In this work, the effects of viscous dissipation on heat transfer and entropy generation of the nanofluid natural convection in an inclined square cavity are numerically investigated. A fractional-step semiimplicit finite difference algorithm based on the projection method on a staggered grid is proposed to solve the laminar natural convection problem, which has the advantage of larger time steps. The square cavity is filled with a nanofluid composed of (Cu) copper nanoparticles and water,and the viscous dissipative behavior of the mixture flow is not negligible. The studied parameters are Rayleigh number Ra (104 and 105), Eckert number Ec (0 − 2), the volume fraction of solid particles ϕ (0 − 0.06), and inclination angle of square cavity α (0 − π/2). The Prandtl number is fixed to Pr = 6.2. The results show that at any inclination angle, the increase in viscous dissipation leads to weakened heat transfer on the hot wall, enhanced heat transfer on the cold wall, and weakened flow in the square cavity. For the base solution without nanoparticles, the Eckert number has the greatest impact, with its effects on the average Nusselt number on the hot wall, maximum streamfunction, and average Nusselt number on the cold wall being ~13, 0.15, 18.69%, and at Ra = 104, and 12, 0.5, 28.87% at Ra = 105, respectively. Research on entropy generation shows that as Eckert number increases, the entropy generation due to heat transfer increases, while due to fluid friction decreases. As the Rayleigh number increases, the effect of viscous dissipation increases. As the inclination angle increases, the effects of volume fraction and Eckert number weaken. Adding solid particles can effectively weaken the effect of viscous dissipation.