Solar-driven water desalination technologies are rapidly developing with various links to other renewable sources. However, the efficiency of such systems severely depends on the design parameters. The present study focused on using graphene oxide (GO) with the Φ = 0.2, 0.4 and 0.6 wt.% dispersed in paraffin, as phase-change materials (PCMs), to improve the productivity of a solar still for desalination applications. The outcomes showed that by adding more graphene oxide to paraffin, the melting temperature got reduced. Solar still with GO/paraffin showed 25% productivity improvement in comparison with the solar still with only PCM. The obtained Nusselt number during the melting time also represented that free convection heat transfer into the melted region of the solar still has been enhanced by adding dispersed GO to the PCM, compared to the base paraffin. Also, increasing the hot wall temperature augments the Nusselt number. Finally, an empirical equation was derived to correlate the average Nusselt number as a function of Rayleigh number (Ra), the Stefan number (Ste), the subcooling factor (Sb), and the Fourier number (Fo). The obtained correlation depicted that Nusselt number enhancement has a reverse relation with Fourier number.