📘 Symbol Reference

▸ Symbol Reference (click to open)

📘 Symbol Reference

Heat Transfer · Fluid Mechanics · Thermodynamics — formatted for quick scanning

Reference:
Symbols and definitions adapted from:
Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine, Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2007. ISBN 978-0-471-45728-2

Page 1

1. Geometry & Areas

area, m²

A_b

area of prime (unfinned) surface, m²

A_c

cross-sectional area, m²

A_ff

free-flow area in compact heat exchanger core (minimum cross-sectional area available for flow through the core), m²

A_fr

heat exchanger frontal area, m²

A_p

fin profile area, m²

A_r

nozzle area ratio

perimeter, m

width of a slot nozzle, m

vapor quality

2. Fluid & Dimensionless Groups

Biot number

Bond number

Confinement number

Fourier number

Froude number

Grashof number

Graetz number

Nusselt number

NTU

number of transfer units

Péclet number (Re·Pr)

Prandtl number

Rayleigh number

Reynolds number

Schmidt number

Sherwood number

Stanton number

Weber number

Eckert number

3. Thermodynamics & Heat Transfer

molar concentration, kmol/m³; heat-capacity rate, W/K

C_t

thermal capacitance, J/K

specific heat, J/(kg·K); speed of light, m/s

c_p

specific heat at constant pressure, J/(kg·K)

c_v

specific heat at constant volume, J/(kg·K)

thermal + mechanical energy, J; emissive power, W/m²

E^total

total energy, J

rate of energy generation, W

Ė_in

rate of energy transfer into a control volume, W

Ė_out

rate of energy transfer out of a control volume, W

Ė_st

rate of increase of stored energy within a control volume, W

internal energy per unit mass, J/kg; surface roughness, m

energy transfer, J

heat-transfer rate, W

q̇

volumetric heat-generation rate, W/m³

q′

heat-transfer rate per unit length, W/m

q″

heat flux, W/m²

dimensionless conduction heat rate

4. Transport Properties

diameter, m

D_AB

binary mass diffusivity, m²/s

D_b

bubble diameter, m

D_h

hydraulic diameter, m

thermal conductivity, W/(m·K); Boltzmann’s constant (context)

dynamic viscosity, kg/(m·s)

kinematic viscosity, m²/s; frequency of radiation, s⁻¹

5. Forces, Fluxes & Constants

force, N; heat-exchanger correction factor; fraction of blackbody radiation in a band; view factor

friction factor; similarity variable

C_D

drag coefficient

C_f

friction coefficient

irradiation, W/m²; mass velocity, kg/(s·m²)

gravitational acceleration, m/s²

g_c

gravitational conversion factor, 1 kg·m/(N·s²)

nozzle height, m; Henry’s constant, bar

electric current, A; radiation intensity, W/(m²·sr)

current density, A/m²; enthalpy per unit mass, J/kg

radiosity, W/m²

Jakob number

J_i^*

diffusive molar flux of species i relative to mixture-average velocity, kmol/(m²·s)

convection heat-transfer coefficient, W/(m²·K)

h_fg

latent heat of vaporization, J/kg

h_sf

latent heat of fusion, J/kg

h_m

convection mass-transfer coefficient, m/s

h_rad

radiation heat-transfer coefficient, W/(m²·K)

R_f

fouling factor, m²·K/W

R_t

thermal resistance, K/W

R_t,c

thermal contact resistance, K/W

R_t,f

fin thermal resistance, K/W

R_t,o

thermal resistance of fin array, K/W

Page 2

1. Mass & Species Transfer

ṁ

mass flow rate, kg/s

mass, kg

m_i

mass fraction of species i, ρ_i/ρ

mass; lanes in flux plot; reciprocal of Fourier number

ṁ_i

rate of mass transfer of species i, kg/s

ṁ_ig

rate of increase of mass of species i due to reactions, kg/s

ṁ_in

mass flow rate into a control volume, kg/s

ṁ_out

mass flow rate out of a control volume, kg/s

ṁ_st

rate of increase of stored mass within a control volume, kg/s

M_i

molecular weight of species i, kg/kmol

temperature increments in flux plot; tube count; enclosure surfaces

N_L, N_T

tubes in longitudinal/transverse directions

2. Fluxes

N_i

molar transfer rate of species i (fixed coords), kmol/s

N_i″

molar flux of species i, kmol/(m²·s)

Ñ_i

molar rate of increase per volume due to reactions, kmol/(m³·s)

Ṅ_i″

surface reaction rate of species i, kmol/(m²·s)

n_i″

mass flux of species i, kg/(m²·s)

ṅ_i

mass rate of increase per volume due to reactions, kg/(m³·s)

3. Energy & Heat Transfer (continued)

volume, m³; (context) velocity magnitude

specific volume, m³/kg

Ẇ

rate at which work is performed, W

4. Resistances

cylinder radius, m

R_m

mass-transfer resistance, s/m³

R_m,n

residual for node (m,n)

5. Coordinates & Geometry

r_o

cylinder or sphere radius, m

r, φ, z

cylindrical coordinates

r, θ, φ

spherical coordinates

x, y, z

rectangular coordinates, m

x_c

critical location for transition to turbulence, m

X, Y, Z

components of body force per unit volume, N/m³

6. Miscellaneous

P_L, P_T

dimensionless longitudinal/transverse tube-bank pitch

solubility; shape factor (2-D conduction), m; nozzle pitch; plate spacing

Page 3

1. Greek Letters

(alpha) thermal diffusivity, m²/s; exchanger area per volume; absorptivity

(beta) volumetric thermal-expansion coefficient, K⁻¹

(Gamma) film-condensation mass flow per width, kg/(s·m)

(delta) hydrodynamic boundary-layer thickness, m

δ_c

(delta) concentration boundary-layer thickness, m

δ_p

(delta) thermal penetration depth, m

δ_t

(delta) thermal boundary-layer thickness, m

(epsilon) emissivity; packed-bed porosity; exchanger effectiveness

η_f

(eta) fin efficiency

η_o

(eta) overall fin-array efficiency

(theta) temperature difference, K; zenith angle, rad

(kappa) absorption coefficient, m⁻¹

(lambda) wavelength, μm

(mu) dynamic viscosity, kg/(m·s)

(nu) kinematic viscosity, m²/s; radiation frequency, s⁻¹

(rho) mass density, kg/m³; reflectivity

(sigma) Stefan–Boltzmann constant; conductivity; viscous stress; surface tension

(Phi) viscous dissipation function, s⁻²

(phi) azimuthal angle, rad

(psi) stream function, m²/s

(tau) shear stress, N/m²; transmissivity

(omega) solid angle, sr

2. Subscripts

A, B

species in a binary mixture

abs

absorbed

arithmetic mean

base of extended surface; blackbody

cross-sectional; concentration; cold fluid

critical insulation thickness

cond

conduction

conv

convection

counterflow

saturated vapor conditions

hydrodynamic; hot fluid; helical

species index; inner; initial condition

saturated liquid

log-mean

momentum-transfer condition

mean value over a tube cross-section

max

maximum fluid velocity

mfp

mean free path

center/mid-plane; outlet; outer

phonon

reradiating surface

r, ref

reflected radiation

rad

radiation

solar conditions

surface; solid properties

sat

saturated conditions

sens

sensible energy

sky

sky conditions

steady state

sur

surroundings

thermal

transmitted

saturated vapor conditions

local surface conditions

spectral

∞

free-stream conditions

3. Other Symbols

diameter; drag

dif

diffusion

excess; emission; electron

evap

evaporation

f_c

forced convection

f_d

fully developed conditions

heat-transfer conditions

based on characteristic length

lat

latent energy

phonon

k₀, k₁, k₁^′

zero-order (kmol/(s·m³)), first-order (s⁻¹), first-order surface (m/s)

4. Superscripts & Overbars

′

fluctuating quantity

molar average; dimensionless

f̄

surface average; time mean

Tip: If any symbol rendering looks cramped, tweak grid-template-columns in .symbol-list.

Heat Transfer Symbols — Collapsible

▸ HEAT TRANSFER SYMBOLS (click to open)

Heat Transfer Symbols

Latin Greek Subscripts Superscripts

Heat Transfer — Latin symbols

Symbol	Meaning
A	Area, m².
A_b	Area of prime (unfinned) surface, m².
A_c	Cross-sectional area, m².
A_fr	Heat-exchanger frontal area, m².
A_p	Fin profile area, m².
a	Acceleration, m/s².
Bi	Biot number.
Bo	Bond number.
C	Molar concentration, kmol/m³; heat-capacity rate, W/K.
C_D	Drag coefficient.
C_f	Friction coefficient.
C_t	Thermal capacitance, J/K.
Co	Confinement number.
c	Specific heat, J/(kg·K); speed of light, m/s (context).
c_p	Specific heat at constant pressure, J/(kg·K).
c_v	Specific heat at constant volume, J/(kg·K).
D	Diameter, m.
D_AB	Binary mass diffusivity, m²/s.
D_b	Bubble diameter, m.
D_h	Hydraulic diameter, m.
E	Thermal + mechanical energy, J; electric potential, V; emissive power, W/m² (context).
Ė_g	Rate of energy generation, W.
Ė_in	Rate of energy transfer into a control volume, W.
Ė_out	Rate of energy transfer out of a control volume, W.
Ė_st	Rate of increase of stored energy in a control volume, W.
E^tot	Total energy, J.
Ec	Eckert number.
e	Internal energy per unit mass, J/kg.
F	Force, N; HX correction factor; band fraction; view factor.
Fo	Fourier number.
Fr	Froude number.
f	Friction factor; similarity variable (context).
G	Irradiation, W/m²; mass velocity, kg/(s·m²).
Gr	Grashof number.
Gz	Graetz number.
g	Gravitational acceleration, m/s².
g_c	Gravitational conversion factor, 1 kg·m/(N·s²) ≈ 32.17 ft·lbm/(lbf·s²).
H	Nozzle height, m; Henry’s constant, bar.
h	Convection heat-transfer coefficient, W/(m²·K).
h_fg	Latent heat of vaporization, J/kg.
h_sf	Latent heat of fusion, J/kg.
h_m	Convection mass-transfer coefficient, m/s.
h_rad	Radiation heat-transfer coefficient, W/(m²·K).
I	Electric current, A; radiation intensity, W/(m²·sr).
i	Current density, A/m²; enthalpy per unit mass, J/kg.
J	Radiosity, W/m².
Ja	Jakob number.
j_i^*	Diffusive molar flux of species i relative to molar average velocity, kmol/(m²·s).
j_i	Diffusive mass flux of species i relative to mass average velocity, kg/(m²·s).
J_H	Colburn j factor (heat transfer).
j_m	Colburn j factor (mass transfer).
k	Thermal conductivity, W/(m·K).
k_s	Surface roughness height, m.
k₀	Zero-order reaction rate, kmol/(s·m³).
k₁	First-order reaction rate, s⁻¹.
k₁^′	First-order surface reaction rate, m/s.
k_B	Boltzmann’s constant.
L	Characteristic length, m.
Le	Lewis number.
M	Mass, kg; lanes in flux plot; 1/Fo (FDM context).
ṁ_i	Mass transfer rate of species i, kg/s.
ṁ_ig	Rate of mass increase of species i due to reactions, kg/s.
ṁ_in	Mass flow rate into a control volume, kg/s.
ṁ_out	Mass flow rate out of a control volume, kg/s.
ṁ_st	Rate of increase of mass stored in a control volume, kg/s.
M_i	Molecular weight of species i, kg/kmol.
m	Mass, kg.
ṁ	Mass flow rate, kg/s.
m_i	Mass fraction of species i, ρ_i/ρ.
N	Temp increments (flux plot); total tubes; enclosure surfaces.
N_L, N_T	Tubes in longitudinal / transverse directions.
Nu	Nusselt number.
NTU	Number of transfer units.
N_i	Molar transfer rate of species i (fixed coords), kmol/s.
N_i^′	Molar flux of species i (fixed coords), kmol/(m²·s).
Ñ_i	Molar rate increase of species i per volume due to reactions, kmol/(m³·s).
N_i^′′	Surface reaction rate, kmol/(m²·s).
n_i^′′	Mass flux (fixed coords), kg/(m²·s).
ṅ_i	Mass rate increase per volume due to reactions, kg/(m³·s).
P	Perimeter, m; general fluid-property designation.
Pe	Péclet number (= Re·Pr).
Pr	Prandtl number.
p	Pressure, N/m².
Q	Energy transfer, J.
q	Heat-transfer rate, W.
q̇	Volumetric heat generation, W/m³.
q′	Heat-transfer rate per unit length, W/m.
q′′	Heat flux, W/m².
q^*	Dimensionless conduction heat rate.
R	Cylinder radius, m.
ℜ	Universal gas constant.
Ra	Rayleigh number.
Re	Reynolds number.
R_e	Electrical resistance, Ω.
R_f	Fouling factor, m²·K/W.
R_m	Mass-transfer resistance, s/m³.
R_t	Thermal resistance, K/W.
R_tc	Thermal contact resistance, K/W.
R_tf	Fin thermal resistance, K/W.
R_to	Thermal resistance of fin.
r_o	Cylinder or sphere radius, m.
r, φ, z	Cylindrical coordinates.
r, θ, φ	Spherical coordinates.
S	Solubility; shape factor; nozzle pitch/plate spacing (context).
S_c	Solar constant.
S_D, S_L, S_T	Tube-bank pitches.
Sc	Schmidt number.
Sh	Sherwood number.
St	Stanton number.
T	Temperature, K.
t	Time, s.
U	Overall heat-transfer coefficient.
u, v, w	Mass-average velocity components.
u^, v^, w^*	Molar-average velocity components.
V	Total volume, m³; (context) velocity magnitude.
v	Specific volume, m³/kg. Exam trap: don’t confuse v (specific volume) with v̄ (average specific volume).
v̄	Average (mean) specific volume, m³/kg.
W	Width of a slot nozzle.
Ẇ	Rate at which work is performed.
We	Weber number.
X	Vapor quality.
X, Y, Z	Body force components per unit volume.
x, y, z	Rectangular coordinates.
x_c	Critical location for transition to turbulence.
x_fd,c	Concentration entry length.
x_fd,h	Hydrodynamic entry length.
x_fd,t	Thermal entry length.
x_i	Mole fraction of species i.

Heat Transfer — Greek letters

Symbol	Meaning
α	Thermal diffusivity, m²/s; …
β	Volumetric thermal-expansion coefficient, K⁻¹.
Γ	Mass flow rate per unit width in film condensation, kg/(s·m).
δ	Hydrodynamic boundary-layer thickness, m.
δ_c	Concentration boundary-layer thickness, m.
δ_p	Thermal penetration depth, m.
δ_t	Thermal boundary-layer thickness, m.
ε	Emissivity; porosity; effectiveness (context).
η	Similarity variable.
η_f	Fin efficiency.
η_o	Overall fin-array efficiency.
θ	Temperature difference; zenith angle (context).
κ	Absorption coefficient, m⁻¹.
λ	Wavelength, μm.
μ	Dynamic viscosity, kg/(m·s).
ν	Kinematic viscosity; radiation frequency (context).
ρ	Mass density; reflectivity (context).
σ	Stefan–Boltzmann const.; conductivity; viscous stress; surface tension.
Φ	Viscous dissipation function, s⁻².
φ	Azimuthal angle, rad.
ϕ	Azimuthal angle, rad. (variant glyph).
ψ	Stream function, m²/s.
τ	Shear stress; transmissivity (context).
ω	Solid angle, sr (context).

Heat Transfer — common subscripts / qualifiers

Mark	Meaning
f_c	Forced convection (externally driven flow).
f_d	Fully developed (profile no longer changes axially).
g	Saturated vapor state.
H	Heat-transfer condition (context-specific marker).
h	Hydrodynamic; hot-fluid side (context).
i	Species index; inner surface; initial; inlet; incident radiation.
L	Based on characteristic length, L.
l	Saturated liquid state.
l_at	Latent energy (phase change).
l_m	Log-mean (e.g., LMTD).
M	Momentum-transfer condition.
m	Cross-section mean (e.g., tube bank).
x_max	Maximum fluid velocity.
x_mfp	Mean free path — avg. molecular distance between collisions; micro/Knudsen effects.
o	Mid-plane; outlet; outer (context).
x_ph	Phonon-related quantity (lattice heat transfer context).
R	Reradiating surface (idealized: emits = absorbs, net q ≈ 0).
x_r, x_ref	Reflected radiation.
x_rad	Radiation-related quantity.
S	Solar conditions (short-wave input).
s	Surface / solid properties.
x_sat	Saturated conditions.
x_sens	Sensible energy (no phase change).
x_sky	Effective sky temperature for outdoor longwave radiation.
x_ss	Steady state (∂/∂t = 0).
x_sur	Surroundings / radiative sink temperature.
t	Thermal.
x_tr	Transmitted radiation/energy.
v	Saturated vapor conditions.
x	Local surface conditions at position x.
λ	Spectral (wavelength-based).
∞	Free-stream (ambient) conditions.

Heat Transfer — superscripts & overbars

Mark	Meaning
′ (prime)	Fluctuating quantity.
* (star)	Molar average; dimensionless quantity (context).
f̄ (overbar)	Surface-average condition; time mean.