Droplet evaporation based cooling techniques, such as the spray cooling, give high heat transfer rates by utilizing latent energy and are usually preferred in thermal applications. However, with the significant rise in heat dissipation levels for high heat flux devices, these devices cannot be thermally managed due to the limited cooling capacity of existing thermal fluids. In this paper, we report the evaporation of the Cu-Al2O3 hybrid nanofluid (HNF) droplet on a copper surface as well as its own residue surface, developed from the evaporation of the first Cu-Al2O3 HNF droplet. As the main novelty, we identify the critical residue size and investigate the residue size effect, above and below the critical residue size, on evaporation rate of the succeeding Cu-Al2O3 HNF droplet resting over a residue surface. We also develop a new analytical model to estimate the Cu-Al2O3 HNF droplet evaporation rate and compare our results with other existing models. The results show that the Cu-Al2O3 HNF droplet gives 17% higher evaporation rate than a water droplet on a copper surface. Also, the evaporation rate of the Cu-Al2O3 HNF droplet on a residue surface sharply increases by 106% with increasing residue size up to the critical residue size. However, further increasing the residue size above its critical value has a negligible effect on the droplet evaporation rate. Moreover, the evaporation rate of the Cu-Al2O3 HNF droplet on its residue surface is enhanced up to 104% when compared to a copper surface.