Bi | Biot number, hL / k
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Bo | Bond number,
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Br | Brinkman number,
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cp | specific heat at constant pressure, J/kg-K
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cv | specific heat at constant volume, J/kg-K
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C | heat capacity, J/K
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CD | drag coefficient
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Cf | friction coefficient
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D/Dt | substantial derivative
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f | degree of freedom; weight function; friction coefficient; solid fraction; wave frequency, 1/s , molecular velocity distribution function
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Fo | Fourier number, αt / L2
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Fr | Froude number, or U2 / (gL)
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g | gravitational acceleration, m/s2; specific Gibbs free energy, J/kg
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G | Gibbs free energy, J; electron-lattice coupling factor, W/m3-K; irradiance, W/m2
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Gr | Grashof number, gβΔTL3 / ν2
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h | heat transfer coefficient, W/(m2-K); specific enthalpy, J/kg
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| latent heat of vaporization, J/kg
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| latent heat of fusion, J/kg
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hsv | latent heat of sublimation, J/kg
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H | enthalpy, J; height, m; magnetic field
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H | magnetic field vector
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I | intensity, W/m2-sr; electrical current, A
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I0 | zeroth order modified Bessel function of the first kind
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I1 | first order modified Bessel function of the first kind
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I | unit tensor
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j | volume flux, m/s; superficial velocity, m/s
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J | total (diffusion + convection) flux; radiosity, W/m2
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J0 | zeroth order Bessel function of the first kind
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J1 | first order Bessel function of the first kind
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Ja | Jakob number,
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k | thermal conductivity, W/(m-K)
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k | thermal conductivity tensor, W /(m-K)
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K0 | zeroth order modified Bessel function of the second kind
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K1 | first order modified Bessel function of the second kind
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kb | Boltzmann constant, J/K
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K | interface curvature, 1/m; Permeability, m2; dielectric constant
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Kjk | momentum exchange coefficient between phases j and k, kg/(m3-s)
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Ka | Kapitza number,
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Kn | Knudsen number, λ / L
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L | (characteristic) length, m
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Le | Lewis number, α / D
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m | mass, kg
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M | molecular mass, kg/kmol
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Ma | Mach number,U / c; Marangoni number,
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n | unit normal vector
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NA | Avogadro’s number (1/mol)
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Nu | Nusselt number, hL / k
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Nux | local Nusselt number, hxx / k
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p | pressure, Pa
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Pe | Peclet number, UL / α
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Pr | Prandtl number, ν / α
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q | heat rate, W
q' || heat rate per unit length, W/m
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q" | heat flux, W/m2
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q" | heat flux vector, W/m2
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q"max | maximum (critical) heat flux in boiling, W/m2
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q"min | minimum heat flux in boiling, W/m2
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q"solar | solar constant, 1368 W/m2
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q"' | internal heat generation per unit volume, W/m3
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Q | total heat transfer, J
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r | radial coordinate, m
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r | position vector m
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R | radius, m
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Rg | gas constant, kJ/kg-K
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Ra | Rayleigh number, gβΔTL3 / (να)
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Re | Reynolds number, UL / ν
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s | specific entropy, J/(kg-K)
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S | entropy, J/K
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Sc | Schmidt number, ν / D; subcooling parameter,
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Sh | Sherwood number, hmL / D12
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St | Stanton number, h / (ρcpU)
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Ste | Stefan number,
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Sr | Strouhal number, Lf / U
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t | time, s
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T | temperature, K
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Tm | melting point, K
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Tsat | saturation temperature, K
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u | velocity in the x- direction, m/s
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U | velocity, m/s;
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v | specific volume, m3/kg; velocity in the y-direction, m/s
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V | volume, m3
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V | velocity vector, m/s
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w | velocity in the z-direction or axial velocity, m/s, specific work, J/kg
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W | work, J; width, m
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We | Weber number, ρU2L / σ
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Wr | Womersley number,
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x | Cartesian coordinate, m; vapor quality
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X | material coordinate, m; dimensionless coordinate
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y | Cartesian coordinate, m
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Y | material coordinate, m
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Y0 | zeroth order Bessel function of the second kind
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Y1 | first order Bessel function of the second kind
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z | Cartesian coordinate, axial coordinate, m
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Z | material coordinate, m; compressibility factor, pv/RT
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α | thermal diffusivity, m2/s; relaxation factor; accommodation coefficient; wave number, void fraction; absorptivity of a surface
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β | wedge angle, rad; coefficient of thermal expansion, 1/K; contact angle measured in degrees; volumetric flow fraction
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βm | composition coefficient of volume expansion
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Γ | general diffusion coefficient; liquid mass flow rate per unit width, kg/m-s
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δ | velocity boundary layer thickness, liquid or vapor film thickness, m; thermal penetration depth, m; laser irradiation penetration depth, m; thickness of the deposited film, m; thickness of surface element, m; Kronecker delta
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δt | thermal boundary layer thickness, m
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εM | momentum eddy diffusivity, m2/s
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εH | thermal eddy diffusivity, m2/s
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η | similarity variable, fin efficiency
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θ | inclination angle, rad; contact or wetting angle, rad; dimensionless temperature
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Θn | eigen function
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λ | mean free path, m; wavelength, m
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λn | eigenvalue
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μ | dynamic viscosity, kg/(m-s); chemical potential, J/mol; magnetic permeability
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ν | kinematic viscosity, m2/s; frequency (Hz)
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ρ | density, kg/m3; reflectivity of a surface
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σ | surface tension force, N/m; collision diameter, Å, Stefan-Boltzmann constant
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τ | shear stress, N/m2; thermal relaxation time, s; dimensionless time,; optical thickness, m
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τ | stress tensor, N/m2
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φ | Lennard-Jones potential, J; inclination angle; wave amplitude; pressure drop multiplier in two-phase flow
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ψ | stream function, m2/s
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0 | reference variables; initial condition
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a | adiabatic, acceleration
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b | control volume face at bottom; blood; blackbody
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c | critical point, condenser, cutoff value
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cap | capillary
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CV | control volume
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E | east neighbor point
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e | equilibrium; evaporator; control volume face at east
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eff | effective value
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f | final; fuel; thin film
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g | gas (vapor); gravity
|
| liquid
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L | left; characteristic length
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m | mean; melting point or mushy zone; metabolic
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men | meniscus
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N | north neighbor grid point
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n | normal to surface; control volume face at bottom
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nb | general neighbor grid points
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P | central grid point under consideration
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p | product; particle; pulse
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rad | radiation
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ref | reference frame
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S | south neighbor grid point
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s | shaft; solid; surface; control volume face at south
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sat | saturation
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T | top neighbor grid point; temperature
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t | turbulent; control volume face at top
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v | vapor phase
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W | west neighbor grid point
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w | wall; control volume face at west
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∞ | ambient or bulk property
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