Notation and Units
Symbol |
Quantity |
Unit |
\(\vec{U_i}=(U_x,U_y,U_z,t)\) |
the velocity of fluid particles at the identified point at time t |
\(m.s^{-1}\) |
\( div(\vec{U_i})= \frac{\partial U_x}{\partial x } + \frac{\partial U_y}{\partial y }+\frac{\partial U_z}{\partial z }\) |
the divergence of a continuously differentiable vector field |
|
\(\rho\) |
density |
\(kg.m^{-3}\) |
\(p\) |
pressure |
\(Pa\) |
\(T\) |
temperature |
\(°C\) |
\(f_{x_i}=f_x, f_y,f_z\) |
velocity body force terms |
|
\(Q_i=K (\frac{\partial T}{\partial x_i})\) |
sink term (volume flow rate) |
\(m^3.s^{-1}\) |
\(S\) |
source term |
|
\(D_{ii}= D_{xx}, D_{yy}, D_{zz}\) |
species concentration diffusion coefficients |
|
\(\sigma_{ii}= \frac{2 \mu }{3 } (2\frac{\partial U_i}{\partial x_i })\) |
normal viscous stress terms |
|
\(\sigma_{ij}= \mu (\frac{\partial U_i}{\partial x_j} +\frac{\partial U_j}{\partial x_i})\) |
tangential viscous stress terms |
|
\(\mu\) |
dynamic viscosity |
\(Pa.s\) |
\(K\) |
thermal conductivity |
\(W/m.K\) |
\(C\) |
concentration of airborne infectious particles |
\(particles/m^2\) |
\(t\) |
time |
\(s\) |
\(\nabla \) = ( \(\frac{\partial }{\partial \zeta}, \frac{\partial }{\partial y})\) |
the two-dimensional gradient operator in the surface of the looping airflow |
|
\(\zeta\) |
denotes the length in the stream-wise direction of the flow |
\(m\) |
\(y \) |
coordinate transverse to the flow |
\(m\) |
\(c_v\) |
von Karman constant |
|
\(Q\) |
total volume flow rate into the room |
\(m^3.s^{-1}\) |
\(V\) |
room volume |
\(m^3\) |
\(N\) |
number of air supply vents |
|
\(c_\epsilon\) |
constant of proportionality in Taylor’s Dissipation Law |
|
\(P\) |
the transmission probability of a specific microorganism for 1 person per hour |
|
\(I\) |
number of infectious sources in 1 space |
|
\(t\) |
time of exposure to a certain microorganism |
\(h\) |
\(d\) |
damping or mass coefficient |
|
\(c\) |
diffusion coefficient |
|
\(\alpha\) |
conservative flux convection coefficient |
|
\(\gamma \) |
conservative flux source term |
|
\(\beta\) |
convection coefficient |
|
\(a\) |
absorption or reaction coefficient |
|
\(f\) |
source term |