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Ratio of kinematic viscosity to thermal diffusivity
The Prandtl number (Pr) is a dimensionless number, named for the German fluid dynamicist Ludwig Prandtl. It is defined as the ratio of momentum diffusivity
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
Turbulent_Prandtl_number
Nondimensional heat transfer coefficient
the Grashof number or Rayleigh number along with the Prandtl number. The mass transfer analog of the Nusselt number is the Sherwood number. The group now
Nusselt_number
German physicist (1875–1953)
layer, thin-airfoils, and lifting-line theories. The Prandtl number was named after him. Prandtl was born in Freising, near Munich, on 4 February 1875
Ludwig_Prandtl
The Magnetic Prandtl number (Prm) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity)
Magnetic_Prandtl_number
Ratio of inertial to viscous forces acting on a liquid
Péclet number and the magnetic Reynolds number. These are therefore related to Re by-products with ratios of diffusivities, namely the Prandtl number and
Reynolds_number
Ratio of a fluid's advective and diffusive transport rates
is equivalent to the product of the Reynolds number and the Prandtl number (Re × Pr). The Péclet number is defined as P e = advective transport rate diffusive
Péclet_number
Layer of fluid in the immediate vicinity of a bounding surface
is governed by the Prandtl number. If the Prandtl number is 1, the two boundary layers are the same thickness. If the Prandtl number is greater than 1
Boundary_layer
Dimensionless number in fluid mechanics
Nusselt number (Nu) in terms of the Reynolds number (Re) and the Prandtl number (Pr) can be used as a mass transfer correlation by replacing the Prandtl number
Sherwood_number
Dimensionless parameter in fluid mechanics
where Nu is the Nusselt number; Re is the Reynolds number; Pr is the Prandtl number. The Stanton number arises in the consideration of the geometric similarity
Stanton_number
Dimensionless quantity associated with free convection of a fluid
relationship between buoyancy and viscosity within a fluid, and the Prandtl number (Pr), which describes the relationship between momentum diffusivity
Rayleigh_number
Ratio of a fluid's kinematic viscosity to mass diffusivity
(kg/m3) Pe is the Peclet Number Re is the Reynolds Number. The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal
Schmidt_number
circular pipe that the Turbulent Prandtl Number is not close to unity but rather a strong function of the molecular Prandtl number amongst other parameters.
Ashok_Malhotra_(professor)
Theoretical construct in flow physics
The Prandtl–Glauert singularity is a theoretical construct in flow physics, often incorrectly used to explain vapor cones in transonic flows. It is the
Prandtl–Glauert_singularity
Equation in convective heat transfer
{\displaystyle \Pr } is the Prandtl number. The Churchill–Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the
Churchill–Bernstein_equation
Ratio of thermal diffusivity to mass diffusivity
number to be the inverse of the above definition. The Lewis number can also be expressed in terms of the Prandtl number (Pr) and the Schmidt number (Sc):
Lewis_number
Dimensionless parameter in fluid mechanics
Reynolds number and Pr is the Prandtl number. This number is useful in determining the thermally developing flow entrance length in ducts. A Graetz number of
Graetz_number
Dimensionless number in fluid mechanics
{\displaystyle \ \sigma } is the Prandtl number, and ζ {\displaystyle \ \zeta } is the magnetic Prandtl number. The Chandrasekhar number is thus defined as: Q
Chandrasekhar_number
Dimensionless quantity in plasma physics
Lundquist number can be greater than 1020. Considerations of Lundquist number are especially important in magnetic reconnection. Magnetic Prandtl number Péclet
Lundquist_number
Quantity relating heat flux and temperature difference
Rayleigh number with respect to this length and Pr is the Prandtl number (the Rayleigh number can be written as the product of the Grashof number and the
Heat_transfer_coefficient
Dimensionless number in fluid mechanics
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
Brinkman_number
Distance a flow travels after entering a pipe before fully developed
Re_{D}} is the Reynolds number (based on the pipe diameter) and P r {\displaystyle Pr} is the Prandtl number. The Prandtl number modifies the hydrodynamic
Entrance length (fluid dynamics)
Entrance_length_(fluid_dynamics)
Type of boiling
thermal conductivity of the liquid, PrL is the Prandtl number of the liquid, Reb is the bubble Reynolds number, R e b = D b G b μ L , {\displaystyle \mathrm
Nucleate_boiling
Topics referred to by the same term
of some voting systems Praseodymium, symbol Pr, a chemical element Prandtl number, in physics and engineering, typically denoted Pr Propyl radicals or
PR
Exchange of mass, energy, and momentum between observed and studied systems
several dimensionless numbers are used such as Nusselt number, Reynolds number, and Prandtl number. The commonly used equation is N u a = h a D k {\displaystyle
Transport_phenomena
Relation in aerospace engineering
where Pr {\displaystyle {\text{Pr}}} is the Prandtl number, Le {\displaystyle {\text{Le}}} is the Lewis number, h 0 , e {\displaystyle h_{0,e}} is the stagnation
Fay-Riddell_equation
In fluid mechanics the Prandtl condition was suggested by the German physicist Ludwig Prandtl to identify possible boundary layer separation points of
Prandtl_condition
Chemical element with atomic number 8 (O)
Oxygen is a chemical element; it has the symbol O and its atomic number is 8. It is a member of the chalcogen group in the periodic table. It is highly
Oxygen
is the Prandtl number based on μ ′ {\displaystyle \mu '} ; when ζ = 0 {\displaystyle \zeta =0} , say as in monoatomic gases, this Prandtl number is just
Becker–Morduchow–Libby solution
Becker–Morduchow–Libby_solution
Chemical element with atomic number 1 (H)
Hydrogen is a chemical element; it has the symbol H and atomic number 1. It is the lightest and most abundant chemical element in the universe, constituting
Hydrogen
Temperature at the boundary layer of a fluid undergoing convection
properties are calculated when using the Prandtl number, Nusselt number, Reynolds number or Grashof number to calculate a heat transfer coefficient,
Film_temperature
Two-dimensional laminar boundary layer that forms on a semi-infinite plate
the plate is not parallel to the flow. Using scaling arguments, Ludwig Prandtl argued that about half of the terms in the Navier-Stokes equations are
Blasius_boundary_layer
Chaotic model of atmospheric convection
representing physical properties of the system: σ is the Prandtl number, ρ is the Rayleigh number, and β relates to the physical dimensions of the fluid
Lorenz_system
diagonals give common symbols for the quantities, and the given dimensionless number is the ratio of the left column quantity over top row quantity; e.g. Re
Dimensionless numbers in fluid mechanics
Dimensionless_numbers_in_fluid_mechanics
Branch of fluid mechanics
increase in Mach number is proportional to only the convex angle of the passage (δ). The expansion corner that produces the Prandtl–Meyer fan can be sharp
Compressible_flow
Organic compound ethane-1,2-diol
viscosity (m2/s) Conductivity (W/(m⋅K)) Thermal diffusivity (m2/s) Prandtl number Thermal expansivity (K−1) 0 1130.75 2.294 7.53×10−5 0.242 9.34×10−8
Ethylene_glycol
Dimensionless quantity; ratio of a fluid's buoyancy to viscosity
Nusselt number. This is only true when the magnitude of Prandtl number is small or prescribed wall heat flux (WHF) is considered. Sherwood number, Bejan
Grashof_number
Dimensionless number in fluid dynamics
Jin; Jang, Seok Pil (2002). "Effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium". International
Darcy_number
Properties of a thermal boundary layer
velocity (momentum) boundary layer description first conceptualized by Ludwig Prandtl. Consider a fluid of uniform temperature T o {\displaystyle T_{o}} and
Thermal boundary layer thickness and shape
Thermal_boundary_layer_thickness_and_shape
Analogy in fluid dynamics
{\displaystyle s} is the Reynolds analogy factor which is coupled to the Prandtl number via s P r ≈ 0.8 {\displaystyle sPr\approx 0.8} ; C f {\displaystyle
Reynolds_analogy
Chemical element with atomic number 2 (He)
refrigeration due to the resulting high heat capacity ratio and low Prandtl number. The inertness of helium has environmental advantages over conventional
Helium
Boundary layer that forms on a wedge
zero. The basis of the Falkner-Skan approach are the Prandtl boundary layer equations. Ludwig Prandtl simplified the equations for fluid flowing along a
Falkner–Skan_boundary_layer
Chemical element with atomic number 7 (N)
Nitrogen is a chemical element; it has symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table,
Nitrogen
Mathematical technique in aerodynamics
The Prandtl–Glauert transformation is a mathematical technique which allows solving certain compressible flow problems by incompressible-flow calculation
Prandtl–Glauert transformation
Prandtl–Glauert_transformation
Chemical compound
Kinematic viscosity (m2/s) Conductivity (W/m K) Thermal diffusivity (m2/s) Prandtl Number Bulk modulus (K−1) −50 1546.75 0.875 3.10×10−7 0.067 5.01×10−1 6.2 2
Dichlorodifluoromethane
Fluid flow that occurs due to heterogeneous fluid properties and body forces
different correlations involving the Rayleigh Number (a function of both the Grashof number and the Prandtl number) must be used. Note that the above equation
Convection
Lubricant used for internal combustion engines
the time in service is supposed to correlate with the number of vehicle trips and capture the number of heating cycles. Oil does not degrade significantly
Motor_oil
Structure formed by diffuse material in orbital motion around a massive central body
Guan, Xiaoyue; Gammie, Charles F. (2009). "The turbulent magnetic Prandtl number of MHD turbulence in disks". Astrophysical Journal. 697 (2): 1901–1906
Accretion_disk
Mechanism by which a celestial body generates a magnetic field
Rayleigh number, E the Ekman number, Pr and Pm the Prandtl and magnetic Prandtl number. Magnetic field scaling is often in Elsasser number units B =
Dynamo_theory
Concept in aerodynamics
the popular analytical methods for calculating drag at high speeds, the Prandtl–Glauert rule, predicts an infinite amount of drag at Mach 1.0. Two of the
Drag-divergence_Mach_number
Passing cold propellant through tubes around a rocket engine to cool it
capacity of the combustion gas (J/kg/K) P r {\displaystyle Pr} is the Prandtl number of the combustion gas p c {\displaystyle p_{c}} is the chamber pressure
Regenerative cooling (rocketry)
Regenerative_cooling_(rocketry)
Mathematical model to quantify lift
The Lanchester–Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing from
Lifting-line_theory
Model of viscous fluid flow between two surfaces moving relative to each other
depend on the Reynolds number R e = U l / ν ∞ {\displaystyle \mathrm {Re} =Ul/\nu _{\infty }} , but rather on the Prandtl number P r = μ ∞ c p ∞ / κ ∞
Couette_flow
Phenomenon in fluid dynamics
convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. Prandtl-Meyer expansions are a subset of centered waves
Prandtl–Meyer_expansion_fan
Chemical compound
broad range of excitations and the ease with which it can be observed in a number of regions has made ammonia one of the most important molecules for studies
Ammonia
Poynting–Robertson effect – John Henry Poynting and Howard P. Robertson Prandtl number – Ludwig Prandtl Primakoff effect – Henry Primakoff Proteus phenomenon – Proteus
Scientific phenomena named after people
Scientific_phenomena_named_after_people
Flow of fluids with zero viscosity (superfluids)
consideration of the fluid sub layers when solid boundaries are involved. Ludwig Prandtl developed the modern concept of the boundary layer. His hypothesis establishes
Inviscid_flow
Type of computer benchmarking tool
numerical analysis of oscillatory instability of convection in low-Prandtl-number fluids 179.art C Image Recognition / Neural Networks Recognizes objects
SPECfp
Technique to solve geological problems by computational simulation
(1990-12-01). "A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry". Geophysical
Numerical_modeling_(geology)
Carbon-oxygen gas
approved for usage in the EU (listed as E number E290), US, Australia and New Zealand (listed by its INS number 290). A candy called Pop Rocks is pressurized
Carbon_dioxide
Poisonous gas consisting of carbon and oxygen
(cm2/s) Thermal conductivity (cW/m °C) Thermal diffusivity (cm2/s) Prandtl number −73.15 200 1.6888 1.045 1.27 0.0752 1.7 0.0963 0.781 −53.15 220 1.5341
Carbon_monoxide
Chemical compound of sulfur and oxygen
viscosity (m^2/s) Conductivity (W/m K) Thermal diffusivity (m^2/s) Prandtl Number Bulk modulus (K^-1) −50 1560.84 1.3595 4.84E-07 0.242 1.14E-07 4.24
Sulfur_dioxide
Chemical propellant and refrigerant
viscosity (m^2/s) Conductivity (W/m K) Thermal diffusivity (m^2/s) Prandtl Number Bulk modulus (K^-1) 230 1416 1.087 3.56E-04 2.51E-07 0.1145 7.44E-08
Chlorodifluoromethane
Turbulence that concerns the regimes of magnetofluid flow at high Reynolds number
P_{M}=\nu /\eta } . The magnetic Prandtl number is an important property of the fluid. Liquid metals have small magnetic Prandtl numbers, for example, liquid
Magnetohydrodynamic turbulence
Magnetohydrodynamic_turbulence
Convection with two density gradients
stability ratio, RaT is the thermal Rayleigh number, Pr is the Prandtl number, and Le is the Lewis number. These are defined as R ρ = α Δ T β Δ S , R a
Double_diffusive_convection
German mechanical engineer and professor (1882–1957)
now called the Grashof number, the Prandtl number, and the Reynolds number. In 1933, A. P. Colburn used the term "Nusselt number" in his paper on convection
Wilhelm_Nusselt
approach by considering variation in the Prandtl number, accounting for entrance effects in the Reynolds number, and moving the flame sheet location to
Hybrid_rocket_fuel_regression
Study of heat-sound interactions
{2\eta }{\omega \rho }}} with η the gas viscosity and ρ its density. The Prandtl number of the gas is defined as P r = η C p M κ . {\displaystyle P_{r}={\frac
Thermoacoustics
In fluid dynamics, Prandtl–Batchelor theorem states that if in a two-dimensional laminar flow at high Reynolds number closed streamlines occur, then the
Prandtl–Batchelor_theorem
Concept applicable to the testing of engineering models
Dimensional analysis is used to rearrange the units to form the Reynolds number ( R e {\displaystyle R_{e}} ) and pressure coefficient ( C p {\displaystyle
Similitude
Overview article
Transition to Oscillatory Thermo capillary Flow in Liquid Bridge of High Prandtl Number Fluid (Fluid Physics Experiment Facility (FPEF) ) Pattern Formation
Scientific research on the International Space Station
Scientific_research_on_the_International_Space_Station
of fluid dynamics, namely in double-diffusive convection of a small Prandtl number fluid. Double diffusive convection occurs when convection of the fluid
Blue_sky_catastrophe
salinity and temperature at bottom layer, Ra is the Rayleigh Number, and Pr is the Prandtl Number. The sign of RaS and RaT will change depending on whether
Non-dimensionalization and scaling of the Navier–Stokes equations
Non-dimensionalization_and_scaling_of_the_Navier–Stokes_equations
Chemical compound
primary alcohols. Thus, in substituted derivatives, the stereospecific numbering labels the molecule with a sn- prefix before the stem name of the molecule
Glycerol
aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than
Prandtl–Meyer_function
Function in fluid mathematics
K_{M}} and K H {\displaystyle K_{H}} can be related with the turbulent Prandtl number P r t {\displaystyle Pr_{t}} , K H K M = 1 P r t > 1 {\displaystyle
Monin–Obukhov similarity theory
Monin–Obukhov_similarity_theory
the Nusselt number and are only valid when the Reynolds number is greater than 10,000. While Dittus-Boelter requires the Prandtl number to be between
Concentric tube heat exchanger
Concentric_tube_heat_exchanger
Pr is the Prandtl number, Fa is the Fanning friction factor, L is the length of the tube, D is the inner diameter of the tube, n is the number of blades
Dynamic scraped surface heat exchanger
Dynamic_scraped_surface_heat_exchanger
Scientific discipline
valve. The Womersley number, or alpha parameter, is another dimensionless parameter like the Prandtl number or Reynolds number that has been used in
Biofluid_dynamics
Phenomenon in fluid dynamics
{\displaystyle Sc} is the Schmidt number, P r {\displaystyle Pr} is the Prandtl number, R e {\displaystyle Re} is the Reynolds number. The expressions above show
Droplet_vaporization
in form of tables, graphs and figures for a fluid with Prandtl number = 0.71 with Rayleigh number (Ra) ranging from 103 to 107 are available in the literature
Higher-order compact finite difference scheme
Higher-order_compact_finite_difference_scheme
Israeli astrophysicist
may develop beyond linear stage in thin, disks with very low magnetic Prandtl number as such structures usually are. Regev is the author of : Physics with
Oded_Regev_(physicist)
Bladeless centripetal flow turbine
boundary-layer turbine, cohesion-type turbine, and Prandtl-layer turbine. The latter is named for Ludwig Prandtl. Bioengineering researchers have additionally
Tesla_turbine
dispersion relation provides the relation between the growth rate and the wave number of the perturbation superposed on a planar premixed flame, named after Paul
Clavin–Garcia_equation
Pran Nath Prandtl-Glauert method Prandtl number Prandtl–Glauert singularity Prandtl–Glauert transformation Prandtl–Meyer expansion fan Prandtl–Meyer function
Index_of_physics_articles_(P)
spinning Magic number (physics) Maglev wind turbine Magnecule Magnesium diboride Magnet Magnet wire Magnetar Magnetic Prandtl number Magnetic Resonance
Index_of_physics_articles_(M)
Paradox by d'Alembert on fluid dynamics
airfoil. To verify, as Prandtl suggested, that a vanishingly small cause (vanishingly small viscosity for increasing Reynolds number) has a large effect
D'Alembert's_paradox
Swiss aeronautical engineer
supervision of Aurel Stodola. From 1921 to 1927 he worked with Ludwig Prandtl at the "Aerodynamische Versuchsanstalt" in Göttingen, witnessing a legendary
Jakob_Ackeret
Turbulence Turbulence kinetic energy Turbulence modeling Turbulent Prandtl number Turbulent jet breakup Turgay Uzer Tuva or Bust! Twin Quasar Twin paradox
Index_of_physics_articles_(T)
{\displaystyle \delta _{L}Pr=\nu /S_{L}} , where P r {\displaystyle Pr} is the Prandtl number (set P r = 1 {\displaystyle Pr=1} ), and t c h = δ L / S L {\displaystyle
Williams_diagram
Propagating disturbance
increased expansion may be achieved through an expansion fan, also known as a Prandtl–Meyer expansion fan. The accompanying expansion wave may approach and eventually
Shock_wave
American experimental physicist (born 1953)
Scaling in Turbulent Rayleigh-Bénard Convection: Effects of Rotation and Prandtl Number". Phys. Rev. Lett. 79 (12): 2257–2260. Bibcode:1997PhRvL..79.2257L.
Robert_Ecke
Geometric representation of material yield
can be chosen to intersect the Mohr–Coulomb yield surface in different number of vertices. One choice is to intersect the Mohr–Coulomb yield surface at
Yield_surface
and Nikuradse naturalized as a German citizen. As PhD student of Ludwig Prandtl in 1920, he later worked as a researcher at the Kaiser Wilhelm Institute
Johann_Nikuradse
thruster, Plasma Engine Magnetic helicity Magnetic mirror Magnetic Prandtl number Magnetic pressure Magnetic proton recoil neutron spectrometer Magnetic
List of plasma physics articles
List_of_plasma_physics_articles
Equation in fluid dynamics
independent of the Reynolds number (and thus the velocity) only in the case of rough pipes in a fully turbulent flow regime (Prandtl-von Kármán equation). In
Darcy–Weisbach_equation
Phenomenon in fluid dynamics
at a critical Reynolds number. The paradox was explained from boundary-layer theory by German fluid dynamicist Ludwig Prandtl. The drag crisis is associated
Drag_crisis
American Navy admiral (1914–1984)
Halligan, James Edward (1943). Investigation into relation between Prandtl number and boundary layer temperature effects in flow (Thesis). Department
William_A._Brockett
German theoretical physicist (1868–1951)
officials in the Reich. In an attachment to Prandtl's 28 April 1941 letter to Reich Marshal Hermann Göring, Prandtl referred to the appointment as "sabotage"
Arnold_Sommerfeld
Sudden increase of undesirable effects when an aircraft approaches the speed of sound
high-speed fighter aircraft experienced the effects of compressibility, a number of adverse aerodynamic effects that deterred further acceleration, seemingly
Sound_barrier
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