for other groups, the value of the second Sect. 10 mm away from the Limen nasi represented the heating results of the anterior nasal area, and the value of the seventh Sect. 60 mm away from the Limen nasi represented the heating results of the entire nasal cavity. The numerical results were shown in Table 4 below.

Table 4.

Nasal group number and the average temperature of the second and seventh sections.

Nasal group number	a1	a2	a3	b1	b2	c1	c2	c3	d1	d2
	6	28	6	20	20	6	28	6	20	20
The second section average temperature/℃	30.2	30.3	30.5	30.3	30.4	31.3	30.2	29.9	29.9	30.8
The seventh section average temperature/℃	33.6	34.9	35.4	35.1	34.5	34.6	34.8	35.2	34.8	34.9

It can be seen from Table 3; Fig. 4 that according to surface-to-volume ratio, there is little difference in the temperature of air flow after heating at the front end. However, after overall heating, group a1 is heated to 33.6℃, group a2 is heated to 34.9℃, and group a3 is heated to 35.4℃. It can be seen that the overall heating function will weaken with the increase of surface-to-volume ratio. According to the average airway width, there was no significant difference in air temperature after heating at the front end. However, after overall heating, group b1 was heated to 35.1℃, and group b2 was heated to 34.5℃. It can be seen that the overall heating function would become weaker with the increase of average airway width. According to the size of the nostril area, there were obvious differences in the temperature of the air flow after heating at the front end. c1 group was heated to 31.3℃ at the front end, c2 group was heated to 30.2℃, and c3 group was heated to 29.9℃, but there was no significant difference in the air flow temperature after overall heating. According to the intake direction Angle of the group, the airflow in the front end and the overall heating d2 group is slightly stronger.

Fig. 4.

(a) Group comparisons according to surface-to-volume ratio, (b) Group comparisons according to airway width, (c) group comparisons according to nostril size, and (d) group comparisons according to intake angle size.

In terms of the overall heating function of the air flow, as shown in Fig. 5a, the ratio of surface area S/volume V has a strong positive correlation with the heating function, and the correlation coefficient is 0.639. As shown in Fig. 5b, there is a negative correlation between the mean airway width and heating function, and the correlation coefficient is −0.572. However, nostril size and air intake direction have no significant correlation with the overall heating, because the back of the nasal cavity has a reserve function, which can compensate for the difference of air flow in the front. As for the heating of airflow in the front area, Fig. 5c shows that there is a negative correlation between the size of nostrils and the heating function of the front of the nasal cavity, with a correlation coefficient of −0.452. However, as shown in Fig. 5d, there is no obvious correlation between intake direction and heating function.

Fig. 5.

(a) Relationship between classification based on surface area-to-volume ratio and overall heating function of the nasal cavity; (b) Relationship between classification based on airway width and overall heating function of the nasal cavity; (c) Relationship between classification based on nostril size and heating function at the anterior end of the nasal cavity; (d) Relationship between classification based on inlet direction and heating function at the anterior end of the nasal cavity.

For the direction of air intake, 3 typical cases of group d1 and d2 were selected here with nostril size between 40 and 70mm². The vector diagram of the lateral section of the nasal cavity of group d1 and group d2 is shown in Fig. 6a and b, showing that most of the airflow in group d1 flows to the middle nasal meatus. In group d2, part of the air flow direction obviously flows to the inferior nasal meatus. The difference of nasal cavity heating at the front end of six cases with different air intake directions was studied, and the temperature of air flow on the flow line of the middle nasal meatus and the inferior nasal meatus was counted. The 0 mm of Fig. 6c is the entrance of the middle nasal meatus, and the 0 mm of Fig. 6d is the entrance of the inferior nasal meatus.

Fig. 6.

(a) Vector diagram of a lateral cross-section in group d1, (b) Vector diagram of a lateral cross-section in group d2, (c) Mean and standard deviation of temperature along the streamline in the middle meatus, (d) Mean and standard deviation of temperature along the streamline in the inferior meatus.

As shown in Fig. 6, excluding the difference caused by the size of nostrils, it can be seen that different air intake directions will affect the airflow direction, resulting in a difference in the inlet temperature of the middle and inferior nasal meatus. The large intake Angle of group d1 will cause most air flow to the middle nasal meatus, and only a small part of air flow to the inferior nasal meatus; the small intake Angle of group d2 will lead to an increase in air flow to the inferior nasal meatus. Therefore, after the front end heating, the inlet temperature of group d1 at the middle nasal meatus was obviously lower than that of group d2, and the inlet temperature of group d1 at the lower nasal passage was obviously higher than that of group d2. In general, the heating function of the inferior nasal meatus belongs to the storage state. The greater the air flow flow to the inferior nasal meatus, the more heating function the inferior nasal meatus will share, and the better the overall heating function will be. It can be seen that although the intake direction is not the main guiding factor in the heating function, it also affects the heating function of the nasal cavity.

Wall heat flux statistics of nasal cavity model

The average area and average heat flux of four regions from the anterior to the posterior of the nasal cavity wall were statistically analyzed. The product of the average area and average heat flux of each region was taken to represent the heat transfer quantity of that region. The total heat transfer quantity of the nasal cavity was obtained by summing the heat transfer quantities of the four regions. The statistical results are shown in Table 5. The average heat flux of the wall surfaces in the four regions for each group was plotted as a bar chart in Fig. 7, where “all” represents the overall data from the 40 nasal cavity models. represents the overall average heat flux of the nasal cavity for this group. Significance tests were conducted separately for each group. The average heat flux of Region 1 was taken as the representative result for the front-end heating effect. The results are shown in Table 6.

Table 5.

Statistics of wall heat flux and total heat transfer in 40 cases of nasal cavity model.

Group	Average area m2				Average heat flux W/m2					Gross heat (W)
	Zone1	Zone2	Zone3	Zone4	Zone1	Zone2	Zone3	Zone4
a1	0.00132	0.00569	0.00737	0.00219	437.84	140.07	89.06	51.6	127.6	2.11
a2	0.00113	0.00635	0.00831	0.00205	535.98	174.10	70.87	39.1	128.2	2.28
a3	0.00129	0.00528	0.00786	0.00185	540.6	221.3	91.3	60.9	172.4	2.80
b1	0.00126	0.00584	0.00822	0.0020	509.35	199.04	78.92	45.5	147.3	2.55
b2	0.00109	0.00634	0.00784	0.0021	520.90	144.15	75.93	44.6	123.7	2.14
c1	0.00089	0.0055	0.00684	0.00222	664.141	152.08	82.23	47.4	136.7	2.11
c2	0.00123	0.00597	0.00777	0.00202	501.446	185.49	80.7	45.8	139.9	2.37
c3	0.00136	0.00685	0.01034	0.00195	434.79	167.67	62.08	40.6	117.9	2.41
d1	0.00116	0.00652	0.00830	0.00187	538.01	159.9	71.05	43.5	128.2	2.28
d2	0.00122	0.00551	0.00779	0.00224	540.09	195.01	85.16	47.1	143.7	2.40
all	0.00119	0.00604	0.00806	0.00204	519.478	176.44	77.69	45.1	137.7	2.39

Fig. 7.

The average heat flux of the regional wall.

Table 6.

Significance Test Among Groups.

Front-end heat flux	a1	a3	p
	437.84 ± 67.42	540.6 ± 76.43	0.033
Total heat flux	127.67 ± 15.94	172.43 ± 55.86	0.0883
	b1	b2	p
Front-end heat flux	509.35 ± 97.73	520.9 ± 176.27	0.95
Total heat flux	147.27 ± 37.27	123.73 ± 26.26	0.048
	c1	c3	p
Front-end heat flux	664.14 ± 234.84	434 ± 79.12	0.0464
Total heat flux	136.76 ± 45.45	117.95 ± 15.56	0.36
	d1	d2	p
Front-end heat flux	538.01 ± 129.37	540.09 ± 160.05	0.5972
Total heat flux	128.19 ± 27.02	148.14 ± 40.12	0.095

This study measured the average heat flux in four regions of the nasal cavity and found that the heating function from the front to the back of the nasal cavity was decreasing. Specifically, at the main heating area at the front end (Region 1), the heat flux of group a3 was significantly higher than that of group a1 (p < 0.05), and group c1 was significantly higher than group c3 (p < 0.01); while there was no significant difference in the front end heat flux between group b and group d. For the overall average heat flux analysis, group b1 was stronger than group b2 (p < 0.05), and group c did not show significant differences. The above results indicate that the heating function of the nasal cavity has a clear spatial gradient feature (stronger in the front and weaker in the back), and groups a3 and c1 enhanced the local heat exchange efficiency through structural differences, while the differences between group b and group d mainly manifested at the overall level rather than in local regions.

From Table 4, it can be seen that the overall average heat flux of the nasal cavity in each group was 116–172.4 W/m². A quantitative relationship model between the overall wall heat flux of the nasal cavity (Y, unit: W/m²) and four key geometric characteristic parameters was established through multiple linear regression: surface area to volume ratio X₁, average airway width X₂, nasal aperture size X₃, and intake angle X₄. The regression analysis results are as follows.

According to the results of the multiple linear regression, the regression coefficient corresponding to the surface area to volume ratio is significantly higher than those of the other three variables, indicating that this parameter best characterizes the heating function of the nasal cavity. The regression coefficient for average airway width is also relatively high, suggesting that this parameter likewise has a considerable influence on nasal warming performance. In contrast, nasal aperture size and intake angle exhibit relatively smaller effects on the overall warming function of the nasal cavity.

All data generated or analysed during this study are included in this published article and its supplementary information files (Table S1).

Discussion

To verify the reliability and accuracy of the numerical model, the temperature increase curves of inhaled airflow in 40 nasal cavity cases were compared with data from existing literature^5,17,23, as shown in Fig. 2b. It can be observed that under similar airflow rates and ambient temperature conditions, the nasal warming of inhaled airflow obtained in this study approximates the results reported by Keck (2000), Phuong (2016), and Kumahata (2010). This indicates that the current numerical simulation method can predict the complex intranasal airflow heating process.

The numerical results of 40 nasal cavity models showed that the faster the airflow, the worse the heating. Similarly, Sara Vahaji and others by comparing the monkey with people, show that high speed have opposite effects on heat transfer, in the speed of the larger area, the heat transfer effect is poorer¹⁶; When the velocity of flow is low, the residence time is prolonged and the heat transfer is better.

For the analysis of the geometric feature, classify four types of nasal cavity, according to the ratio of surface area/volume classification, The smaller the ratio, the worse the heating effect to the end. Sara Vahaji et al. also compared the heat transfer function of the nasal cavity of human and monkey and found that the surface area to volume ratio of monkey nasal cavity was smaller than that of human nasal cavity, and the heat transfer effect of monkey was more effective. This is because the smaller the ratio, the smaller the heat transfer area of the air flow at the same volume, the worse the heating effect¹⁶. Xiao Q et al.¹⁸ conducted a comparative study on 10 healthy subjects before and after nasal congestion relief. They found that after nasal congestion was relieved, the amount of heat absorbed from inhaled air decreased; while after nasal congestion was alleviated, the airflow velocity in the nasal cavity decreased, the airway cavity expanded, and the surface area-to-volume ratio was also affected accordingly.The airway width was also explained when comparing heat transfer in the monkey and human nasal cavity. The airway channel was relatively wider in the human model, which resulted in the formation of a velocity distribution and maximum velocity near the center of the cross section. However, due to the narrower airway channels in the monkey model, the heat transfer effect was more effective than in the human model. For the nostril size, it can be considered that the smaller the nostril, the narrower the nasal cavity in the front of the nasal meatus, and the easier the front heating. However, the nasal cavity has functional reserve, and the air flow through the middle and back of the nasal meatus will make up for the difference in front heating, so the nostril size will not affect the temperature of the air flow after the overall heating.

Repeated simulations of the study by Naftali S et al. showed that the heating of inhaled air was reduced by 12% without the middle turbinate and by 16% without the inferior turbinate, This is because after removal of the middle turbinate and removing the inferior turbinate model surface area volume ratio becomes smaller²⁴; And there is no middle turbinate, a large number of air current will flow to the middle meatus, will let the middle meatus to assume some heating function. It’s the same without the inferior turbinate. This provides evidence that the surface area to volume ratio and the direction of air flow also affect the nasal heating function.

This study, through statistical analysis, found that the overall average heat flux of the nasal cavity ranges from 116 to 172.4 W/m², which is in good agreement with the reference range of single nasal cavity heat flux for healthy adults reported by Borojeni et al.¹¹(94 ± 29 to 281 ± 58 W/m²). The research indicates that the distribution characteristics of nasal cavity heat flux are closely related to geometric structure parameters, among which the surface-to-volume ratio is a key factor affecting the wall heat flux. Notably, the nasal threshold region, as the main heat exchange functional area, has a significantly higher local wall heat flux than other anatomical sites. A quantitative relationship model between the overall wall heat flux of the nasal cavity and four key geometric characteristic parameters was established through multiple linear regression. This model can assist in evaluating the severity of clinical symptoms such as nasal congestion by predicting the heat flux level, providing an objective quantitative reference for clinical diagnosis and treatment decisions.

The four geometric features have an impact on the heating function of the nasal cavity and there are also strengths and weaknesses among each other. In the overall heating, the surface-to-volume ratio has a strong positive correlation with the heating ability of the nasal cavity, and the correlation coefficient r is 0.639, but there is no obvious correlation in the front heating. The size of the average airway width of the nasal cavity also has a negative correlation, the correlation coefficient r is −0.572, but there is no significant correlation in the front heating, because the surface area to volume ratio and the average airway width are the overall geometric parameters, so the front heating ability cannot be measured by the overall geometric parameters. In front heating, nostril size also has a negative correlation with the heating ability of the nasal cavity, the correlation coefficient r is −0.452, but there is no obvious correlation with the heating function of the nasal cavity in the overall heating, because the difference in the middle and back of the nasal cavity will make up for the difference in the front end. The size of the nostrils cannot determine the structure of the entire airway but can determine the airflow velocity before the Limen nasi. There is no obvious correlation between the intake direction and the heating function, but the intake direction will influence the direction of the air flow and indirectly affect the overall heating function. Therefore, in the overall heating process, the heating effect is ranked from large to small as surface area to volume ratio, average airway width, nostril size, and intake direction.

Conclusion

On the heating of the airflow throughout the whole nasal cavity, the ratio of surface area to volume ratio has a strong positive correlation with the heating ability of the nasal cavity, and the average airway width has a negative correlation. Nostril size and intake direction have no strong correlation with the overall heating ability. However, in the front heating, Nostril size has a negative correlation with the front heating of the nasal cavity, and there is no obvious correlation between the inlet direction, but the inlet direction will directly affect the direction of air flow into the nasal meatus, which will also indirectly affect the heating ability of the nasal cavity. In the overall heating process, the heating effect was ranked from large to small as surface area to volume ratio, average airway width, nostril size, and inlet direction. The four geometric parameters have different effects on the overall heating effect, and the numerical analysis results can provide some basis for clinical treatment plans. For example, in the correction of nasal structure, the human nasal cavity can achieve normal heating function by changing the geometric structure.The overall average heat flux of the nasal cavity ranges from 116 to 172.4 W/m2. The statistical data of the heat flux on the nasal cavity wall surfaces can provide a boundary condition for subsequent numerical simulation calculations considering the nasal mucosa., It can also provide data support for nasal clinical surgery.

Limitations

This study focused on investigating the influence of nasal structure on air warming function using 40 nasal models. Accordingly, certain simplifications were made in the boundary condition settings. For instance, the inspiratory flow rate was set uniformly at 200 ml/s for all nasal models. At this flow rate, the intranasal airflow was assumed to be laminar, whereas at higher flow rates, it may become transitional or turbulent^13,17. Moreover, the temperature of the nasal wall surface normally fluctuates periodically with the respiratory cycle. However, as this study assumed steady-state flow, the temperature boundary conditions were assigned fixed temperature values to different anatomical regions¹⁴. In future studies, a more accurate comparison of the nasal warming function between individuals should incorporate subject-specific tidal volume and realistic mucosal temperature variations.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

**Shen Yu** : contributed to conduct execution of the numerical simulation, data analysis and original manuscript writing. **Yuewen Wu** : wrote, reviewed, and revised the original manuscript. **Yan Guo** : The experimental data of nasal heat transfer are provided and analyzed. **Jizhe Wang** : provided CT scan data and reconstructed a 3D model of the nasal airway geometry. **Yuanbo Li** :Participate in data analysis and literature research.

Funding

This work was supported by the National Nature Science Foundation of China (12172082).

Data availability

All data generated or analysed during this study are included in this published article and its supplementary information files. The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.