Concept Of Heat Transfer Coefficient Research Articles

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.

Heat in history Isaac Newton and Heat Transfer

An attempt is made to provide historical perspectives on the influences of Newton's law of cooling (1701) on the development of heat transfer theory. Newton's cooling law provides the first heat transfer formulation and is the formal basis of convective heat transfer. The cooling law was incorporated by Fourier (1822) as the convective boundary condition (Biot number) in his mathematical theory of heat conduction. The decisive step in the application of the concept of heat transfer coefficient occurred with the publication of the “basic law of heat transfer” by Nusselt in 1915. Newton's law is valid only for forced convection with constant physical properties. The close relationships for various heat transfer theories are pointed out. Heat transfer phenomena can also be classified based on the relationship between surface heat flux and temperature difference as a driving force.