## 3 Results and Discussion  
In the present section, the average water wall tube temperature was extracted at different loads, and the maximum allowable stress was calculated at the average tube temperature via linear interpolation that assures the safe operation of the water tubes in the furnace section of the boiler. Furthermore, the stress of working pressure S\({}_{\text{working\, Pressure}}\) was calculated via Equation (10). Increasing tube thickness can increase the average tube temperature but combining it with increasing deposit thickness leads to higher temperatures. In other words, the effect of the deposit on the tube with higher thickness is higher than on the tube with lower thickness. The following sections will analyze the impact of the deposits in full load, 75% of full load, and 50% of full load.  
As shown in Figure 6, the high temperature concentrates on the region exposed to direct fire. So, this region is prone to overheating failure. Also, the temperature on the internal surface in this region is higher than in the opposite region. So, the Scale deposition in the area near the flame will be higher than in the other area.  
As shown in Figure 7, the increase in the average temperature of the water wall tube is conjugated with accumulating deposit layer of Magnetite with low thermal conductivity. For example, the average temperature \(T_{average}\) reaches 400.19, 395.56, 391.49, 387.90, 384.68, and 381.77 \({}^{\circ}\)C at \(t_{p}=6,\ 5,\ 4,\ 3,\ 2,\ \text{and}\ 1\ \text{mm}\), respectively, in the case of \(t_{d}=0.2\ \text{mm}\) compared with 342.71, 341.48, 340.44, 339.51, 338.67, and 337.94 \({}^{\circ}\)C in the case of \(t_{d}\ =\ 0.02\ \text{mm}\) at \(t_{p}=6,\ 5,\ 4,\ 3,\ 2,\ \text{and}\ 1\ \text{mm}\), respectively. Therefore, an increase in the tube and deposit thickness leads to a significant reduction in yield strength (Figure 3) or allowable  
Figure 6: Average temperature distribution of water wall tube at full load.  
stress based on the ASME code (Figure 3). It can be noticed that in the deposit layer with \(k=0.625\) W/m K, the allowable stress divided by hoop stress Equation (9) at full load reaches 1.3, 0.72 in 6 mm and 3 mm tube thickness, respectively. See Figures 7 and 8.  
Overall, the minimum value of the wall tube thickness is 4 mm, with magnetite thickness less than 0.16 mm, which is approximately equal to the maximum allowable stress in the ASME code at full load.  
A similar analysis, as previously discussed, is conducted in the present section to determine the minimum tube thickness and shows the effect of magnetite deposit on the average tube temperature under 75% of full load. As shown in Figure 9, the average tube temperature was also affected by the deposits' thickness. However, it is noted that the temperatures here are lower than what was previously discussed. Furthermore, it can be  
Figure 8: The effect of the deposits’ thickness on the tube stress at full load.  
Figure 7: Thickness variation effects of deposit layer on average water wall tube temperature at full load.  
noticed that the deposit layer with k = 0.625 W/m K, the allowable stress divided by hoop stress Equation (9) at 75% of full load, reaches 1.39, 0.75 in 6 mm and 3 mm tube thickness, respectively; see Figure 10. The minimum thickness of the water wall tube is 4 mm, with magnetite thickness less than 0.18 mm.  
In addition, the average temperature at 50% of full is discussed. As shown in Figure 11, the increase in the average temperature of the water wall tube is conjugated with accumulating deposit layer of Magnetite with low thermal conductivity. For example, the average  
Figure 10: The effect of the deposits’ thickness on the tube stress at 75% of full load.  
Figure 9: Thickness variation effects of deposit layer on average water wall tube temperature at 75% of full load.