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Schmidt Number
Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after German engineer Ernst Heinrich Wilhelm Schmidt (1892–1975). The Schmidt number is the ratio of the shear component for diffusivity ''viscosity/density'' to the diffusivity for mass transfer ''D''. It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. It is defined as: :\mathrm = \frac = \frac = \frac where: * \nu is the kinematic viscosity or (/\,) in units of (m2/s) * D is the mass diffusivity (m2/s). * is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s) * \rho is the density of the fluid (kg/m3). The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal diffusivity to mass diffusivity is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Entanglement
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl Number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as: : \mathrm = \frac = \frac = \frac = \frac where: * \nu : momentum diffusivity (kinematic viscosity), \nu = \mu/\rho, ( SI units: m2/s) * \alpha : thermal diffusivity, \alpha = k/(\rho c_p), (SI units: m2/s) * \mu : dynamic viscosity, (SI units: Pa s = N s/m2) * k : thermal conductivity, (SI units: W/(m·K)) * c_p : specific heat, (SI units: J/(kg·K)) * \rho : density, (SI units: kg/m3). Note that whereas the Reynolds number and Grashof number are subscripted with a scale variable, the Prandtl number contains no such length scale and is dependent only on the fluid and the fluid state. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. The mass transfer analog of the Prandtl number is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Numbers Of Fluid Mechanics
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-form Expression
In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context. Example: roots of polynomials The solutions of any quadratic equation with complex coefficients can be expressed in closed form in terms of addition, subtraction, multiplication, division, and square root extraction, each of which is an elementary function. For example, the quadratic equation :ax^2+bx+c=0, is tractable since its solutions can be expressed as a closed-form expression, i.e. in terms of elementary functions: :x=\frac. Similarly, solutions of cubic and quartic (third and fourth degree) equations can be expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Density
Power density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volume power density, expressed as W/m3. In reciprocating internal combustion engines, power density (power per swept volume or brake horsepower per cubic centimeter) is an important metric, based on the ''internal'' capacity of the engine, not its external size. Examples See also *Surface power density, energy per unit of area *Energy density, energy per unit volume * Specific energy, energy per unit mass * Power-to-weight ratio/specific power, power per unit mass **Specific absorption rate Specific absorption rate (SAR) is a measure of the rate at which energy is absorbed per unit mass by a human body when exposed to a radio frequency (RF) electromagnetic field. It can also refer to absorption of other forms of energy by tissue, inc ... ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling Engine
A Stirling engine is a heat engine that is operated by the cyclic compression and expansion of air or other gas (the ''working fluid'') between different temperatures, resulting in a net conversion of heat energy to mechanical work. More specifically, the Stirling engine is a closed-cycle regenerative heat engine with a permanent gaseous working fluid. ''Closed-cycle'', in this context, means a thermodynamic system in which the working fluid is permanently contained within the system, and ''regenerative'' describes the use of a specific type of internal heat exchanger and thermal store, known as the ''regenerator''. Strictly speaking, the inclusion of the regenerator is what differentiates a Stirling engine from other closed-cycle hot air engines. In the Stirling engine, a gas is heated and expanded by energy supplied from outside the engine's interior space (cylinder). It is then shunted to a different location within the engine, where it is cooled and compressed. A piston (o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Péclet Number
In continuum mechanics, the Péclet number (, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. In the context of species or mass transfer, the Péclet number is the product of the Reynolds number and the Schmidt number (). In the context of the thermal fluids, the thermal Péclet number is equivalent to the product of the Reynolds number and the Prandtl number (). The Péclet number is defined as: : \mathrm = \dfrac For mass transfer, it is defined as: :\mathrm_L = \frac = \mathrm_L \, \mathrm Such ratio can also be re-written in terms of times, as a ratio between the characteristic temporal intervals of the system: :\mathrm_L = \frac = \frac = \frac For \mathrm \gg 1 the diffusion happens in a much longer time compared to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vorticity
In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings. Mathematically, the vorticity \vec is the curl of the flow velocity \vec: :\vec \equiv \nabla \times \vec\,, where \nabla is the nabla operator. Conceptually, \vec could be determined by marking parts of a continuum in a small neighborhood of the point in question, and watching their ''relative'' displacements as they move along the flow. The vorticity \vec would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. In a two-dimensional fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulent Prandtl Number
The turbulent Prandtl number (Prt) is a non-dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity. It is useful for solving the heat transfer problem of turbulent boundary layer flows. The simplest model for Prt is the Reynolds analogy, which yields a turbulent Prandtl number of 1. From experimental data, Prt has an average value of 0.85, but ranges from 0.7 to 0.9 depending on the Prandtl number of the fluid in question. Definition The introduction of eddy diffusivity and subsequently the turbulent Prandtl number works as a way to define a simple relationship between the extra shear stress and heat flux that is present in turbulent flow. If the momentum and thermal eddy diffusivities are zero (no apparent turbulent shear stress and heat flux), then the turbulent flow equations reduce to the laminar equations. We can define the eddy diffusivities for momentum transfer \varepsilon_M and heat transfer \varepsilon_H a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eddy Diffusion
Eddy diffusion, eddy dispersion, or turbulent diffusion is a process by which substances are mixed in the atmosphere, the ocean or in any fluid system due to eddy motion. In other words, it is mixing that is caused by eddies that can vary in size from subtropical ocean gyres down to the small Kolmogorov microscales. The concept of turbulence or turbulent flow causes eddy diffusion to occur. The theory of eddy diffusion was first developed by Sir Geoffrey Ingram Taylor. In laminar flows, material properties (salt, heat, humidity, aerosols etc.) are mixed by random motion of individual molecules (see molecular diffusion). By a purely probabilistic argument, the net flux of molecules from high concentration area to low concentration area is higher than the flux in the opposite direction. This down-gradient flux equilibrates the concentration profile over time. This phenomenon is called molecular diffusion, and its mathematical aspect is captured by the diffusion equation. In turbule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulence Modeling
Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real life scenarios, including the flow of blood through the cardiovascular system, the airflow over an aircraft wing, the re-entry of space vehicles, besides others. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows. The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real life turbulent flows, CFD simulations use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows. Closure problem The Navier–Stokes equations govern the velocity and pressure of a fluid flow. In a turbulent flow, each of these quantities may be decomposed into a mean part and a fluctuating part. Averaging the equations gives the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Number
The Lewis number (Le) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer. The Lewis number puts the thickness of the thermal boundary layer in relation to the concentration boundary layer. The Lewis number is defined as :\mathrm = \frac = \frac . where \alpha is the thermal diffusivity and D the mass diffusivity, \lambda the thermal conductivity, \rho the density, D_ the mixture-averaged diffusion coefficient, and c_p the specific heat capacity at constant pressure. In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition. The Lewis number can also be expressed in terms of the Prandtl number and the Schmidt number : :\mathrm = \frac. It is named after Warren K. Lewis (1882–1975), who was the first head of the Chemical Engineering Department at MIT. Some workers in the field of combustion assume (i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
