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