| • | scalar product |
 | tensorial product |
| : | contracted tensorial product |
 | nabla operator, gradient 0 |
 | rotational |
 |  , Laplacian |
| tr | trace of a tensor |
 | material derivative |
 | partial derivative in relation to time |
| α | isothermal expansion coefficient |
| β | thermal expansion coefficient |
| χT | isothermal compressibility coefficient |
| γ | specific heat ratio |
| δij | Kronecker delta |
| εij | components of the stress tensor |
 | curvature of an interface |
| λ | compression viscosity |
 | dissipation function |
| φ | heat flux density |
| μ | shear viscosity |
| μsm | subgrid viscosity |
| μt | turbulent viscosity |
| ν | kinematic viscosity |
| ρ | density |
| σ | surface tension, Poisson coefficient |
 | stream function |
| γ | acceleration |
| ε | strain tensor |
| ω | vector potential |
| ωo | equilibrium vector potential |
| σ | stress tensor |
| τ | viscous stress tensor |
| Γ | curvilinear contour |
| Φ | scalar potential |
| Σ | surface of a domain |
| Ω | volume of a domain |
| Ω | rotation rate tensor |
| (x, y, z) | Cartesian coordinates |
| (r, θ) | polar coordinates |
| (r, θ, z) | cylindrical coordinates |
| (r, θ, φ) | spherical coordinates |
| (e1,e2,e3) | unit vectors |
 | area of a surface |
 | domain, control volume |
 | linear operator |
 | molar mass |
 | nonlinear operator |
 | power |
 | volume |
| a | heat diffusivity |
| cp | specific heat at constant pressure |
| cv | specific heat at constant volume |
| d | distance |
| dij | components of the strain rate tensor |
| e | specific internal energy |
| f | scalar function |
| k | heat conductivity, turbulent kinetic energy |
| h | specific enthalpy |
| m | mass |
| p | pressure, scalar potential |
| po | equilibrium scalar potential |
| p* | driving pressure |
| pB | Bernouilli pressure |
| q | heat production per volume |
| qm | mass flowrate |
| qυ | volume flowrate |
| r | perfect gas constant |
| s | specific entropy, curvilinear abscissa |
| t | time |
| υ | specific volume |
| D | flowrate |
| Dh | hydraulic diameter |
| E | Young’s modulus, total energy |
| J | Jacobian of the transformation |
| R | molar constant of gases |
| L | reference distance |
| S | entropy |
| T | temperature |
| To | equilibrium temperature |
| T0 | reference temperature |
| V0 | reference velocity |
| f | body volume force |
| g | acceleration due to gravity |
| n | outward normal |
| q | momentum |
| t | tangential unit vector |
| v′ | fluctuation of velocity |
| v | perturbation of velocity |
| D | strain rate tensor |
| F | force |
| I | identity matrix or tensor |
| K | permeability tensor |
| M | mobility tensor |
| N | outward normal to a free surface |
| T | stress |
| V | velocity component |
| |W| | velocity modulus |
| W | velocity |
 | averaged velocity |
| Bi | Biot number |
| Da | Darcy number |
| M | Mach number |
| Ma | Marangoni number |
| Ra | Rayleigh number |
| Re | Reynolds number |
| We | Weber number |