Fluid friction and heat transfer in cylindrical pipes: Relationship between lumped and distributed parameters



Physical phenomena may be described from the “microscopic” point of view, in terms of distributed parameters, or from the “macroscopic” viewpoint, using lumped parameters. Engineering correlations almost always involve lumped parameters. A lumped parameter is equal or proportional to some average value of the corresponding distributed parameter. Like any average quantity it gives no information regarding the form of the distribution. The use of lumped parameters therefore requires some assumptions, expressed or implied, regarding the form of the distribution within the system.

The characteristic lumped parameters used in problems of heat transfer and fluid friction are overall or average fluxes of heat energy or momentum, arbitrarily defined as described in this paper. Common dimensionless groups, such as f, NBe, NSt and others are ratios of these energy or momentum fluxes. Such dimensionless groups, since they are ratios of lumped parameters, are themselves lumped parameters. In their definition, therefore, several assumptions regarding the distributions of velocity and temperature are implicit. When these assumptions are not valid, correction factors such as diffusivity ratios or length-to-length ratios are needed to allow for deviations from the distributions used for reference.

Using this approach the form of empirical equations becomes easy to predict. Dimensional analysis is not needed. In addition, this approach suggests that some accepted correlations may contain weaknesses not predicted by other methods.