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The purpose of this work is to investigate the formation and evaporation ofthe primordial black holes in the inflationary scenarios. Thermodynamicparameters such as mass, temperature and entropy are expressed in terms ofNANOGrav frequency. By numerical calculations we show that the constraint onthe mass range $10^{-5}kg-10^{50}kg$ is well confirmed. We discuss the relationbetween the redshift and the probability for gravitational wave sourcepopulations. A new parameter associated with the frequency and Hubble rate ispresented, by which for the spectral index $n_{s}\approx 0.996$ and the Hubbleconstant $H_{0}\approx 67.27km.s^{-1}.Mpc^{-1}$, the effective Hubble constantis calculated to be $H_{eff,0}\approx 73.24km.s^{-1}.Mpc^{-1} $ which iscompatible with the observational data. We make a comparison between the Hubbletension and the primordial perturbations and the expression of the mass lossrate, chemical potential and central charge needed to describe the Hawkingevaporation will be established.

Implications of the NANOGrav results for primordial black holes and Hubble tension