The capabilities of nanofluids in boosting the heat transfer features of thermal, electrical and power electronic devices have widely been explored. The increasing need of different industries for heat exchangers with high efficiency and small dimensions has been considered by various researchers and is one of the focus topics of the present study. In the present study, forced convective heat transfer of an ethylene glycol/magnesium oxide-multiwalled carbon nanotube (EG/MgO-MWCNT) hybrid nanofluid (HNF) as single-phase flow in a heat exchanger (HE) with elliptical corrugated tubes is investigated. Three-dimensional multiphase governing equations are solved numerically using the control volume approach and a validated numerical model in good agreement with the literature. The range of Reynolds numbers (Re) 50 < Re < 1000 corresponds to laminar flow. Optimization is carried out by evaluation of various parameters to reach an optimal case with the maximum Nusselt number (Nu) and minimum pressure drop. The use of hybrid nanofluid results in a greater output temperature, a higher Nusselt number, and a bigger pressure drop, according to the findings. A similar pattern is obtained by increasing the volume fraction of nanoparticles. The results indicate that the power of the pump is increased when EG/MgO-MWCNT HNFs are employed. Furthermore, the thermal entropy generation reduces, and the frictional entropy generation increases with the volume fraction of nanoparticles and Re number. The results show that frictional and thermal entropy generations intersect by increasing the Re number, indicating that frictional entropy generation can overcome other effective parameters. This study concludes that the EG/MgO-MWCNT HNF with a volume fraction (VF) of 0.4% is proposed as the best-case scenario among all those considered.