The present paper deals with the Buongiorno's model for nanofluids with a novel TVD1 Hybrid Lattice Boltzmann technique. It is well known tha twhen the diffusion fluxes (with Dissipation behaviors) own negligible values regarding convective fluxes, almost all classical methods suffer serious instability errors. The Lattice Boltzmann method also is not an exception to this rule. In order to resolve this issue, many novel techniques and methods (e. g. MRT-LBM) are developed. Here we propose a novel TVD Hybrid LB method to solve Buongiorno's model for Al2O3-Water nanofluid in the presence of an elliptic cold obstacle. The Model naturally possesses small values of diffusion coefficients and thereby, explicit methods are not considered as primitive choices to be applied in the simulation of this model. But the TVD characteristics of the following Hybrid LB method made it a valuable asset in resolving these kinds of problems.Moreover, the heat transfer and entropy generation of a square cavity with sinusoidal temperature and concentration boundary conditions were numerically examined and different aspect ratio combinations, as well as different obstacle locations, were tested. The results indicated that for a moderate Ra number like Ra=105, total entropy generation of the system and the heat transfer rate from the walls are reduced with an increment in the obstacle size. In addition, it was found that site 4 presents the highest rate of entropy generation amongst all, yet still, the average Be number is not remarkably raised for this location.

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