I developed a method to calculation the entropy production of earth Please read it and let me know about your comments. I have considered some problem in it so I should correct it.
Equations 3 and 6 violate each other. In a reversible machine (Carnot), the entropy production is equal to zero, so there is no lost work and QH/TH=QL/TL.
I recommend you to study professor Adrian Bejan's theory of "Constructal Law" for a better understanding of sources of entropy production (in brakes and engines) in life.