In this study, the natural convection heat transfer and entropy generation in horizontal eccentric cylinders with different arrangements of two constant temperature sources are investigated numerically. The distance between eccentric cylinders was filled with pure fluid and Cu_ water nanofluid. The sources with constant temperature T-h and T-c were located on the inner and outer cylinders and the other walls were assumed to be insulated. Governing equations were formulated by using Boussinesq approximation and non-Boussinesq state (density inversion) and were solved on a non-uniform mesh in eccentric cylinders by using the finite volume method. The numerical calculation was carried out for Rayleigh number (10(4) <= Ra <= 5 x 10(5)), volume fraction of nanoparticles (0 <= Phi <= 0.08) and different arrangements of heat sources with different angles in Pr = 13.31 and constant eccentricity (e(v) = 0.7). The results were compared with concentric cylinders and presented from streamlines and isotherms flow field, local and average Nusselt number, local and total entropy generation. The results showed that eccentricity, different arrangements, discrete constant temperature sources and non-Boussinesq state affected the best state of heat transfer. In addition, increasing Rayleigh number and volume fractions of nanoparticles caused an increase in the rate of heat transfer and total entropy generation. It was concluded that Boussinesq approximation and eccentric cylinders had higher rate of heat transfer and entropy generation than non-Boussinesq state and concentric cylinders, respectively. The results indicated which arrangements and kinds of cylinders were optimum and applicable to use in industry and heat exchanger. (C) 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.