The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different un...

In the present study, an analysis is carried out to study the variable viscosity and chemical reaction effects on the flow, heat, and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equati...

Inadequate hole cleaning can lead to many problems in horizontal and directional wells. In this work, we tried to investigate the cutting transport phenomenon by an experimental directional drilling simulator, considering the differences between the operational and experimental conditions. The inclination, fluid type (water, foam, viscous, and dense), rotary speed (0 and 110 rpm), nozzle bit si...

For the problem of large dimensionless index fluctuations in rotating machinery complex fault and that the corresponding scope is difficult to determine. In this paper proposes a rotating machinery complex fault method that combined dimensionless and the least squares method filtering. This method implementation filtering and determine the scope of the dimensionless index. By doing experiments ...

A numerical study is made of laminar, unsteady flow behind a rotationally oscillating circular cylinder using a recently developed higher order compact (HOC) scheme. The stream function vorticity formulation of Navier-Stokes (N-S) equations in cylindrical polar coordinates are considered as the governing equations. The temporal behaviour of vortex formation and relevant streamline patterns of t...

Multizone airflow network models assume that in a zone air temperature and contaminant concentrations are uniform, and air momentum effects are neglected. These assumptions could cause errors for airflow with strong buoyancy, large contaminant concentration gradient, or strong momentum. This study has found the correlations of the errors and some dimensionless air parameters. The assumption of ...

Electrospinning refers to the process of generating nanofibers from electrified viscous polymeric jets. Though relatively easy to perform, this process is quite complex in its nature, given the large number of parameters that are involved. This study attempts to derive a relation between the final fiber diameter and the major process parameters. Two new dimensionless numbers describing viscous ...

The behavior of biosensors is based on the well-defined physical, chemical and biological reactions, which are expressed by nonlinear differential equations. The characteristics of diffusion reaction of choline biosensor are analyzed mathematically for wide range of input parameters such as initial concentration of choline and thickness of choline oxide enzyme layer. The mathematical simulation...

Electrokinetic pumps are a novel microfluidic technology being pursued for microscale high performance liquid chromatography (HPLC) and heat transfer applications. These pumps are typically reported to have efficiencies of only a few percent or less. We present an analytical and numerical investigation of the thermodynamic efficiency of electrokinetic pumping, solving the hydrodynamic and fully...

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed ...