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

[+] Author and Article Information
K. C. Cheng

University of Alberta, 4327-115 Street, Edmonton, AB, T6J 1P5, Canada

Because of the nature of this paper, quotations will be used often to give proper credit to the authors of articles and books.

Appl. Mech. Rev 62(6), 060803 (Aug 05, 2009) (17 pages) doi:10.1115/1.3090832 History: Received December 23, 2008; Revised January 21, 2009; Published August 05, 2009

## Abstract

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.

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