Residence time of energy in Earth's atmosphere and in the Sun

In atmospheric chemistry, a parameter called residence time can be defined for each gas as T=M/F, where M represents the average mass in the atmosphere and F is the total average influx or outflux, which in time averages are equal. In this paper we extend this concept from matter to energy which is also a conservative quantity and estimate the average residence time of energy in Earth's atmosphere and in the Sun. For our atmosphere, the estimation amounts about 56 days and for the Sun the residence time is about 2.6 x 10^7 yr, which agrees with the Kelvin-Helmholtz time scale.