COMSOL 6.4 - Symbols


Notation	SI Unit	Description
A	1/s	Frequency factor, damage integral analysis
A	m2	Total boundaries area
a	dimensionless	Weight factors
a1,…, a12	dimensionless	Legendre coefficients
Ac	m2	Cross-sectional area of domain
Al	m2	Cross-sectional area of thin rod
Bi	m	Spectral band i
b	dimensionless	Thermal conductivity supplement
c	mol/m3	Concentration
c	kg/m3	Concentration
cl	mol/m2	Liquid water concentration on moist surface
Cp, b	J/(kg·K)	Specific heat capacity at constant pressure, blood
Cp, l	J/(kg·K)	Specific heat capacity at constant pressure of thin rod
Cμ	dimensionless	Turbulence modeling constant
Cp	J/(kg·K)	Specific heat capacity at constant pressure
Cp, a	J/(kg·K)	Specific heat capacity at constant pressure, dry air
Cp, A	J/(kg·K)	Specific heat capacity at constant pressure, Austenite state
Cp, d	J/(kg·K)	Specific heat capacity at constant pressure, damaged tissue
Cp, f	J/(kg·K)	Specific heat capacity at constant pressure, fluid phase
Cp, imf	J/(kg·K)	Specific heat capacity at constant pressure of immobile fluid in porous media
Cp, imfi	J/(kg·K)	Specific heat capacity at constant pressure of immobile fluid i in porous media
Cp, m	J/(kg·K)	Specific heat capacity at constant pressure, mixture (moist air)
Cp, M	J/(kg·K)	Specific heat capacity at constant pressure, Martensite state
Cp, s	J/(kg·K)	Specific heat capacity at constant pressure, solid phase
Cp, si	J/(kg·K)	Specific heat capacity at constant pressure of solid material i in porous media
Cp, v	J/(kg·K)	Specific heat capacity at constant pressure, water vapor
Cp, s	J/(kg·K)	Specific heat capacity at constant pressure of thin layer
Cp, si	J/(kg·K)	Specific heat capacity at constant pressure of layer i in thin layer
csat	mol/m3	Saturation concentration of water vapor
custr	mol/m3	Upstream concentration of water vapor
Cp, w	J/(kg·K)	Specific heat capacity at constant pressure of water
cv	mol/m3	Water vapor concentration
d	m	Average particle diameter
D	m	Cylinder diameter (heat transfer coefficient)
D	m	Cylinder or sphere diameter (heat transfer coefficient)
D	W/(m·K)	Dispersion tensor
D	m	Parallel-plate gap average gas particle diameter
D	1/s	Strain-rate tensor
D	m2/s	Vapor diffusion coefficient in air
Deff	m2/s	Vapor diffusion coefficient in moist porous media
Da	dimensionless	Darcy number
ΔE	J/mol	Activation energy, damage integral analysis
df	m	Thickness of thin film
dfr	m	Thickness of fracture
dpe	m	Average pellets diameter
DP1	m2/s	P1 method diffusion coefficient
ds	m	Thickness of shell or thin layer
dsi	m	Thickness of layer i in thin layer
DT	m2/s	Turbulent diffusivity
Dw	m2/s	Moisture diffusivity
dz	m	Thickness of domain in the out-of-plane direction
DPTamb	K	Ambient dew point temperature
e	m	Beam orientation
E	J/kg	Internal energy
E	Pa	Young’s modulus
E0	J/kg	Total internal energy
EΩ	J	Internal energy of a body
eb, λ(λ, T)	W/m2	Blackbody spectral emissive power
eb(T)	W/m2	Blackbody total emissive power
Econtact	Pa	Effective contact interface Young’s modulus
Ed	Pa	Young’s modulus, down contact surface
Ek	J/kg	Kinetic energy
ep	m2/s3	Turbulent dissipation rate
Ep	J/kg	Potential energy
Eu	Pa	Young’s modulus, up contact surface
etot	W/m2	Total energy flux
F	N/m3	Body force vector
F	dimensionless	Deformation gradient tensor
Famb	dimensionless	Ambient view factor
Famb, d	dimensionless	Ambient view factor, downside
Famb, u	dimensionless	Ambient view factor, upside
g	m/s2	Acceleration of gravity
Gevap	kg/(m3·s)	Evaporation source
gevap	kg/(m2·s)	Evaporation flux
G	kg/(m3·s)	Moisture source
G	1/m	Reciprocal wall distance
G	W/m2	Surface irradiation
Gamb	W/m2	Ambient irradiation
Gamb, d	W/m2	Ambient irradiation, downside
Gamb, u	W/m2	Ambient irradiation, upside
Gd	W/m2	Surface irradiation, downside
Gext	W/m2	External irradiation
Gext, d	W/m2	External irradiation, downside
Gext, u	W/m2	External irradiation, upside
Gl	kg/(m3·s)	Liquid water source
glc	kg/(m2·s)	Liquid water capillary flux
Gm	W/m2	Mutual surface irradiation
Gm, d	W/m2	Mutual surface irradiation, downside
Gm, u	W/m2	Mutual surface irradiation, upside
GrL	dimensionless	Grashof number associated with characteristic length L
Gu	W/m2	Surface irradiation, upside
Gv	kg/(m3·s)	Water vapor source
gw	kg/(m2·s)	Vapor diffusive flux
H	m	Chimney height (heat transfer coefficient)
H	J/kg	Enthalpy
h	W/(m2·K)	Gap conductance (thermal contact)
h	W/(m2·K)	Heat transfer coefficient
H0	J/kg	Total enthalpy
HB	Pa	Brinell hardness
hc	W/(m2·K)	Constriction conductance
Hc	Pa	Microhardness
hd	W/(m2·K)	Out-of-plane heat transfer coefficient, downside
Hd	J/kg	Enthalpy, downside
Hext	J/kg	External enthalpy
hg	W/(m2·K)	Parallel-plate gap gas conductance
hm	m/s	Moisture transfer coefficient
hr	W/(m2·K)	Radiative conductance
Href	J/kg	Reference enthalpy
hsf	W/(m2·K)	Interstitial heat transfer coefficient
hth	W/K	Thermal conductance (isothermal domain interface)
hu	W/(m2·K)	Out-of-plane heat transfer coefficient, upside
Hu	J/kg	Enthalpy, upside
hz	W/(m2·K)	Out-of-plane heat transfer coefficient, 1D
I(Ω)	W/(m2·sr)	Radiative intensity traveling in direction Ω
Ib(T)	W/(m2·sr)	Blackbody radiative intensity
Idiff	W/m2	Diffuse irradiance
Iext	W/(m2·sr)	Incident radiative intensity
Ii	W/(m2·sr)	Radiative intensity traveling in ith discrete direction
is	dimensionless	Incident radiation direction (external radiation source)
Is	W/m2	Solar irradiance
Is,amb	W/m2	Ambient solar irradiance
Ish,amb	W/m2	Clear sky noon diffuse horizontal irradiance
Isn,amb	W/m2	Clear sky noon beam normal irradiance
isx, isy, isz	dimensionless	Solar source direction vector components
Iwall	W/(m2·sr)	Boundary radiative intensity
J	W/m2	Surface radiosity
Jd	W/m2	Surface radiosity, downside
Ju	W/m2	Surface radiosity, upside
k	W/(m·K)	Thermal conductivity
k	J/kg	Turbulent kinetic energy (turbulent nonisothermal flow)
ka	W/(m·K)	Dry air thermal conductivity
kA	W/(m·K)	Thermal conductivity of Austenite state
kB	J/K	Stefan–Boltzmann constant
kbnd	W/(m·K)	Thermal conductivity in shell local coordinate system
kcontact	W/(m·K)	Harmonic mean of contacting surface conductivities
k d	W/(m·K)	Thermal conductivity, damaged tissue
kdisp	W/(m·K)	Dispersive thermal conductivity tensor
keff	W/(m·K)	Effective thermal conductivity
Kevap	1/s	Evaporation rate
kf	W/(m·K)	Thermal conductivity, fluid phase
kimf	W/(m·K)	Thermal conductivity of immobile fluid in porous media
kgap	W/(m·K)	Parallel-plate gap gas thermal conductivity
kimfi	W/(m·K)	Thermal conductivity of immobile fluid i in porous media
kl	W/(m·K)	Thermal conductivity of thin rod
kL	W/(m·K)	Thermal conductivity of mobile fluid in porous media
kM	W/(m·K)	Thermal conductivity of Martensite state
kR	W/(m·K)	Rosseland radiative conductivity
ks	W/(m·K)	Thermal conductivity, solid phase
ksi	W/(m·K)	Thermal conductivity of solid material i in porous media and fractures
ks	W/(m·K)	Thermal conductivity of thin layer
ksi	W/(m·K)	Thermal conductivity of layer i in thin layer
kT	W/(m·K)	Turbulent thermal conductivity
kv	W/(m·K)	Water vapor thermal conductivity
K	m/s	Evaporation rate factor
KΩ	J	Kinetic energy of a body
L	J/kg	Latent heat
L	m	Total edge length
L	m	Wall height or plate diameter, distance, or length (heat transfer coefficient)
Ld, c	J/kg	Damage enthalpy change, cryogenic analysis
Ld, h	J/kg	Damage enthalpy change, hyperthermia analysis
Lit, c	J/kg	Transformation enthalpy change, overcooling analysis
Lit, h	J/kg	Transformation enthalpy change, overheating analysis
Lv	J/kg	Latent heat of evaporation
lvG	dimensionless	van Genuchten model constitutive constant
m	kg	Mass
ma	kg	Dry air mass
Ma	kg/mol	Dry air molar mass
masp	m	Asperities average slope (surface roughness)
Mg	m	Parallel-plate gap gas parameter
Mn	kg/mol	Mean molar mass
mtot	kg	Total mass (moist air)
mv	kg	Water vapor mass
Mv	kg/mol	Water vapor molar mass
mvG	dimensionless	van Genuchten model constitutive constant
n	dimensionless	Refractive index, transparent media
n	dimensionless	Normal vector toward exterior
na	mol	Amount of dry air
nr	dimensionless	Refractive index, participating media
ntot	mol	Amount of moist air
Nu	dimensionless	Nusselt number
NuL	dimensionless	Nusselt number associated with characteristic length L
nv	mol	Amount of water vapor
O	m	Beam origin point
om	1/s	Specific dissipation rate
p	Pa	Contact pressure, pressure
P	N/m2	First Piola–Kirchhoff stress tensor
P	V	Peltier coefficient
P0	W	Heat rate
pa	Pa	Dry air partial pressure
pA	Pa	Absolute pressure
Pb	W	Heat rate, boundary heat source
Pc	m	Cross-sectional perimeter of domain
pec	Pa	Entry capillary pressure
pext	Pa	External absolute pressure
Pext	W	Power of applied forces
pgap	Pa	Parallel-plate gap gas pressure
Pl	W	Heat rate, line heat source, deposited beam power
Pr	dimensionless	Prandtl number
pamb	Pa	Ambient absolute pressure
pref	Pa	Reference pressure
PrT	dimensionless	Turbulent Prandtl number
Ps	W	Heat rate, layer heat source
Ps	W	Source power (external radiation source)
psat	Pa	Saturation pressure of water vapor
Pstr	W	Stress power
pustr	Pa	Upstream absolute pressure
pv	Pa	Water vapor partial pressure
pv,eq	Pa	Equilibrium vapor pressure
q	W/m2	Conductive heat flux
qf	W/m2	Conductive heat flux in fluid phase
qs	W/m2	Conductive heat flux in solid phase
Q	W/m3	Heat source
q0	W/m2	Inward heat flux
Q0	W/m3	Distributed heat source
q0, d	W/m2	Out-of-plane heat flux, downside
q0, s	W/m2	Source heat flux (external radiation source)
q0, u	W/m2	Out-of-plane heat flux, upside
Qb	W/m2	Boundary heat source
Qb, tot	W/m2	Total boundary heat source
Qe	W/m3	Electromagnetic heat source
Qevap	W/m3	Latent heat source in domains
qevap	W/m2	Latent heat source on surfaces
Qexch	W	Exchanged heat source rate
Qf	W/m3	Heat source in fluid phase
qgeo	W/kg	Radiogenic heating per mass
Qgeo	W/m3	Geothermal heat source
QInt	W	Total heat source over interior boundaries
Qit	W/m3	Irreversible transformation heat source
Ql	W/m	Line heat source
Qmet	W/m3	Metabolic heat source
Qp	W	Point heat source
Qp	W/m3	Pressure work
Qr	W/m3	Radiative heat source term
qr	W/m2	Radiative heat flux
qr, net	W/m2	Net radiative heat flux
qr, out	W/m2	Radiative heat flux striking the wall
qs	W/(m3·K)	Production/absorption coefficient
Qs	W/m3	Heat source in solid phase
Qs	W/m3	Thin layer heat source
qsf	W/(m3·K)	Interstitial convective heat transfer coefficient
Qsi	W/m3	Layer i heat source
Qted	W/m3	Thermoelastic damping
qtot	W/m2	Total heat flux
Qtot	W/m3	Total domain heat source
Qvd	W/m3	Viscous dissipation
r	m	Distance of the irradiated surface from the source
r	dimensionless	Heat partition coefficient (thermal friction)
R	m	Heat source radius, beam radius
R	J/(mol·K)	Universal gas constant
Ra	dimensionless	Rayleigh number
RaD	dimensionless	Rayleigh number associated with cylinder diameter D
RaL	dimensionless	Rayleigh number associated with characteristic length L
Reinf	dimensionless	Reynolds number at infinity
ReL	dimensionless	Reynolds number associated with characteristic length L
Rep	dimensionless	Particle Reynolds number
rh	m	Hydraulic radius
rl	m	Rod radius
rpe	m	Average pellets radius
Rs	J/(kg·K)	Specific gas constant
Rt,s	K·m2/W	Surface thermal resistance
Rt	K/W	Thermal resistance
Sb	1/m	Specific surface area
sd	m	Vapor diffusion equivalent air layer thickness
S	N/m2	Second Piola–Kirchhoff stress tensor
S	V/K	Seebeck coefficient
ScT	dimensionless	Turbulent Schmidt number
Si	dimensionless	Unit vector of discrete direction in space, ith component (angular space discretization)
sl	dimensionless	Liquid water saturation
Sp	dimensionless	Sparrow number
T	K	Temperature
T0	K	Equilibrium temperature
T’	K	Complex amplitude of harmonic perturbation
T+	dimensionless	Dimensionless temperature
Tamb	K	Ambient temperature
Tamb, d	K	Ambient temperature, downside
Tamb, u	K	Ambient temperature, upside
Tb	K	Arterial blood temperature
Td	K	Temperature, downside
td, c	s	Damage time, cryogenic analysis
Td, c	K	Damage temperature, cryogenic analysis
td, h	s	Damage time, hyperthermia analysis
Td, h	K	Damage temperature, hyperthermia analysis
Text	K	External temperature
Text, d	K	Out-of-plane external temperature, downside
Text, u	K	Out-of-plane external temperature, upside
Text, z	K	Out-of-plane external temperature, 1D
Tf	K	Temperature, fluid phase
tit, c		Transformation time, overcooling analysis
Tit, c		Transformation temperature, overcooling analysis
tit, h		Transformation time, overheating analysis
Tit, h		Transformation temperature, overheating analysis
Tn, c	K	Temperature of necrosis, cryogenic
Tn, h	K	Temperature of necrosis, hyperthermia
Tpc	K	Phase change temperature
Tref	K	Reference temperature
Tref	K	Strain reference temperature
Ts	K	Temperature, solid phase
Tu	K	Temperature, upside
Tustr	K	Upstream temperature
Tw	K	Wall temperature
u	m/s	Fluid velocity vector
u, v, w	m/s	Fluid velocity vector’s components
uf	m/s	Average linear velocity
ug	m/s	Moist air velocity vector
ul	m/s	Liquid water velocity vector
up	m/s	Porous velocity field
utrans	m/s	Translational motion velocity vector
vamb	m/s	Wind velocity
V	V	Electric potential
V	m3	Total domain volume
W	W/m3	Work source
w	kg/m3	Moisture storage function
WInt	W	Work from custom volume forces
Wdiss	W	Dissipative work from momentum equation
Xa	dimensionless	Molar fraction of dry air
xpl	m	Position along the plate (heat transfer coefficient)
xs	m	Source location (external radiation source)
Xv	dimensionless	Molar fraction of water vapor
xvap	dimensionless	Moisture content
xvap,amb	dimensionless	Ambient moisture content
Y	m	Parallel-plate gap mean separation thickness

Greek Symbols


Notation	SI Unit	Description
(ρCp)eff	J/(m3·K)	Effective volumetric heat capacity at constant pressure
∂Ω	-	Geometry domain’s boundaries
∂Ωext	-	Geometry domain’s exterior boundaries
∂Ωint	-	Geometry domain’s interior boundaries
∇t	-	Tangential gradient operator
α	1/K	Coefficient of thermal expansion tensor in a solid
α	dimensionless	Degree of tissue injury (Arrhenius equation)
α	dimensionless	Irreversible transformation indicator (Arrhenius equation)
α	dimensionless	Parallel-plate gap gas thermal accommodation parameter
α	dimensionless	Surface absorptivity
α	m2/s	Thermal diffusivity
α	dimensionless	Damaged tissue indicator
αnecr	dimensionless	Necrosis time indicator
αm	dimensionless	Vapor mass fraction
αp	1/K	Coefficient of thermal expansion in a fluid
β	1/m	Extinction coefficient
βp	s/m	Moisture transfer coefficient
β	dimensionless	Parallel-plate gap gas property parameter
βR	1/m	Rosseland mean extinction coefficient
γ	dimensionless	Ratio of specific heats
γTeq	Pa/K	Psychrometer constant
ΔR	m	Size of transition zone (deposited beam power)
ΔT	K	Temperature offset for periodic condition
ΔT0	K	Temperature perturbation
δ	s	Vapor permeability of still air
δp	s	Vapor permeability
δw	m	Distance between the computational fluid domain and the wall
εp	dimensionless	Porosity
ε	dimensionless	Surface emissivity
εd	dimensionless	Surface emissivity, downside
ελ	dimensionless	Surface spectral emissivity
εu	dimensionless	Surface emissivity, upside
εz	dimensionless	Surface emissivity, 1D out-of-plane radiation
θ	rad	Angle between the normal to the irradiated surface and the direction of the source
θd	dimensionless	Volume fraction of necrotic tissue
θimf	dimensionless	Volume fraction of immobile fluid in porous media
θimfi	dimensionless	Volume fraction of immobile fluid i in porous media
θit	dimensionless	Fraction of transformation
θg	dimensionless	Volume fraction of mobile fluid in porous media
θs	dimensionless	Volume fraction of solid material in porous media and fractures
θsi	dimensionless	Volume fraction of solid material i in porous media
θs	rad	Zenith angle of the Sun
κ	1/m	Absorption coefficient (radiation)
κ	m2	Permeability (porous media)
κrg	dimensionless	Moist air relative permeability (porous media)
κrl	dimensionless	Liquid water relative permeability (porous media)
λ	W/(m·K)	Thermal conductivity (turbulent nonisothermal flow)
λ	m	Wavelength
Λ	m	Parallel-plate gap gas mean free path
λi	m	Wavelength band i endpoint
λijkl	m	Fourth-order dispersivity tensor’s component
λlo	m	Longitudinal dispersivity
λp	dimensionless	Pore size distribution index
λtr	m	Transverse dispersivity
λtr, h	m	Transverse horizontal dispersivity
λtr, v	m	Transverse vertical dispersivity
μ	Pa·s	Dynamic viscosity
μ	dimensionless	Vapor resistance factor
μ0	dimensionless	Scattering angle
μa	Pa·s	Dry air dynamic viscosity
μf	Pa·s	Dynamic viscosity
μm	Pa·s	Mixture dynamic viscosity (moist air)
μT	Pa·s	Turbulent dynamic viscosity
μTh	V/K	Thomson coefficient
μv	Pa·s	Water vapor dynamic viscosity
ν	dimensionless	Poisson ratio
νd	dimensionless	Poisson ratio, down contact surface
νu	dimensionless	Poisson ratio, up contact surface
ρ	kg/m3	Density
ρ	dimensionless	Surface reflectivity
ρb	kg/m3	Density, blood
ρd	kg/m3	Density, damaged tissue
ρf	kg/m3	Density, fluid phase
ρimf	kg/m3	Density of immobile fluid in porous media
ρgeo	kg/m3	Geothermal density
ρimfi	kg/m3	Density of immobile fluid i in porous media
ρl	kg/m3	Density of thin rod
ρg	kg/m3	Mixture density (moist air)
ρs	kg/m3	Density of solid material
ρsi	kg/m3	Density of solid material i in porous media
ρs	kg/m3	Density of thin layer
ρsi	kg/m3	Density of layer i in thin layer
σ	Pa	Cauchy stress tensor
σ	m	Standard deviation (deposited beam power)
σ	W/(m2·K4)	Stefan–Boltzmann constant
σ	N/m	Surface tension coefficient
σasp	m	Asperities average height (surface roughness)
σs	1/m	Scattering coefficient
τ	dimensionless	Optical thickness
τ	Pa	Viscous stress tensor
ϕw	dimensionless	Relative humidity
ϕamb	dimensionless	Ambient relative humidity
ϕ	rad	Tilt angle (heat transfer coefficient)
ϕw,ext	dimensionless	External relative humidity
ϕw,d	dimensionless	Relative humidity, downside
ϕw,s	dimensionless	Surface relative humidity
ϕw,u	dimensionless	Relative humidity, upside
ϕw,ustr	dimensionless	Upstream relative humidity
Φd → u	kg/s	Mass flow rate, positive direction
Φu → d	kg/s	Mass flow rate, negative direction
φ(Ω', Ω)	dimensionless	Scattering phase function
φs	rad	Azimuth angle of the Sun
φd → u	kg/(m2·s)	Mass flux, positive direction
φu → d	kg/(m2·s)	Mass flux, negative direction
Ψ	J/kg	Force potential
Ω	dimensionless	Unit vector of a direction in space
Ω	-	Geometry domain
ω	dimensionless	Specific humidity
ω	rad/s	Angular frequency
ωb	1/s	Blood perfusion rate
ωi	W/(m2·K)	Discrete incident radiation vector, ith component
ωv	dimensionless	Water vapor mass fraction
ξ	kg/m3	Moisture storage capacity
ξ	dimensionless	Martensite state volume fraction