**1. Introduction**

Over the past decades, China has been experiencing the world's fastest growth in vehicle population. As a result, commuters inevitably spend a substantial amount of time in vehicle cabins due to increased traffic congestions and vehicle population especially in major cities [1]. Epidemiological studies show that long-time exposure to air pollutants is associated with increased risks of morbidity and mortality [2–4], especially high volatile organic compounds (VOCs) concentrations emitted from cabin interiors [5–7] that could lead to respiratory irritation and cancer [8]. Developing advanced methods to identify in-cabin emission sources [9] has become a public health priority for consumers, car producers and government. Some attempts have been made to provide indoor air quality (IAQ) guidelines for passenger cars. For example, the Ministry of Environmental Protection of the People's Republic of China has promulgated national standard the HJ/T 400 "Determination of Volatile Organic Compounds and Carbonyl Compounds in Cabin of Vehicles" and GB/T 27,630 "Guideline for air quality assessment of passenger car". The Japan Automobile Manufacturers Association (JAMA) has

introduced a voluntary approach for reducing the concentration levels of VOCs in the vehicle cabins. The World Health Organization (WHO) provides a guideline of 0.1 mg/m<sup>3</sup> for the protection of public health from risks due to a number of chemicals commonly found in indoor air [10,11].

The factors controlling in-vehicle VOCs levels have been identified as a combined impact of interior materials, vehicle age [12,13], microenvironment in the cabin such as temperature, relative humidity and ventilation mode [14,15], and pollutants outside the vehicle like exhaust gases [16] and fuel leakage [9]. However, for a certain parked vehicle with the engine and ventilation off, the cabin becomes a completely closed space ignoring the air leakage, and it can be reasonably inferred that temperature becomes the main factor. Some researchers have addressed that VOCs diffusing from building materials are strongly associated with temperature [17–19]. Similar studies also were carried out in vehicle with an increased focus on cabin air quality. Many evidences have proved that the VOCs concentrations significantly increased with the increase in surface and ambient temperature. Yoshida et al. [20] indicated that the total volatile organic compounds (TVOC) concentrations in summer exceeded the indoor guideline value of 300 μg/m3; the interior temperature was the main factor affecting the interior concentrations of most compounds. Geiss et al. [21] found the VOC concentrations in the hot cabin with 70 ◦C were 40% higher through measuring in 23 old private cars in both summer and winter. Faber et al. [22] presented that chemical composition in vehicle air strongly depends on temperature. Chen et al. [23] investigated the VOCs in taxi cabins and found vehicle age is the most important factor, followed by interior temperature. Xiong et al. [24] derived a theoretical correlation between the steady state concentration and temperature for VOC emission from materials performing on three cars at different temperatures. Xu et al. [13] found toluene, styrene, ethylbenzene, and xylene were the most sensitive VOCs to temperature, which increased by 513.6%, 544.8%, 767.0%, and 597.7%, respectively, as the temperature increased from 11 ◦C to 25 ◦C. Huang et al. [25] found that the TVOC emission rate exponentially increased with the increase in in-cabin temperature.

As mentioned above, the VOCs emission is significantly associated with the in-cabin thermal environment, which is currently a hot topic. To evaluate the thermal comfort in cabin and further optimize the heating, ventilation, and air conditioning (HVAC) system [26–28], both experimental and numerical simulation studies have investigated the unsteady temperature and airflow profiles in buildings and passenger compartments [29–36]. Some studies have documented the dangerously high temperature in passenger compartments during exposure to the sun when parked outdoors [37]. Solar radiation is identified as the main heat source for a static vehicle in summer. More than 40% of solar heat flux enters the vehicle via the windshield. The vehicle exposed to direct solar radiation performs comparably to a greenhouse with severe thermal accumulation [38]. The cabin tends to be overheated quickly during the thermal soak period, the terminal temperature of the air and interior can reach about 60 ◦C and 80 ◦C, respectively [39,40].

This brief review shows that VOCs released from cabin interiors are proven to be temperature-dependent, and thermal simulation of the cabin environment has been conducted before. However, they were not linked together to discuss the in-cabin air quality. How VOC concentrations in the cabin vary with temperature under parked conditions is still a problem that has not been investigated quantitatively before. Gas sensing in real conditions with the use of cost-acceptable sensors is not trivial task [41], therefore, the numerical approximation of VOC distribution modeling in the car will be better justified. This research was aimed at bridging this knowledge gap and providing an effort to quantify the impact of the solar radiation on the cabin temperature and VOCs emission. This paper is organized as follows. We first evaluate the model performance by comparing it to the experiment in Section 2. Then, in-vehicle VOCs distribution from interior surfaces under solar radiation is modelled in Section 3. Section 4 presents the results and discussions. Concluding remarks are provided in Section 5.
