## 1 Introduction  
Water is the most common and widely used cooling medium due to its availability, low cost and lack of negative impact on the environment and humans. While water cooling a surface at a high temperature, a boiling phenomenon occurs which allows for the dissipation of significant amounts of heat from hot surfaces. The heat flux (HF), describing the amount of heat removed from the cooled surface, is conditioned by the type of boiling regimes that occur on the cooled surface. During the cooling of hot materials, the individual stages of the boiling process are opposite to the boiling regimes observed during pool-boiling, described by [PERSON] [1]. The first stage of boiling, while cooling a hot surface at a high temperature, is film-boiling, which is characterized by a low HF. Small values of HF during this boiling regime are caused by the vapor film forming on the cooled surface, which isolates the surface and limits the inflow of liquid. That in turns reduces the heat dissipation from the cooled surface. When the surface temperature decreases, transition boiling occurs in which the liquid intensively wets the cooled surface and the HF increase up to a maximum value called the critical heat flux (CHF). After reaching the maximum, the HF decrease with the decrease in the surface temperature due to the formation of increasingly smaller amounts of vapor bubbles on the cooled surface. It is a nucleate boiling regime. The last stage of the boiling process is a single-phase convection. The most popular methods of cooling with water include the following: cooling with a water jet (JET) [2; 3; 4], water spray (WS) [5; 6; 7; 8; 9; 10] and air-assisted water spray (AAS) [11; 12; 13]. The cooling process with these methods allows for achieving large amounts of heat dissipating from the cooling surface, which, in practice, is unattainable in the field of single-phase convection. During JET-cooling, the liquid flowing freely from the nozzle hits the cooled surface. Cooling with a JET is used, among others, in the metallurgical industry during quenching [3] and rolling plates on a hot steel mill [14; 15]. This type of cooling is also commonly used during the cooling of turbine components [16]. An equally common method of cooling, which uses water as a coolant, is WS. WS is a mixture of water molecules dispersed in a gaseous medium [17]. There are two most common spraying methods: the hydraulic method (WS) and the pneumatic method (AAS) [17]. In the hydraulic method, water is sprayed through a pressure nozzle. Pneumatic atomization (AAS) is caused by the action of a compressed gas, usually air, on a liquid. Spray-cooling, both hydraulic (WS) and pneumatic (AAS), is used in practice, among others, in microelectronics [18; 19; 20], ventilation systems [21], nuclear industry [22; 23], energy industry [24; 25; 26; 27], the metallurgical industry [5; 7; 12; 28] and many others. JET-cooling and spray-cooling, both pneumatic (AAS) and hydraulic (WS), are competitive methods in applications where there is a need to dissipate large amounts of heat from the cooled surface. The selection of an appropriate cooling method, ensuring an appropriate rate of heat dissipation from the cooled surface, is particularly important in high-temperature metallurgical processes which include quenching, rolling or the continuous casting of steel or other alloys. Providing an appropriate rate of heat dissipation guarantees the formation of the desired microstructure of the cooled product, which affects the properties of the manufactured product. In publicly available literature, there are several studies in which researchers mainly focused on comparisons: two cooling methods [6; 12; 29; 30] and cooling methods for a specific boiling phase [29]. [PERSON] [29] compared heat transfer during pneumatic (AAS) and hydraulic spray-cooling (WS) in the field of film-boiling. These research studies showed that the heat transfer coefficient (HTC) in the film boiling regime was 10 times higher for pneumatic spray-cooling compared to the hydraulic one.