List the non-dimensional number involved in boundary layer modelling
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Name
Standard symbol
Definition
Field of application
Abbe number
V
{\displaystyle V={\frac {n_{d}-1}{n_{F}-n_{C}}}}
optics (dispersion in optical materials)
Activity coefficient
{\displaystyle \gamma }
{\displaystyle \gamma ={\frac {a}{x}}}
chemistry (Proportion of "active" molecules or atoms)
Albedo
{\displaystyle \alpha }
{\displaystyle \alpha =(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}}
climatology, astronomy (reflectivity of surfaces or bodies)
Archimedes number
Ar
{\displaystyle \mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}}
fluid mechanics (motion of fluids due to density differences)
Arrhenius number
{\displaystyle \alpha }
{\displaystyle \alpha ={\frac {E_{a}}{RT}}}
chemistry (ratio of activation energy to thermal energy)[1]
Atomic weight
M
chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u)
Atwood number
A
{\displaystyle \mathrm {A} ={\frac {\rho _{1}-\rho _{2}}{\rho _{1}+\rho _{2}}}}
fluid mechanics (onset of instabilities in fluid mixtures due to density differences)
Bagnold number
Ba
{\displaystyle \mathrm {Ba} ={\frac {\rho d^{2}\lambda ^{1/2}\gamma }{\mu }}}
fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)[2]
Bejan number
(fluid mechanics)
Be
{\displaystyle \mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \alpha }}}
fluid mechanics (dimensionless pressure drop along a channel)[3]
Bejan number
(thermodynamics)
Be
{\displaystyle \mathrm {Be} ={\frac {{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}}{{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}+{\dot {S}}'_{\mathrm {gen} ,\,\Delta p}}}}
thermodynamics (ratio of heat transferirreversibility to total irreversibility due to heat transfer and fluid friction)[4]
Bingham number
Bm
{\displaystyle \mathrm {Bm} ={\frac {\tau _{y}L}{\mu V}}}
fluid mechanics, rheology (ratio of yield stress to viscous stress)[1]
Biot number
Bi
{\displaystyle \mathrm {Bi} ={\frac {hL_{C}}{k_{b}}}}
heat transfer (surface vs. volume conductivity of solids)
Blake number
Bl or B
{\displaystyle \mathrm {B} ={\frac {u\rho }{\mu (1-\epsilon )D}}}
geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)
Bodenstein number
Bo or Bd
{\displaystyle \mathrm {Bo} =vL/{\mathcal {D}}=\mathrm {Re} \,\mathrm {Sc} }
chemistry (residence-time distribution; similar to the axial mass transfer Peclet number)[5]
Bond number
Bo
{\displaystyle \mathrm {Bo} ={\frac {\rho aL^{2}}{\gamma }}}
geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) [6]
Brinkman number
Br
{\displaystyle \mathrm {Br} ={\frac {\mu U^{2}}{\kappa (T_{w}-T_{0})}}}
heat transfer, fluid mechanics (conduction from a wall to a viscousfluid)
Brownell–Katz number
NBK
{\displaystyle \mathrm {N} _{\mathrm {BK} }={\frac {u\mu }{k_{\mathrm {rw} }\sigma }}}
fluid mechanics (combination of capillary number and Bond number) [7]
Capillary number
Ca
{\displaystyle \mathrm {Ca} ={\frac {\mu V}{\gamma }}}
porous media, fluid mechanics (viscous forces versus surface tension)
Chandrasekhar number
Q
{\displaystyle \mathrm {Q} ={\frac {{B_{0}}^{2}d^{2}}{\mu _{0}\rho \nu \lambda }}}
magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection)
Colburn J factors
JM, JH, JD
turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
Coefficient of kinetic friction
{\displaystyle \mu _{k}}
mechanics (friction of solid bodies in translational motion)
Coefficient of static friction
{\displaystyle \mu _{s}}
mechanics (friction of solid bodies at rest)
Coefficient of determination
{\displaystyle R^{2}}
statistics (proportion of variance explained by a statistical model)
Coefficient of variation
{\displaystyle {\frac {\sigma }{\mu }}}
{\displaystyle {\frac {\sigma }{\mu }}}
statistics (ratio of standard deviation to expectation)
Cohesion number
Coh
{\displaystyle Coh=
Standard symbol
Definition
Field of application
Abbe number
V
{\displaystyle V={\frac {n_{d}-1}{n_{F}-n_{C}}}}
optics (dispersion in optical materials)
Activity coefficient
{\displaystyle \gamma }
{\displaystyle \gamma ={\frac {a}{x}}}
chemistry (Proportion of "active" molecules or atoms)
Albedo
{\displaystyle \alpha }
{\displaystyle \alpha =(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}}
climatology, astronomy (reflectivity of surfaces or bodies)
Archimedes number
Ar
{\displaystyle \mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}}
fluid mechanics (motion of fluids due to density differences)
Arrhenius number
{\displaystyle \alpha }
{\displaystyle \alpha ={\frac {E_{a}}{RT}}}
chemistry (ratio of activation energy to thermal energy)[1]
Atomic weight
M
chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u)
Atwood number
A
{\displaystyle \mathrm {A} ={\frac {\rho _{1}-\rho _{2}}{\rho _{1}+\rho _{2}}}}
fluid mechanics (onset of instabilities in fluid mixtures due to density differences)
Bagnold number
Ba
{\displaystyle \mathrm {Ba} ={\frac {\rho d^{2}\lambda ^{1/2}\gamma }{\mu }}}
fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)[2]
Bejan number
(fluid mechanics)
Be
{\displaystyle \mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \alpha }}}
fluid mechanics (dimensionless pressure drop along a channel)[3]
Bejan number
(thermodynamics)
Be
{\displaystyle \mathrm {Be} ={\frac {{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}}{{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}+{\dot {S}}'_{\mathrm {gen} ,\,\Delta p}}}}
thermodynamics (ratio of heat transferirreversibility to total irreversibility due to heat transfer and fluid friction)[4]
Bingham number
Bm
{\displaystyle \mathrm {Bm} ={\frac {\tau _{y}L}{\mu V}}}
fluid mechanics, rheology (ratio of yield stress to viscous stress)[1]
Biot number
Bi
{\displaystyle \mathrm {Bi} ={\frac {hL_{C}}{k_{b}}}}
heat transfer (surface vs. volume conductivity of solids)
Blake number
Bl or B
{\displaystyle \mathrm {B} ={\frac {u\rho }{\mu (1-\epsilon )D}}}
geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)
Bodenstein number
Bo or Bd
{\displaystyle \mathrm {Bo} =vL/{\mathcal {D}}=\mathrm {Re} \,\mathrm {Sc} }
chemistry (residence-time distribution; similar to the axial mass transfer Peclet number)[5]
Bond number
Bo
{\displaystyle \mathrm {Bo} ={\frac {\rho aL^{2}}{\gamma }}}
geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) [6]
Brinkman number
Br
{\displaystyle \mathrm {Br} ={\frac {\mu U^{2}}{\kappa (T_{w}-T_{0})}}}
heat transfer, fluid mechanics (conduction from a wall to a viscousfluid)
Brownell–Katz number
NBK
{\displaystyle \mathrm {N} _{\mathrm {BK} }={\frac {u\mu }{k_{\mathrm {rw} }\sigma }}}
fluid mechanics (combination of capillary number and Bond number) [7]
Capillary number
Ca
{\displaystyle \mathrm {Ca} ={\frac {\mu V}{\gamma }}}
porous media, fluid mechanics (viscous forces versus surface tension)
Chandrasekhar number
Q
{\displaystyle \mathrm {Q} ={\frac {{B_{0}}^{2}d^{2}}{\mu _{0}\rho \nu \lambda }}}
magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection)
Colburn J factors
JM, JH, JD
turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
Coefficient of kinetic friction
{\displaystyle \mu _{k}}
mechanics (friction of solid bodies in translational motion)
Coefficient of static friction
{\displaystyle \mu _{s}}
mechanics (friction of solid bodies at rest)
Coefficient of determination
{\displaystyle R^{2}}
statistics (proportion of variance explained by a statistical model)
Coefficient of variation
{\displaystyle {\frac {\sigma }{\mu }}}
{\displaystyle {\frac {\sigma }{\mu }}}
statistics (ratio of standard deviation to expectation)
Cohesion number
Coh
{\displaystyle Coh=
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