## 1 Introduction  
Increasing air pollution due to vehicle exhausts and increasingly stringent emission regulations require the advanced purification technology of automobile exhaust or further optimized control strategies to improve purification efficiency [1, 2]. As one of the major mobile source pollutants, nitrogen oxides (NO\({}_{\mathrm{x}}\)) are mainly released by diesel vehicles [3]. Selective catalytic reduction (SCR) is a state-of-the-art method to reduce NOx emissions with minimal impact on engine efficiency [4]. Ammonia (NH\({}_{3}\)) is usually chosen as the reductant to selectively reduce NOx to nitrogen (N\({}_{2}\)) [5]. In mobile source applications, the urea water solution (UWS) is generally adopted as an ammonia precursor due to its nontoxicity and convenient storage [6, 7]. UWS is sprayed into the SCR system through an injector, and NH\({}_{3}\) is finally generated through the processes of evaporation, pyrolysis, and hydrolysis. This series of processes strongly influences the reduction efficiency of the SCR system. Due to the relatively long time scale required for urea decomposition and the trend toward the compact design of the post-treatment system [8], the incomplete decomposition of urea and spray impingement are inevitable. Spray impingement can lead to the local cooling of the exhaust pipe and mixer, which causes the formation of liquid film when the wall temperature drops. The heat transfer between the liquid film and the wall furtherly occurs, which results in a number of problems, such as the nonhomogeneous distribution of urea [9] and the low decomposition efficiency of urea [10; 11] as well as deposit formation [12; 13] when the temperature of the liquid film reaches a specific interval. The spatial distribution uniformity of the reductant and the conversion efficiency of the reductant are crucial factors for the denitration efficiency of the SCR system. These two factors can be affected by spray/wall interaction besides evaporation and decomposition. Therefore, it is necessary to recognize the heat transfer characteristics during spray impingement. There have been many findings on the heat transfer of spray/wall interaction during spray impingement so far. [PERSON] et al. [14] investigated the evaporation characteristics of a single UWS droplet on a heated surface and found that the evaporation pattern can be classified into two different forms, namely, rapid evaporation and slow evaporation, with the critical heat flux as the demarcation point. [PERSON] et al. [15] reached similar conclusions via an electric furnace experiment under static conditions about the multi-stage evaporation behavior of UWS droplets. The first stage is the evaporation of water that follows the D\({}^{2}\) law. The second stage is characterized by a micro-explosion, the extent of which is determined by the ambient temperature. Meanwhile, some academics realized the significance of spray/wall interaction and investigated its mechanism. [PERSON] [16] considers all relevant impingement phenomena by classifying them into four regimes based on the Mundo number K and the wall temperature: spread (or deposition), rebound, splash, and dry splash (thermal breakup). The deposition and splash regimes lead to the formation of a wall film. [PERSON] et al. [17] adopted the synthetic Schlieren method to enable the transient visualization study of liquid film and used Mie scattering to show a side view of the spray penetration distribution under exhaust flow conditions. Eventually, the global spray evaporation rate is derived from consecutive distributions. [PERSON] et al. [18] measured temperatures at different positions of the wall during air-assisted spray impingement by thermocouples and investigated the effect of an aqueous polymer additive on the heat flux. [PERSON] et al. [19] investigated the correlation between different spray inclination angles and the temperature of the spray impingement zone and deduced the optimal angle at which the heat flux density is maximized. [PERSON] et al.