## 4 Conclusions  
In this study, forced convection HT of a HNF in a heat exchanger with elliptical corrugated tubes was investigated. Three-dimensional (3D) multiphase governing equations were solved computationally using a control volume approach based on the SIMPLE algorithm. The range of Reynolds numbers 50 \(<\) Re \(<\) 1000 corresponds to laminar flow. Optimization was carried out by evaluation of various parameters to reach an optimal case with the maximum Nu and minimum PD and minimum entropy generation. The implications of the results achieved are summarized into the following six characteristics:  
1. At \(T\) = 323K, the use of the EG/MgO-MWCNT NHF with a VF of 0.4% leads to higher Nu in comparison with the base fluid for all Re. However, at this temperature, the use of the EG/MgO-MWCNT HNF with a VF of 0.1% and 0.2% is more appropriate at very low Re.  
Figure 18: Effects of HNF with different VF on dimensionless entropy generation for different Re and inlet temperatures of **(a)**\(T\) = 313 K and **(b)**\(T\) = 323 K.  
* As the Re increases, the pumping power increases. The value of pumping power for the EG/MgO-MWCNT HNF with a volume fraction of 0.4% is more than that for other cases at all Re.
* Higher temperatures lead to larger PD. EG/MgO-MWCNT HNF with a volume fraction of 0.4% has less PD compared to the other HNF with a lower VF.
* Thermal entropy generation reduces and frictional entropy generation increases with the VF of NPs and fluid velocity (Re).
* Since irreversible HT is the cause of increase in thermal entropy, the variations of \(\dot{S}_{gen,T}\) are more important at lower Re.
* The EG/MgO-MWCNT HNF with a VF of 0.4% is introduced as the optimum case among all studied ones.  
In order to continue this study, the effect of different pipe cross-sections on the performance of the heat exchanger can be investigated. The effect of the presence of internal microfins in the pipes on thermal efficiency and also the effect of the type of nanofluid can be investigated.  
Conceptualization, Y.K., H.M.A.-D., A.K.A. and Z.S.; methodology, Y.K., H.M.A.-D. and A.K.A.; software, Y.K., H.M.A.-D., A.K.A., Z.S. and S.M.; validation, S.B., M.S., Z.S, Y.K., H.M.A.-D. and A.K.A.; formal analysis, Y.K., H.M.A.-D., A.K.A. and Z.S.; investigation, Y.K., H.M.A.-D., A.K.A., S.M., Z.S. and M.S.; resources, Y.K., H.M.A.-D., A.K.A., Z.S., S.M., S.B. and M.S.; data curation, Y.K., H.M.A.-D. and A.K.A.; writing--original draft preparation, Y.K., H.M.A.-D., A.K.A., Z.S., S.M., S.B. and M.S.; writing--review and editing, S.M., Z.S., S.B., M.S., Y.K., H.M.A.-D. and A.K.A.; visualization, Z.S., S.B., M.S., Y.K., H.M.A.-D. and S.M; supervision, H.M.A.-D., A.K.A. and Z.S.; project administration, Z.S., S.M., Y.K., H.M.A.-D., A.K.A., S.B. and M.S.; funding acquisition, Z.S., S.M., Y.K., H.M.A.-D., A.K.A., S.B. and M.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Taif University Researchers Supporting Grant (TURSP-2020/266) of Taif University, Taif, Saudi Arabia.  
Not applicable.  
The authors thank Taif University and corresponding international collaboration for working on this hybrid nanofluids project.  
The authors declare no conflict of interest.