Nanofluids play an important role in many different industries for an improvement of heat transfer. The modeling and simulation of such fluids is developing continuously. Two important models for studying nanofluids are mixture (or single-phase) and two-phase (or Buongiorno) forms, which have been examined in various ways. Non-Newtonian behavior of nanofluids (shear-thinning and viscoplasticity) has been observed in experimental tests and simulated in several studies. However, a lattice Boltzmann method (LBM), which can employ either model depending on the particular non-Newtonian constitutive equation, has not been considered to date within the suite of available numerical methods. Here, we propose a comprehensive LBM to simulate both Newtonian and non-Newtonian nanofluids. The approach has the potential to incorporate any format of extra tensor directly and is independent to the relaxation time; the upshot is that our method is appropriate for studying non-Newtonian nanofluids. The derivations for both models are presented and discussed in some detail. To evaluate the proposed method, it was compared with previous studies into a benchmark problem, natural convection in a square enclosure filled with Newtonian nanofluids and non-Newtonian fluids. Then, the applied macroscopic and LBM equations, using the power-law and viscoplastic models, for the benchmark are derived and the results are presented.
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