Remarks on the Analogy Between Heat Transfer and Momentum Transfer

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Abstract
This paper presents an extension of Von Kármán’s analysis of heat transfer to fluids in closed conduits, based on the analogy between heat transfer and momentum transfer. For a particular ideal system, an expression for the temperature distribution in a fluid in turbulent motion being heated or cooled inside of a circular pipe is derived and a relation is obtained between Nusselt’s modulus and the pipe-friction factor for “isothermal” heat transfer. This equation is extended to apply in cases in which the physical properties of the fluid vary across the section of the pipe. The apparent variation of the dimensionless distance parameter y+ with ratio of wall viscosity to laminar sublayer viscosity and Reynolds’ number is obtained. A comparison between the equation developed in the paper and the Nusselt empirical equation, including the constants evaluated by Dittus and Boelter, is made.

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