This study investigates natural convective heat transfer of copper–water nanofluids in a square enclosure with alternating temperature at one vertical wall, relatively low temperature at the opposite sidewall and adiabatic at the other walls. The transport equations are solved numerically with finite volume approach using SIMPLEC algorithm. Calculations are performed for nanoparticle volume fractions from 0 to 0.2 and dimensionless amplitude from 0 to 1.0 with consideration of three typical alternating waves (trapezoid wave, sine wave and triangle wave). Results show the utilization of nanoparticles enhances heat transfer and the percentage increase in the time-averaged Nusselt number is around 38% d from ϕ =0 to ϕ =0.2 under the certain conditions. The oscillating waveform has a degree effect on the heat transfer enhancement and the trapezoid wave is more conducive to the enhancement of heat transfer than sine and triangle waves. And the oscillating area is introduced to combine the oscillating waveform and its amplitude and the percentage increase in the time-averaged Nusselt number is around 14.5% from S =0 to S =0.075. In the end, the regression equation about the time-averaged Nusselt number is obtained as parameters of the solid volume fraction and the oscillating area.