As the demand for solar energy increases, so too does the demand for efficient absorption of solar energy and solar energy cost reduction. Prior research has shown that nanofluids improve the efficiency of solar thermal collector absorption. Nanofluids are a composition that consists of varying-sized nanoparticles within a base fluid. This research introduces linear and non-linear programs that are formulated and solved to determine two optimally efficient nanoparticle combinations. The first optimal combination maximizes the absorption of heat within a heterogeneous nanofluid while the second minimizes the cost of another heterogeneous nanofluid. The nanoparticles analyzed for optimal efficiencies are silver, aluminum, gold, cobalt, copper, chromium, iron, manganese, nickel, palladium, titanium, vanadium, and graphite, and all range in size from 10 nm to 150 nm. All of these nanoparticles form the database of particles which is optimized, however multiple subsets of the database are also optimized in this research. The optimal combinations of these nanoparticles are determined numerically for varying particle concentration, container height, and temperature. (C) 2018 Elsevier Ltd. All rights reserved.