# CFD Analysis of a Tubular Heat Exchanger for the Conditioning of Olive Paste
## 3 Results and Discussion
### Temperature Variation in Different Scenarios  
Figure 4 shows the average temperature of the olive paste at the outlet section of the inner tube under different inlet conditions. As expected, the difference in temperature between the inlet and the outlet (\(\Delta\)T\({}_{\text{p}}\)) decreases as the paste flow rate and its inlet temperature increases. Indeed the water, which flows with a mass flow rate of about 1.8 kg/s, has an inlet temperature that is kept to 40 \({}^{\circ}\)C in each scenario. However, it is possible to note that the inlet temperature of the paste has a lower influence on the \(\Delta\)T\({}_{\text{p}}\), especially when the paste flow rate increases. At 3000 kg/h, the maximum \(\Delta\)T\({}_{\text{p}}\) is 1.45 \({}^{\circ}\)C when the paste enters at 7 \({}^{\circ}\)C, and \(\Delta\)T\({}_{\text{p}}\) is 0.90 \({}^{\circ}\)C when enters at 20 \({}^{\circ}\)C. This means a difference of 0.55 \({}^{\circ}\)C between the extreme case. Instead, when the minimum flow rate is used (i.e., 1000 kg/h), \(\Delta\)T\({}_{\text{p}}\) is 2.78 \({}^{\circ}\)C when the temperature of the paste at inlet is 7 \({}^{\circ}\)C and 1.71 at 20 \({}^{\circ}\)C. In this case, the difference between the extreme case is about 1.1 \({}^{\circ}\)C. This means that when the paste flow rate increases, to avoid an excessive increase in the heat exchange surface, it is necessary that the system improves the heat transfer. In fact, it is not desirable to increase the temperature of the service fluid in order to avoid compromising the product quality and prevent extensive fouling on the internal surface of the inner tube. Figure 4: Average values of temperature paste at the outlet of inner tube. As stated, the above is confirmed by the results reported in Figure 5a-c, which shows the temperature contours inside the heat exchanger when the paste flow rate is 3000 kg/h, and the inlet temperature is 7, 15 and 20 \({}^{\circ}\)C, respectively. Two cut plots, the first along the longitudinal middle plane and second along the cross section at the end of the straight part of the heat exchanger, describe well the temperature distributions. It should be noted that the core temperature of the product remained virtually unchanged from entry to exit. This means that to obtain the desired temperature throughout the product, a part of it (near the internal surface) will inevitably undergo a qualitative degradation, compromising the quality of the olive oil extracted. In fact, it is easy to note that a large amount of the product (about 80%) still remained at the inlet temperature. The temperature increases from the middle towards the periphery of the section. Figure 5: Temperature contours at paste flow rate of 3000 kg/h. (**a**) “Temperature paste in” equal to 7 \({}^{\circ}\)C; (**b**) “Temperature paste in” equal to 15 \({}^{\circ}\)C; (**c**) “Temperature paste in” equal to 20 \({}^{\circ}\)C.  
When the inlet temperature is 15 \({}^{\circ}\)C, the product near the wall experiences a maximum temperature of about 20.6 \({}^{\circ}\)C (Figure 5b), which becomes about 24.5 \({}^{\circ}\)C when it enters at 20 \({}^{\circ}\)C (Figure 5c). This is due to the rheology of the paste, which always produces a laminar flow and limits mixing, resulting in the absence of uniformity of heating for all portions of olive paste. The laminar flow of the olive paste is also demonstrated by Figure 6a,b, which shows the path lines and velocity values of both olive paste and water. Figure 6a shows very low variation of velocity in the straight part of the inner tube, with a slight variation in the elbows due to gravity. The average velocity of the paste in the inner tube is about 0.14 m/s, while the water flows (Figure 6b) at about 9 m/s in the supply tube, and ones in the jacket undergo a sudden reduction (reaching about 1.5 m/s in the middle of the straight part) and then rise again in the outlet tube.