Non-dimensional

In science and engineering, 'non-dimensional' (also spelled 'nondimensional') describes a quantity, equation, or system of units that lacks explicit physical dimensions, like length, mass, or time. Non-dimensionalization is the process of removing these dimensions, often by dividing a dimensional quantity by a quantity with the same dimensions. This process simplifies equations, reduces the number of variables needed to describe a system, and facilitates the comparison of different physical situations, allowing for scaling analysis and the generalization of results. The resulting non-dimensional parameters represent ratios or combinations of dimensional quantities, highlighting the relative importance of different physical effects.

Non-dimensional meaning with examples

• In fluid dynamics, the Reynolds number is a non-dimensional number used to predict flow patterns in different fluid flow situations. It is calculated using fluid density, velocity, characteristic length, and viscosity. By using the Reynolds number, engineers can model flow characteristics without the need for full-scale experiments, leading to better designs. This provides for a basis of comparison across different scales of size of fluid systems.
• When studying heat transfer, the Nusselt number represents the ratio of convective to conductive heat transfer at a boundary. It is a non-dimensional number that helps in determining the heat transfer coefficient and is thus crucial for designing heat exchangers, managing energy transfer and improving energy efficiency. The Nusselt number allows for easy comparison of convective efficiency across diverse materials and temperature gradients.
• In structural mechanics, the Euler number is a non-dimensional number that expresses the critical load at which a slender column will buckle. This parameter allows for evaluating the stability of columns under compressive forces without the need for directly scaling the overall sizes. It helps engineers design structures that resist buckling and ensure structural integrity under diverse loading scenarios and sizes.
• In chemical engineering, the Damköhler number compares the rate of chemical reaction to the rate of transport phenomena, such as mass transfer or diffusion. It provides insight into the interplay between reaction kinetics and transport processes in a reactor, supporting optimisation of reaction conditions and reactor design, leading to effective chemical processing. The Damköhler number is, thus, useful in reactor scaling and industrial processes.