# Studies on Influence of Chromium Layer on Inner Surface of Steel Tube on Heat Transfer
## 1 Introduction  
The low service life of a tube loaded with an intense heat impulse is related to the erosion of its internal surface caused by mechanical and chemical factors [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. Studies have demonstrated that the tube's wear mechanism is directly influenced by the maximum temperature of its surface [12]. It is important to keep the temperature of the tube wall below the value of approximately 800 \({}^{\circ}\)C specified by the producers [12; 13]. The maximum temperature limit of the internal surface of the tube in operation is dictated by the tube's steel grade characteristics. In 30 HN2 MFA steel, a temperature above 750 \({}^{\circ}\)C causes allotropic change related to the reconstruction of the crystal lattice of the alloy, which is manifested by material shrinkage [14; 15; 16]. The inner surface of the tube is exposed to temperature, which changes the volume of the surface layer and leads to the formation of cracks. The depth of the cracks on the inner surface of the tube can be as high as 0.3 mm, e.g., for a tube composed of 30 HN2 MFA steel with a thin layer of chrome after 1000 heat impulses [17]. The presence of cracks on the inner surface of the tube can lead to degradation of the protective coating, which is typically composed of electroplated chromium in older manufacturing methods or nitride in newer designs. The erosion of the protective coating is attributed to changes in the structure of the underlying material, which are related to the phase transition between ferrite and austenite [3; 15; 18]. To simulate heat transfer, both the constant thermophysical properties of the tube steel and temperature-dependent properties are assumed [12; 18; 19; 20; 21; 22; 23; 24]. Typically, changes in the density of tube materials due to temperature are small and, therefore, neglected [21]. The correct thermophysical properties of the new steelgrades are important, as input data for tube heat-transfer calculations are critical to obtain accurate results. The authors recommend considering only the phase change of thermal conductivity [25]. During a series of heat impulses, the temperature of the tube material will steadily increase. On each temperature curve, we can determine the so-called highest peak temperature and lowest temperature of the peak base (the temperature of the inner surface of the tube) [25]. It seems important to consider the chromium layer's influence on the tube's heat transfer. Authors of some articles believe that the thermal contact resistance of the interlayer between the steel tube and the chrome coating can be neglected [25; 26; 27; 28]. Other publications assume that the thermal contact resistance \(R\) exists and is constant, for example, \(R=0.00053\) m\({}^{2. }\)\({}^{\circ}\)C/\(W\), which leads to the adoption of the join conductance (precisely: the constriction conductance from the contact spots) at the level of approx. 1900 W/(m\({}^{2. }\)\({}^{\circ}\)C) [29; 30; 31; 32; 33]. It seems that, both for thin chromium layers and for layers above 100 \(\upmu\)m, the constant values of thermal contact resistance are unreliable, leading to overestimation of the temperature results of the inner surface of the tube. According to the authors, in the case of thin chromium layers where we can talk about the plastic deformation of surface asperities, the pressure of the gas virtually eliminates thermal contact resistance [31]. In the case of thick chromium layers, we can talk about the elastic deformation of surface asperities, which also depends on the pressure of the gas. In this case, due to the lack of reliable data, the authors also assumed no thermal contact resistance of the interlayer between the steel cylinder and the chrome coating. In this work, an initial boundary value problem (IBVP) of heat transfer in the wall of a 35 mm inner diameter tube was solved for a single and a sequence of seven heat impulses.