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Brinkman Number
The Brinkman number (Br) is a dimensionless number related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing. It is named after the Dutch mathematician and physicist Henri Brinkman. There are several definitions; one is \mathrm = \frac = \mathrm \, \mathrm where * ''μ'' is the dynamic viscosity; * ''u'' is the flow velocity; * ''κ'' is the thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...; * ''T0'' is the bulk fluid temperature; * ''Tw'' is the wall temperature; * Pr is the Prandtl number * Ec is the Eckert number It is the ratio between heat produced by viscous dissipation and heat transported by molecular conduction. i.e., the ratio of viscous heat generation to external heating. The higher its value, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless
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] |
Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compounds, produces unique physical properties including toughness, high elasticity, viscoelasticity, and a tendency to form amorphous and semicrystalline structures rather than crystals. The term "polymer" derives from the Greek word πολύς (''polus'', meaning "many, much") and μέρος (''meros'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Brinkman
Henri Coenraad Brinkman (Amsterdam, 30 March 1908 – Delft, 11 February 1961) was a Dutch mathematician and physicist. He was a professor at the University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a public research university of more than 30,000 students in the city of Groningen in the Netherlands. Founded in 1614, the university is th .... The dimensionless Brinkman number is named after him. References {{DEFAULTSORT:Brinkman, Henri 1908 births 1961 deaths 20th-century Dutch physicists 20th-century Dutch mathematicians University of Groningen faculty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Velocity
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). Definition The flow velocity ''u'' of a fluid is a vector field : \mathbf=\mathbf(\mathbf,t), which gives the velocity of an '' element of fluid'' at a position \mathbf\, and time t.\, The flow speed ''q'' is the length of the flow velocity vector :q = \, \mathbf \, and is a scalar field. Uses The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow: Steady flow The flow of a fluid is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Conductivity
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials like Rockwool or Styrofoam. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications, and materials of low thermal conductivity are used as thermal insulation. The reciprocal of thermal conductivity is called thermal resistivity. The defining equation for thermal conductivity is \mathbf = - k \nabla T, where \mathbf is the heat flux, k is the thermal conductivity, and \nabla T is the temperature gradient. This is known as Fourier's Law for heat conduction. Although commonly expressed as a scalar, the most general form of th ... [...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] |
Eckert Number
The Eckert number (Ec) is a dimensionless number used in continuum mechanics. It expresses the relationship between a flow's kinetic energy and the boundary layer enthalpy difference, and is used to characterize heat transfer dissipation. It is named after Ernst R. G. Eckert. It is defined as : \mathrm = \frac = \frac where * ''u'' is the local flow velocity of the continuum, * ''cp'' is the constant-pressure local specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ... of the continuum, * \Delta T is the difference between wall temperature and local temperature. References Dimensionless numbers of fluid mechanics Dimensionless numbers of thermodynamics Continuum mechanics {{Fluiddynamics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Screw Extruder
Extrusion is a process used to create objects of a fixed cross-sectional profile by pushing material through a die of the desired cross-section. Its two main advantages over other manufacturing processes are its ability to create very complex cross-sections; and to work materials that are brittle, because the material encounters only compressive and shear stresses. It also creates excellent surface finish and gives considerable freedom of form in the design process. Drawing is a similar process, using the tensile strength of the material to pull it through the die. It limits the amount of change that can be performed in one step, so it is limited to simpler shapes, and multiple stages are usually needed. Drawing is the main way to produce wire. Metal bars and tubes are also often drawn. Extrusion may be continuous (theoretically producing indefinitely long material) or semi-continuous (producing many pieces). It can be done with hot or cold material. Commonly extruded material ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sy ... [...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] |
