## 1 Introduction  
Materials such as high temperature alloys (nickel, titanium, etc.) are usually employed in the manufacturing processes of high added value products, especially in the space, aircraft and military industries [1]. These sorts of materials have excellent mechanical and thermal properties which are maintained even when the materials are exposed to high temperatures. Additionally, such materials have low thermal conductivity and get plastically hardened at high temperatures, hence their extremely poor machinability [2]. The nickel-based alloy Inconel 718, which is the subject of the research in this paper, is a high temperature alloy. It is a corrosion (oxidation) resistant material that can be used at high temperatures while maintaining its hardness characteristics. This is due to its good tensile strength, fatigue life, creep properties and rupture strength. However, due to these specific material characteristics, this alloy is generally difficult to machine [3]. According to these mentioned facts, it could be possible to machine those materials by the usage of cooling lubrication fluids, such as a high-pressure jet and liquefied nitrogen, etc. The development of the industry in the field of machining processes has been striving to achieve a higher level of productivity and environmental awareness. This includes minimizing the use of cooling lubrication fluids based on artificial ingredients and increasing cutting speeds. The use of ecologically impeccable cooling lubrication fluids that do not harm people's health and are environmentally friendly has been promoted. Thus, it is necessary to use an environmentally acceptable coolant in the manufacturing industry. For this purpose, liquefied nitrogen as a cryogenic coolant has been explored since the 1950s in the metal cutting industry [4]. The main characteristic of this technology is the use of a cryogenic fluid (liquefied nitrogen) as a cooling fluid during the cutting process, at very low temperatures. The main advantage of liquefied nitrogen is the cooling of the cutting zone, where it is the highest temperature. A deficiency of using liquefied nitrogen as cooling fluid during the machining process is a lack of knowledge in terms of the physical properties of the used media and consequently there are very few publications about them in scientific journals. In past publications on the field of cryogenic machining, artificial intelligence methods were only used to predict machinability aspects: tool wear, cutting forces and surface roughness. In the field of measuring temperatures during the machining process and designing empirical models, the few works are the following. [PERSON] and [PERSON] [5] conducted experiments on measuring temperatures in the hard turning of AISI 1060 steel with coated carbide inserts and developed the predictive empirical model of cutting temperatures with neural networks. [PERSON] and [PERSON] [6] performed experiments on the machining of hardened steel and reached the modeling of the correlations between cutting parameters and different machine aspects including tool wear, chip morphology and surface integrity. [PERSON] et al. [7] reached a correlation between cutting parameters and output process parameters such as tool wear and cutting force in the high speed machining of Inconel 718 with neural networks. [PERSON] et al. used a genetic algorithm [8] and particle swarm optimization (PSO) [9] as a learning method of the adaptive neuro-fuzzy inference system (ANFIS) in order to optimize the positions of membership functions (MFs) (making the search space significantly bigger since more independent variables were included in optimization) and increase the ANFIS's accuracy based on leave out cross-validation. The aim of the paper is to explain in detail the influence of the characteristic aspects of the placement of the nitrogen inlet on the treatment process. Designing an empirical model can help us to understand the influence of the cooling medium used in the machining process.