## 3 Results and Discussions
### The Influence of Temperature and Velocity Contours on Hybrid Nanofluid Flow
Figure 16 illustrates the effect of hybrid nanofluid with different volume fractions on entropy generation for various Reynolds numbers and inlet temperatures \(T\) = 313 K and \(T\) = 323 K. Thermal entropy generation \(\hat{S}_{gen,T}\) and frictional entropy generation \(\hat{S}_{gen,F}\) are demonstrated in Figures 16 and 17. They are due to irreversibility. As shown in Figure 16a,b, thermal entropy generation decreases, and frictional entropy generation increases with the  
Figure 14: Influence of HNF with different VF on hydraulic power for different Re and inlet temperature \(T\) = 323 K.  
Figure 6:0 Effects of HNF with different VF on pressure reduction for different Re and inlet temperatures (a) \(T\) = 313 K and (b) \(T\) = 323 K.  
VF of NPs and Re. It must be noted that frictional entropy generation is approximately zero at low flow velocities for both inlet temperatures. It is found that the diagrams of frictional and thermal entropy generations have an intersection, indicating the frictional entropy generation can overcome other effective parameters. The irreversibility due to HT leads to the generation of thermal entropy. Therefore, the variation in \(\dot{S}_{gen,T}\) is more important at low Re. In addition, the changes in \(\dot{S}_{gen,F}\) which describe the frictional irreversibility are more important at high Re, because the fluid friction in flow fields enhances with the Re. Figure 17a reveals that the values of frictional entropy generation of the EG/MgO-MWCNT HNF with a volume fraction of 0.4% are very close to those of the base fluid. However, the values of frictional entropy generation of the EG/MgO-MWCNT HNF with a VF of 0.2% are superior compared to the base fluid. Frictional entropy generation increases with the Re for both volume fractions of 0.2% and 4%. This is due to an increase in the velocity gradients and consequently an enhancement of viscous forces. Figure 17b shows that the values of frictional entropy generation for hybrid nanofluid with volume fractions of 0.1% and 0.2% are very close to that for the base fluid. Frictional entropy generation for HNF with a VF of 0.4% is more than that for ethylene glycol. Figure 6:1 Effects of HNF with different VF on thermal entropy generation for different Re and inlet temperatures of **(a)**\(T=313\) K and **(b)**\(T=323\) K.  
The Influence of Hybrid Nanofluid with Various Volume Fractions on Dimensionless Entropy at Various Re and Selected Inlet Temperature  
Figure 18 illustrates the influence of the HNF with different VF on dimensionless entropy generation for various Reynolds numbers and inlet temperatures \(T\) = 313 K and \(T\) = 323 K. It is witnessed that the entropy generation reduces initially and then increases by increasing the fluid velocity (increasing the Reynolds number). This is because the entropy generation increases with HT and PD. For high fluid velocities (high Reynolds numbers) and inlet temperature of 313 K, HNF with a volume fraction of 0.2% is the most efficient case. Minimum dimensionless entropy generation corresponds to the HNF with volume fractions of 0.1% and 0.2% at inlet temperature 323 K. The results imply that the  
Figure 6:2 Effects of HNF with different VF on entropy generation for different Re and inlet temperatures (**a**) \(T\) = 313 K and (**b**) \(T\) = 323 K.  
EG/MgO-MWCNT HNF with a VF of 0.4% is introduced as the optimum case among all studied ones.