Newtons law of cooling vs conduction equation in solids

kundukoustav

I know that Newtons law of cooling is useful when a solid is transferring heat to a fluid. And conduction equation is used in solids.
My question is: 1) Can Newtons law of cooling be applied in case of solids (apart from Heat conduction equation)? 2) Can Newtons law of cooling be applied in case of fluid to fluid heat transfer (like, for example, hot water to ambient air)?
Thanks in advance!!

Studiot

The two equations are not really completely separate equations.

Both can be applied to solids, and less effectively to liquids and gasses because there are other possible significant effects like evaporation/condensation and convection in play.

Newton's law does not directly deal with heat transfer (heat and temperature are not the same thing) however the rate of heat transfer is proportional to the temperature difference and the rate of cooling is often proportional to the rate of heat transfer so the equations are linked.