Dimensionless numbers in fluid mechanics and dimensional analysis of microchannel steam reforming reactors

Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have an important role in analyzing the behavior of fluids. Common examples include the Reynolds or the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed. As a general example of how dimensionless numbers arise in fluid mechanics, the classical numbers in transport phenomena of mass, momentum, and energy are principally analyzed by the ratio of effective diffusivities in each transport mechanism. The six dimensionless numbers give the relative strengths of the different phenomena of inertia, viscosity, conductive heat transport, and diffusive mass transport. These same quantities may alternatively be expressed as ratios of characteristic time, length, or energy scales. Such forms are less commonly used in practice, but can provide insight into particular applications. In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed. Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are originally expressed in differing units of measure. Incommensurable physical quantities are of different kinds and have different dimensions, and cannot be directly compared to each other, no matter what units they are originally expressed in meters and kilograms, seconds and kilograms, meters and seconds. Any physically meaningful equation, or inequality, must have the same dimensions on its left and right sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It also serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation. Dimensional analysis is most often used in physics and chemistry, and in the mathematics thereof, but finds some applications outside of those fields as well. In fluid mechanics, dimensional analysis is performed to obtain dimensionless pi terms or groups. According to the principles of dimensional analysis, any prototype can be described by a series of these terms or groups that describe the behavior of the system. Using suitable pi terms or groups, it is possible to develop a similar set of pi terms for a model that has the same dimensional relationships.
Contributor: Junjie Chen, E-mail address: [e-mail], ORCID: 0000-0002-5022-6863, Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, 2000 Century Avenue, Jiaozuo, Henan, 454000, P.R. China