This paper concerns an economic and exergetic efficiency analysis of a plate heat exchanger placed in a solar installation with TiO2:SiO2/DI:EG nanofluid. This device separates the primary circuit—with the solar fluid—and the secondary circuit—in which domestic hot water flows (DHW). The solar fluid is TiO2:SiO2 nanofluid with a concentration in the range of 0.5–1.5%vol. and T = 60 °C. Its flow is maintained at a constant level of 3 dm3/min. The heat-receiving medium is domestic water with an initial temperature of 30 °C. This work records a DHW flow of V˙DHW,in = 3–6(12) dm3/min. In order to calculate the exergy efficiency of the system, first, the total exergy destruction, the entropy generation number Ns, and the Bejan number Be are determined. Only for a comparable solar fluid flow, DHW V˙nf=V˙DHW 3 dm3/min, and concentrations of 0 and 0.5%vol. is there no significant improvement in the exergy efficiency. In other cases, the presence of nanoparticles significantly improves the heat transfer. The TiO2:SiO2/DI:EG nanofluid is even a 13 to 26% more effective working fluid than the traditional solar fluid; at Re = 329, the exergy efficiency is ηexergy = 37.29%, with a nanoparticle concentration of 0% and ηexergy(1.5%vol.) = 50.56%; with Re = 430, ηexergy(0%) = 57.03% and ηexergy(1.5%) = 65.9%.