Many of Indian school textbooks claim a proof of Newton's law of cooling from Stefan's law of black-body radiation.
As far as I am aware of, Newton's law is based on cooling from convection currents and Stefan's law on radiation. There is not supposed to be any relation between them.
Question: Is there any relation between them, and can Newton's law of cooling be derived from Stefan's law?
I found many answers and resources on Google, but an answer referring to a well-established paper, book or resource of same kind will be highly appreciated.
There's a question in the syllabus they teach us such as "Derive Newton's law of Cooling from Stefan's Law." And here's one of the links which show the solution. They are approximating Stefan's law to Newton's law(mathematically) by considering $T-T_0$ very small. They even claim that Newton's law is applicable for even small temperature differences whereas in reality Newton's law is applicable for all temperature ranges.
Please help. Is there any strong reference which can help shut down this misconception. I understand why are they different but a reference might help much.