# Studies on Influence of Chromium Layer on Inner Surface of Steel Tube on Heat Transfer
## 4 Discussion  
In this study, the results of numerical calculations of the heat transfer in the wall of a tube composed of 30 HN2 MFA steel with different thicknesses of the chrome layer, i.e., 0, 10, 20, 30 and 200 \(\upmu\)m, on its inner surface are presented. The calculations were carried out for thermophysical parameters of the steel as a function of temperature for a tube divided into 30 zones. An interior ballistics code was developed to compute in each zone the heat transfer coefficient \(h_{i}(t)\) and gas temperature \(T_{g}(t)\). The division of the 3150 mm long tube into 30 zones made it possible to determine the temperature distribution along the length of the tube covered with a chrome layer. Figure 16: Distribution of the highest peak temperatures (**a**) and the lowest temperatures of the peak base (**b**) along the tube length with different chromium layer thicknesses after 7 heat impulses. The thermal resistance of the contact between the chromium and steel layers was not taken into account, as there are no reliable values for this resistance [25; 32]. According to [PERSON], such a case could only be considered for a chromium layer with a thickness greater than 100 \(\upmu\)m [31; 32]. Adopting a constant value of the so-called constriction conductance from the contact spots at the level of approx. 1900 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\), as is the case in the cited works, inflates the calculation results and is non-physical because this parameter depends on the value of the gas pressure, which changes as a function of time [25; 32]. For a single heat impulse--temperature distribution in the tube with different chromium layer thicknesses:  
It can be assumed that the distribution of the lowest peak base temperatures along the tube length (Figure 12) is actually the temperature distribution of the tube's inner surface \(T_{i}(t,r_{in},z)\), where \(I\) = 1,..., 30, up to a depth of approximately 0.5 mm below its surface--Figure 13. This assumption covers all cases of the thickness of the chromium layers on the inner surface of the tube, i.e., 10, 20, 30 and 200 \(\upmu\)m, and the maximum crack depth of the 30 HN2 MFA steel, which was assumed to be 0.3 mm [17]. The 200 \(\upmu\)m thick chrome layer lowers the highest peak temperature the most but, at the same time, increases the lowest temperature of the peak base the most, i.e., the temperature of the inner surface of the tube--Table 3.  
For a sequence of seven heat impulses--the temperature on the inner surface of the tube:  
The influence of the thickness of the chromium layer on the highest peak temperatures and the lowest peak base temperatures of the inner surface of the tube is particularly visible in the analysis of the first heat impulse--Figure 14. Then, for the inner surface of the tube without a chrome layer and with a chrome layer of 200 \(\upmu\)m, the differences between the highest peak temperatures are the greatest. These differences in the temperatures decrease with each successive impulse. The opposite is true for the lowest peak base temperatures. With each successive impulse, for the inner surface of the tube without a chrome layer and with a chrome layer of 200 \(\upmu\)m, these differences of temperatures are bigger and bigger. For a sequence of seven heat impulses--the calculation of heat transfer along the wall thickness:  
On each curve of the temperature distribution \(T_{i}(t,r,z)\) along the wall thickness for a tube with different thicknesses of the chromium layer for a sequence of seven heat impulses, we can distinguish the so-called maximum peak temperature and the minimum base temperature, which is equivalent to the temperature of the inner wall of the tube. This temperature is practically identical to the temperature of the wall at a depth of 0.5 mm below its inner surface regardless of the thickness of the chrome layer--Figure 15. The lowest peak base temperature is read after each heat impulse, i.e., \(t\) = 100 ms for the first impulse, 200 ms for the second impulse, etc.