In this paper, forced convection of a multiwalled carbon nanotube (MWCNT)–water nanofluid (NF) in a new flat plate solar collector (FPSC) equipped with elliptical pipes instead of circular ones is investigated. The three-dimensional conservation equations were solved in the domain with the finite volume method (FVM) based on the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The laminar-turbulent range of the Reynolds number (Re) and the volume fraction of the NF (ϕ) were 50–12,000 and 0–0.1, respectively. The optimization process was accomplished through the comparison of diverse parameters to attain the optimal case with the highest exergy efficiency. In this study, it was concluded that, in the case of using elliptical pipes instead of circular tubes, the time that the fluid was inside the FPSC increased, which led to an increase in the outlet temperature, while the exergy efficiency of the FPSC increased. Additionally, it was observed that using elliptical pipes enhanced the outlet fluid temperature, energy efficiency, and exergy efficiency. Generally, while the trend of exergy efficiency variation with effective parameters was rising, applying elliptical pipes caused the efficiency to increase. In addition, the exergy efficiency variation decreased when these parameters were changed. The highest value of exergy efficiency was 7.1%. On the other hand, for each specific FPSC, there was a unique mass flow rate at which the exergy efficiency reached its maximum value, and for higher mass flow rates, the efficiency was slightly diminished and then remained unchanged. Finally, the highest exergy efficiency was achieved for ϕ = 0.10%.