Abstract Fourier and Reynolds correlations are presented for determining the values of thermal parameters defined in terms of the half cooling times and seven-eighths cooling times for spheres and cylinders being cooled in air or water flows. In this respect, an experimental, modeling and literature-survey investigation was conducted. In the experiments, several spheres and cylinders were cooled in air and water flows, and their centre temperatures measured. In the modeling part, a methodology was used to determine the cooling parameters, and using experimental data, together with some experimental data from the literature, the following Fourier-Reynolds correlations for half and seven-eighths cooling times were developed: Fo s = 0·3693Re −0·11871 and Fo z = 1·2951Re −0·16003 respectively for water-cooling applications; Fo s = 42·465Re −0·54426 and Fo z = 125·21Re −0·53913 respectively for air-cooling applications. The results of the present study show that there is a strong relationship between the Fourier and Reynolds numbers, and the developed Fourier-Reynolds correlations reasonably determine the cooling thermal parameters for spherical or cylindrical bodies cooled in water and air flows. These correlations could be of benefit in the refrigeration industry.