1 Introduction

As the city develops and lifestyle changes, vehicle gradually changes from luxury to mass consumer product. Allnutt ‘s research [1] shows that thermal discomfort can reduce driver’s efficiency and may cause misoperation. Uncomfortable thermal environment can easily lead to nausea, chest tightness and other symptoms that affect driving safety [2].Therefore, it is increasingly important to guarantee the thermal comfort of vehicle driver.

However, due to the particularity of the structure and operation of vehicle, the thermal environment inside the vehicle cabin is very different from that of the building. Firstly, its internal thermal environment is susceptible to the external. Secondly, vehicles are more affected by solar radiation than buildings. Thirdly, the inner space is small and the layout is complex, which is greatly affected by the air conditioning. Therefore, the thermal environment of vehicle cabin has a feature of high non-uniformity and transient state.

Due to the above reasons, many studies on thermal comfort in buildings cannot be directly applied to vehicle cabin. Many scholars have studied the thermal sensation or thermal comfort of vehicle cabin’s passengers based on the characteristics of vehicle environment. Mezrhab and Bouzidi [3] developed a numerical model that studies thermal comfort of cars in terms of changes in solar radiation, type of glass, color of car, and the radiation characteristics of the materials in the car. Han [4] et al. used a three-dimensional model in the RadTherm which is an advanced thermal management design and analysis tool developed by ThermoAnalytics and Ford Motor Company to evaluate the effects of different environmental thermal loads on thermal comfort. Kaynakli [5] used the empirical equations to calculate the human sweat rate and the average skin temperature based on the body heat balance equation, and analyzed the effect of heating and cooling process on body heat exchange. A numerical model for the exchange of heat and mass between the human body and thermal environment inside the vehicle under steady-state conditions was established [6], which could calculate total sensible and latent heat loss, skin temperature, skin moisture rate, PMV and PPD value. Guan et al. [7] used environmental chambers to simulate 16 typical winter and summer conditions for human comfort experiments and examined data from vehicle cabins under high transient conditions. Their following study established a thermal sensation model [8] that combines both physical and psychological factors and uses environmental and personal parameters to determine physiological responses. Taniguchi [9] developed a multiple linear regression model based on tests. The overall thermal sensation in this model is only related to the thermal sensation of the facial part while ignores the effect of other body parts. Zhang [10,11,12] et al. established a local and overall thermal sensation and thermal comfort model by thermal reaction experiments through a sleeve of conditioned air that enclosed the segment. Zhang Wencan [13] conducted a cooling experiment on the idle vehicle in South China and used the human thermal regulation model coupling with the cabin environment to make simulations.

Nevertheless, the existing studies on thermal sensation in vehicle cabin are mostly tested under idle condition or laboratories. Few of them have been conducted under driving condition [14,15,16]. Therefore, we conducted experiments in vehicle cabin respectively in driving and idle state in summer and winter to study the difference of thermal environment, human objective and subjective response. This paper reports our findings.

2 Methodologies

The experiment was carried out in a vehicle cabin whose model is BYD E6. The vehicle was placed under an outdoor carport to avoid direct solar radiation under idle condition. The direction which faced the direct solar radiation was avoided as far as possible and the car visor was always kept open. Therefore, the subsequent analysis only considers the temperature variation inside the car caused by diffuse solar radiation without considering direct solar radiation.

2.1 Participants

A total of 15 male and 15 female college students (mean values ±standard deviation of age, 25.5 ± 2.25 years; height, 169.4 ± 7.22 cm; weight, 59.7 ± 9.62 kg) were recruited for the experiments. All subjects were healthy, non-smokers who were not taking any prescription medication and were all approved by the local research ethics committee. Subjects were asked to avoid alcohol, smoking, and intense physical activity at least 24 h prior to each experimental session. In order to avoid the impact of clothing differences on test results, all subjects were required to wear uniform clothes of short sleeves, shorts and sandals in summer while long sleeves, trousers and sneakers in winter.

2.2 Design of Experiment

2.2.1 Arrangement and time schedule

Before the start of the experiment, each sensor was arranged in the vehicle cabin. The subjects involved in the experiment rested in the office where the temperature was close to the thermal comfort zone, and they could only sit still or walk around. After the arrangement of the measuring points was completed, the passenger compartment doors were kept open for one hour, so that the environment of the vehicle cabin could be consistent with the external. After an hour, close all the doors and let the cabin lay for an hour. During this time, the skin temperature probes were placed on the test positions of the driver. After the phase was over, the driver entered the car, turned on the air conditioning and set the temperature of the automatic mode. The direction of the air vents were kept horizontal. All instruments were turned on and kept for an hour. It should be noted that since the driver needs to drive the car under driving condition, the rear row also enters a recorder at the same time. Multiple experiments were performed per person per condition.

2.2.2 Experimental conditions

The experimental conditions are shown in Table 1. The set status of air conditioning is automatic and inner loop.

Table 1 Experimental conditions.
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Table 2 Main equipment configuration.
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Fig. 1
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Front view of the measuring points

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Fig. 2
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Top view of the measuring points

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Fig. 3
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Human skin temperature measurement points map

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Fig. 4
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Thermal sensation scale used in the experiment

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Fig. 5
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Driving speed map under driving condition

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Fig. 6
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Variation of air temperature in refrigeration condition

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Fig. 7
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Variation of relative humidity in refrigeration condition

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Fig. 8
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Variation of mean skin temperature (MST) and overall thermal sensation (OTS) in refrigeration condition

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Fig. 9
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Variation of heat transfer in refrigeration condition (C + R: convective and radiant heat loss, Con: conductive heat loss, Re: respiratory heat loss, E: evaporative heat loss)

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Fig. 10
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Driving speed map under driving condition

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Fig. 11
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Variation of air temperature in heating condition

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Fig. 12
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Variation of relative humidity in heating condition

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Fig. 13
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Variation of mean skin temperature (MST) and overall thermal sensation (OTS) in heating condition

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Fig. 14
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Variation of heat transfer in heating condition (C + R: convective and radiant heat loss, Con: conductive heat loss, Re: respiratory heat loss, E: evaporative heat loss)

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Fig. 15
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Variation of total heat exchange and heat storage rate in refrigeration condition

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Fig. 16
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Variation of total heat exchange and heat storage rate in heating condition

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Fig. 17
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Relationship between mean skin temperature (MST) and overall thermal sensation (OTS)

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Fig. 18
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Relationship between actual thermal sensation (OTS) and PMV value in summer condition

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Fig. 19
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Relationship between actual thermal sensation (OTS) and PMV value in winter condition

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2.2.3 Parameter measurement

The location of the collection points is shown in Figs. 1 and 2. The 1st-3rd point measure the temperature and wind speed around foot, abdomen and head. The 4th–5th point measure the temperature of base and back of seat. The 6th point measures the relative humidity around the driver and the 7th point measures globe temperature (refers to the comprehensive temperature expressed by temperature index when a person or an object is subjected to the combined effects of radiant heat and convective heat in a radiant heat environment). The temperature data was collected every 5 s, the relative humidity data was collected every 5 min and the globe temperature was collected every 1 min.

2.2.4 Driver’s parameter measurement

The objective parameters of body are the skin temperature. The position of each measuring point of body is shown in Fig. 3. The 1st-4th point is the skin temperature of the head, chest, back, and abdomen respectively. The 5th–7th is that of left upper arm, left lower arm, and left hand skin, respectively. The 8th -10th is that of the corresponding right arm. The 11th -13th is that of left thigh, left calf, and left foot respectively. The 14th -16th is that of the corresponding right leg. Skin temperatures were collected every 5 s.

The overall thermal sensation is the overall cold or hot feeling of people in an environment. As shown in Fig. 4, the subjective thermal sensation evaluation was evaluated by the thermal comfort questionnaire proposed by the ASHRAE standard [17]. This article only surveyed the overall thermal sensation and recorded it every 5 min. The driver’s voting value was recorded by the rear recorder under driving condition.

2.2.5 Experimental equipment

The main device configuration of the test system is shown in Table 2:

3 Data manipulation

Before the data processing, normality test was carried out for multiple experiments of single-person and single-condition. The experiments with large deviation were excluded and the mean value of the remaining experiments was taken as the experimental result of single-person and single-condition. Finally, the average of experimental data of 30 people in single-condition was taken as the experimental result of the condition.

3.1 Mean skin temperature

Due to non-uniform environment inside the car, using area weighted values is a safe measure to consider the local skin temperature difference. Thus, mean skin temperature is an area-weighted value as shown in formula (1-1):

$$ \overline{t_{sk}}=\int {t}_{sk}d{A}_{sk}/A $$
(1-1)

where tsk is the local skin temperature, dAsk is the corresponding local surface area, and A is the total area. The specific values refer to Butera’s research results [18].

3.2 Mean air temperature, wind speed and mean radiant temperature

The temperature-weighted PMV model of Matsunaga [19] used weighted air temperature to calculate the PMV in a non-uniform thermal environment. This article refers to its method and calculation is shown in formula (2-1):

$$ {t}_a=0.1\times {t}_{head, air}+0.7\times {t}_{abdomen, air}+0.2\times {t}_{foot, air} $$
(2-1)

where thead,air, tabdomen,air and tfoor,air are the temperature of air around head, abdomen and foot. The mean wind speed is calculated by referring to the influence factors in (2–1). Its calculation is shown in formula (2-2):

$$ {v}_a=0.1\times {v}_{head, air}+0.7\times {v}_{abdomen, air}+0.2\times {v}_{foot, air} $$
(2-2)

where vhead,air, vabdomen,air and vfoor,air are the speed of the air around head, abdomen and foot. va is the mean wind speed.

According to the ISO7726 [20] standard, the mean radiant temperature calculation for forced convection is as shown in eq. (2-3):

$$ {\displaystyle \begin{array}{l}{t}_r=\left[{\left({t}_g+273\right)}^4\right.\\ {}\kern1.98em {\left.+\frac{1.1\times {10}^8\times {v_a}^{0.6}}{\varepsilon_g\times {D}^{0.4}}\times \left({t}_g-{t}_a\right)\right]}^{1/4}-273\\ {}\kern1.98em \end{array}} $$
(2-3)

where tr is the mean radiant temperature, εg is the black ball emissivity which is about 0.95, D is the diameter of black ball which is 0.04 m in our experiment and tg is the globe temperature.

3.3 Human body heat exchange

Heat dissipates from the body to immediate surroundings by several modes of heat exchange: sensible heat flow (including convection and radiation), latent heat flow from sweat evaporation and from evaporation of moisture diffused through the skin, sensible heat flow and latent heat flow from evaporation of moisture during respiration.

The following expression is the thermal balance equation:

$$ {\displaystyle \begin{array}{l}\left(M-W-S\right)\cdot A={C}_v\cdot {A}_v+{C}_d\cdot {A}_d+R\cdot {A}_r+\\ {}\kern8.249999em {E}_{sk}\cdot A+\left({E}_{res}+{C}_{res}\right)\cdot A\end{array}} $$
(2-4)

The M of driver is about 1met when the car is idle and 1.2–1.7met when the car is driving [21]. An average-1.45met under driving condition was taken (1met = 58.15 W·m-2). The W is generally 0 [22]. A, Av, Ad, Ar are respectively the area of total area of the human, that of convective heat, that of conduction and that of radiant heat.

Fanger [23, 24], Gagge [25], Hardy [26] and Rapp [27] give quantitative information on calculating heat exchange, which has been adopted in ASHRAE [28] and related standard. The calculation formulas used in this paper are mainly based on the ASHRAE standard [28] assisted with other studies.

Convective heat loss:

$$ {C}_v={f}_{cl}{h}_c\left({t}_{cl}-{t}_a\right) $$
(2-5)

Radiant heat loss:

$$ R={f}_{cl}{h}_r\left({t}_{cl}-{t}_r\right) $$
(2-6)

In addition:

$$ {h}_r=4\varepsilon \sigma \frac{A_r}{A}{\left(273+\frac{t_{cl}+{t}_r}{2}\right)}^3 $$
(2-7)
$$ {C}_v+R=\frac{\overline{t_{sk}}-{t}_{cl}}{0.155{I}_{cl}} $$
(2-8)

The Cv and R can be solved by combing above four formulas.

Heat loss from respiration:

$$ {E}_{res}=0.0173M\left(5.87-{p}_a\right) $$
(2-9)
$$ {C}_{res}=0.0014M\left(34-{t}_a\right) $$
(2-10)
$$ {R}_e={E}_{res}+{C}_{res} $$
(2-11)

Heat loss from conduction:

$$ {C}_d={k}_{cl}\cdot \frac{t_{sk}-{t}_i}{x_{cl}} $$
(2-12)

where tsk is temperature of the skin which occurs conduction and ti is temperature of seat.

Evaporative heat loss from skin:

$$ {E}_{sk}={E}_{sw}+{E}_{dif} $$
(2-13)
$$ {E}_{sw}={w}_{sw}{E}_{\mathrm{max}}={w}_{sw}\cdot h^{\prime}\cdot {i}_m\cdot LR\cdot \left({P}_{sk,s}-{P}_a\right) $$
(2-14)
$$ {E}_{dif}=0.06\left(1-{w}_{sw}\right){E}_{\mathrm{max}} $$
(2-15)

To solve Esk, we need to know wsw. Therefore, we import another method to calculate Esw as shown formula (2-16):

$$ {E}_{sw}={r}_{ev}{m}_{sw}{h}_{fg}/3600=\left(1-\frac{w^2}{2}\right){m}_{sw}{h}_{fg}/3600 $$
(2-16)

The study of Kubota’s study [29, 30] proposed an assumption that the regulatory thermal sweating rate is a linear function of the deviation of mean skin temperature from that of thermal neutrality and it has been verified based on Stolwijk’s data for none-heat acclimated people:

$$ {m}_{sw}=0.63\left(M-W-58\right)+50\left(\overline{t_{sk}}-\overline{t_{sk,0}}\right) $$
(2-17)

In addition:

$$ w=0.06+0.94{w}_{sw} $$
(2-18)

The wsw can be solved by combing the formula (2–14), (2–16), (2–17), (2–18) and then the Esk can be solved. The other values are determined according to ASHRAE Handbook [25] too.

In the subsequent analysis, when body absorbs heat from the environment, the heat is negative, and when body releases heat to the environment, the heat is positive.

The PMV model proposed by Fanger [23] meaning the Predicted Mean Vote of subjects is also calculated to compare with the actual overall thermal sensation. The formula is as follows:

$$ \mathrm{PMV}=\left(0.303{e}^{-0.036M}+0.028\right) TL $$
(2-19)

TL means human thermal load reflecting the degree of deviation from the body’s thermal balance. Its specific calculation can be seen ASHRAE Handbook [25].

4 Results

4.1 Summer condition

4.1.1 Vehicle speed, air temperature and relative humidity

As Fig. 5 shows, the driving speed distribution basically conforms to the normal distribution, which 35% of driving time keeps driving speed in 61–80 km/h and the percentage on both sides is lower. The percentage in 0–20 km/h doesn’t match normal distribution, which is because the vehicle needs to deal with various traffic conditions during driving.

Figures 6 and 7 show the variation of air temperature and relative humidity in refrigeration condition. It can be seen that as the cooling progresses, the temperature continues to drop and the relative humidity rises and eventually stabilizes. On the other hand, air temperature under driving condition is always higher than that under the idle condition and as a result the relative humidity is exactly the opposite. This may be due to the movement of vehicle enhances heat transfer between the vehicle surface and the external environment [31].

4.1.2 Mean skin temperature and overall thermal sensation

Figure 8 shows the variation of mean skin temperature and overall thermal sensation in refrigeration condition. It can be seen that due to the excessive initial temperature in the car, the mean skin temperature has experienced a brief rapid increase, then slowly declines and eventually stabilizes. The trend of overall thermal sensation is similar. It is worth noting that the rising phase under driving condition lasts longer and the maximum skin temperature is higher. The skin temperature difference is small when stable, but the overall thermal sensation is lower under idle condition.

4.1.3 Heat transfer

Figure 9 shows the variation of heat transfer in refrigeration condition. The amount of heat loss from respiration is small and does not change much. The heat conduction gradually becomes 0 as the temperature difference between back and seat decreases. Convective and radiative heat transfer gradually shifts from absorption to release. Evaporative heat transfer undergoes a process of slowly increasing and then slowly decreasing because of change in body sweat. Respiration and conduction heat are not much different in different driving states. The amount of convective and radiative heat and evaporative heat under driving condition are always more than that under idle. This may prove that the increase in speed can promote the heat transfer coefficient between body and surrounding system. In addition, this shows that in summer the car air-conditioning system can further reduce the blowing temperature and relative humidity within the first 20–30 min to improve the sensible and latent heat exchange of body, thereby reaching thermal comfort faster.

4.2 Winter condition

4.2.1 Vehicle speed, air temperature and relative humidity

As Fig. 10 shows, the driving speed distribution is similar to that in summer. Figures 11 and 12 show the variation of air temperature and relative humidity in heating condition. The trend of change is basically the same as the summer condition, but the direction is opposite. Air temperature under driving condition is always lower than the idle, which leads the diversity in relative humidity.

4.2.2 Mean skin temperature and overall thermal sensation

Figure 13 shows the variation of mean skin temperature and overall thermal sensation in heating condition. It can be seen that the mean skin temperature experiences a slow rise and eventually stabilizes, which is similar as overall thermal sensation because of increase of temperature inside the car. There is no turning point that exists in the summer condition. Mean skin temperature is always higher under driving condition than that under idle. The overall thermal sensation at initial stage is almost the same, but it is higher under driving condition in late stage of the experiment.

4.2.3 Heat transfer

Figure 14 shows the variation of heat transfer in heating condition. Except the convection and radiation heat transfer, the other forms of heat exchange are small and change little. Convection and radiation heat transfer rapidly decrease in the first ten minutes and they are higher under driving condition, which further demonstrates that the increase in speed can promote the heat transfer coefficient between body and the surrounding system. But when this stage is over, they only slowly decrease and are almost identical under different driving conditions. In addition, from the view of control, in the winter the car air conditioner can further increase the blowing temperature in the first 20–30 min without considering the relative humidity (relative humidity needs to be considered in summer), thereby making the subject reach thermal comfort faster.

5 Discussions

5.1 Total heat exchange and heat storage rate

Figures 15 and 16 show the variation of total heat exchange and heat storage rate in refrigeration and heating condition. Q is the total heat exchange of the human body. Sa is the total heat storage rate. Under the refrigeration condition, the total heat has undergone a change of direction and reaches the maximum and stabilizes at 20 min. To the opposite, heat storage rate reduces quickly first and then gradually flatten. Total heat exchange under driving condition is always higher than that under idle. The change of total heat under heating condition is similar as convection and radiation heat transfer under heating condition. On the other hand, no matter which season, heat storage rate under driving condition is always higher than that under idle. Therefore, it can be concluded that divergence of heat storage rate is mainly caused by differences in metabolic rate in different driving states instead of discrepancy in heat exchange.

At the same time, it can be seen that, heat storage rate is almost stable after 20 min. But the overall thermal sensation is stable until the last 10 min of the experiment. Therefore, the overall thermal sensation of body in the dynamic thermal environment of the car is not suitable to be characterized by the heat storage rate.

6 Linear relationship between mean skin temperature and overall thermal sensation

Figure 17 shows the relationship between mean skin temperature and overall thermal sensation. It can be seen that they have such a good linear correlation under different conditions that skin temperature can be used to characterize overall thermal sensation, which is consistent with Zhou’s [32] view. However, there are differences in linear coefficients under different conditions. The linear coefficient in summer under driving condition is lower than that under idle. Although there are also differences of linear coefficients in winter, the difference is small. Therefore, for winter condition, skin temperature under idle condition can be used to characterize overall thermal sensation under driving. Accuracy will be lower if this method is adopted in summer.

6.1 Applicability of PMV model

Figures 18 and 19 show the relationship between actual thermal sensation and PMV value. They show that in idle state data points are almost in the range of −0.5 to +0.5, which demonstrate that PMV can reflect the true overall thermal sensation accurately. However, in driving state accuracy will be reduced to some extent. The degree of reduction under summer condition is very low. Therefore PMV can still reflect the true thermal sensation. Nevertheless, in winter condition the deviation is mainly concentrated in +0.5 to +1, which demonstrates that PMV can’t reflect the true overall thermal sensation. Thus, except the driving condition in winter, PMV can be used to represent true overall thermal sensation.

7 Conclusions

We conducted experiments in the automatic mode of air conditioning in a vehicle respectively in summer and winter in different driving states, measuring the cabin’s environmental parameters and human objective and subjective parameters. The heat transfers of body were calculated and analyzed. The study led to the following conclusions:

  1. 1)

    The temperature and humidity‘s change with time of the passenger compartment will be affected by the driving state under the same set temperature as well as occupant’s skin temperature and overall thermal sensation.

  2. 2)

    Convective and radiative heat transfer in both seasons and evaporative heat transfer in summer change dramatically over time and are affected by the driving state while other forms of heat transfer keep basically stable.

  3. 3)

    The total heat storage rate is mainly affected by the difference in metabolic rate under different driving conditions of body rather than the difference in total heat transfer.

  4. 4)

    OTS and MTS have a good linear correlation but different linear coefficients under different conditions, which are less affected by driving states in winter.

  5. 5)

    PMV can accurately reflect real OTS under idle condition in both seasons and under driving condition in summer. But PMV has a large deviation under driving condition in winter.

There are still some limitations in this article. For example, this article ignores the effects of direct solar radiation which has an important influence in the actual driving process. In addition, when there are a large number of people in the car, environment inside the car will change due to human heat dissipation, which means thermal sensation is different when the same vehicle is populated with full-capacity and under-capacity. On the other hand, this article only analyzes the overall thermal sensation, without examining the local thermal sensation. Future research will be carried out from above perspectives and then more reliable and practical control strategies can be put forward.