Some Observations on the Origins of Newton’s Law of Cooling and Its Influences on Thermofluid Science

The exact mathematical analogy exists between Newton’s law of cooling and Proposition II, Book II (The motion of bodies in resisting mediums) of the Principia. Several approaches for the proof of Proposition II are presented based on the expositions available in the historical literature. The relationships among Napier’s logarithms (1614), Euclid’s geometric progression (300 B.C.), and Newton’s law of cooling (1701) are explored. Newton’s legacy in the thermofluid sciences is discussed in the light of current knowledge. His characteristic parameter for the temperature fall ratio, $ΔT/(T−T∞)$⁠, is noted. The relationships and connections among Newton’s cooling law (1701), Fourier’s heat conduction theory (1822), and Carnot’s theorem (1824)based on temperature difference $(ΔT)$ as a driving force are noted. After tracing the historical origins of Newton’s law of cooling, this article discusses some aspects of the historical development of the heat transfer subject from Newton to the time of Nusselt and Prandtl. Newton’s legacy in heat transfer remains in the form of the concept of heat transfer coefficient for conduction, convection, and radiation problems. One may conclude that Newton was apparently aware of the analogy of his cooling law to the low Reynolds number motion of a body in a viscous fluid otherwise at rest, i.e., its drag is approximately proportional to its velocity.