Application of Similarity Principles to Thermal Transport Systems

Abstract

THE use of similarity laws is well established for mechanical transport systems, that is, systems in which the dependent variable (A) is the flow or transport of matter. Examples of dimensionless numbers (B) used in such systems are the Froude number for mechanical systems depending solely upon the action of gravity, the Reynolds number (R_e) for mechanical systems depending upon the action of viscosity, and the number introduced by Davis¹ for systems depending upon the action of density changes in hot gases. Although heat transfer is involved in the last of these three examples, it is really a mechanical system, since the heat is conveyed by the mechanical motion of the fluid concerned. The applicability of model results expressed in the form A = f(B) to the original system is based upon the fact that the motion of any element of the fluid obeys the fundamental law of dynamics, p = mf, even though the integration of this law for the three dimensional extended system is too complex for mathematical treatment.