The natural convection fluid flow and heat transfer in an annulus of two differentially heated confocal elliptic cylinders filled with the Cu–water nanofluid are investigated numerically. The outer cylinder is maintained at a constant temperature Tc while the inner cylinder is kept at a differentially higher constant temperature Th. Equations of continuity, momentum, and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional steady, laminar, and incompressible flow, which is expressed in terms of stream function, vorticity, and temperature. The basic equations are discretized using the finite-volume method. Using a developed code, calculations were performed for Rayleigh number (103 ≤ Ra ≤ 3 × 105), volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.12), and eccentricity of the inner ellipse, ε1 = 0.7, 0.8, and 0.9. The eccentricity of outer ellipse and the angle of orientation are fixed at 0.6 deg and 0 deg, respectively. Results are presented in the form of stream lines, isotherm plots, and local and average Nusselt numbers. The results discussed in this present work show the existence of a very good agreement between the present results and those from the previous researches.