## 3 Results and Discussion
### Computed Results
In the FEM technique, an element consisted of a number of nodes, each associated with a shape function (\(N_{i}\)) and a temperature (\(T_{i}\)), so the element temperature would be \(T_{element}=\sum_{i=1}^{M}(N_{i}\times T_{i})\), where \(T_{element}\) was the temperature in the element, \(M\) was the total number of nodes in a specific element, \(N_{i}\) and \(T_{i}\) were the shape function and temperature of the \(i\)th node within the element, respectively. The average temperature of the domain was determined through the arithmetic mean of temperatures of elements in the domain. The average temperatures over the outlet nozzle are shown in Figure 11. For \(t<2.0\) s, the average temperature (i.e., the bulk temperature of the flow) of the mixture in the outlet nozzle domain for the mixing chamber with obstacles was higher than that without obstacles. The increase in the temperature here was explained by the chamber filling and subsequent mixing between the injected blood and plasma. When steady state was achieved after \(t>\sim\)2.0 s, the average temperature of the mixture in the outlet nozzle domain for both chambers became \(\sim\)308.55 K. Moreover, the heat transfer between these two different fluids was controlled by the heat flux (\(q^{*}\)) and the spatial distribution of temperature, so, as result of the increased contact between blood and plasma in the mixing chamber, the final temperature of the mixture would be regulated based on the initial temperature of both fluids. In addition, it could be concluded that heat transfer could be enhanced by the increased contact as a result of mixing, and at the same time the reaction between the plasma constituents and the blood would be further enhanced. The results of temperature distribution inside the device with the flow streamlines are shown in Figures 12 and 13 for mixing chambers with and without obstacles, respectively. The snapshots were taken from the system every  
Figure 10: Distribution of velocity streamlines over the mixing chamber without obstacles at: (**a**) 0 s; (**b**) 2 s; (**c**) 4 s; (**d**) 6 s; (**e**) 8 s; and (**f**) 10 s. Different velocities are represented by different colors as shown in the color bar (in m s\({}^{-1}\)). 2.0 s over the total simulation runtime of 10.0 s in which the mixing chamber was fully filled with blood and plasma. The temperature distributions over the mixing chambers shown in Figures 12 and 13 show the temperature variations between the injected blood and plasma as a result of heat transfer and subsequent mixing. The temperature distributions over the mixing chamber with obstacles were more gradual when compared to those for no obstacles. As shown in Figure 12f, the final mixture temperature at the outlet boundary was \(\sim\)308 K. The gradual color changes of the flow streamlines characterized the temperature distribution of the mixture of blood and plasma. As observed in Figure 13f, the temperature in the middle part of the outlet nozzle was almost equivalent to the  
Figure 11: Average temperature of mixture over outlet nozzle domain (shown in blue) for mixing chambers with and without obstacles (Note: outlet nozzle domain is marked in blue). Figure 12: Distribution of flow streamlines and temperature over the mixing chamber with obstacles at: (**a**) 0 s; (**b**) 2 s; (**c**) 4 s; (**d**) 6 s; (**e**) 8 s; and (**f**) 10 s. Different temperatures are represented by different colors as shown in the color bar (in K). temperature of the injected blood (\(\sim\)310 K). Moreover, the heat distribution tended to be less effective in a mixing chamber without obstacles, as shown in Figure 13f, which did not show gradual changes in the heat color map throughout the device's domain. In addition, the distribution of blood and plasma volume fractions in both mixing-chamber designs when the chambers are fully filled and when steady-state is reached (i.e., \(t=10.0\) s) are shown in Figure 14a,b for chambers with and without obstacles, respectively.