The objective of this numerical assessment is to examine the hydrothermal and irreversibility behaviour of a biologically synthesized water-silver nano-fluid in a wavy microchannel heat sink (MCHS). The green tea leaf extract is utilized to prepare silver nanoadditives. The impacts of nanoadditives volume fraction, Reynolds number, amplitude and wavelength of the channel on the convective heat transfer coefficient, CPU surface temperature, pumping power, as well as the thermal, frictional, and total irreversibilities are investigated. The results show that enhancing the Reynolds number and nanoadditives fraction intensifies the performance of heat sink by boosting the convective heat transfer coefficient of the working fluid which favorably reduces the CPU surface temperature and the rate of thermal and total irreversibilities and importantly leads to the temperature uniformity of the CPU surface. However, increase in Reynolds number adversely affects both the pumping power and the frictional irreversibility in the system. In addition, it is found that the nano-fluid always has a better cooling performance in comparison with the pure water. Moreover, it is reported that augmenting the wavelength results in an increase in the hydrothermal performance of nano-fluid and decrease in the global total entropy generation rate.