# Problem modeling

Problem modeling 1- Lists of symbols & subscripts

Symbols:

Here are the list of all symbols and subscripts used in the study.

• $h$    liquid thickness
• $L$    container height dimension
• $l_c$    capillary length
• $a$    depth
• $b$    length
• $S_{flux}=a b$    flux surface ($m^2$)
• $\rho$    density of the gas mixture ($kg/m^3$)
• $P$    pressure ($Pa$)
• $u$    the projection of velocity vector along the x-axis ($m/s$)
• $\mu$    the dynamic viscosity of the gas mixture  ($Pa.s$)
• $\nu$    the cinematic viscosity of the gas mixture ($m^2/s$)
• $v$    the projection of velocity vector along the y-axis ($m/s$)
• $g$    standard gravity ($m/s^2$)
• $C_p$    specific heat ($J.kg^{-1}.K^{-1}$)
• $T$    temperature of the mixture ($K$)
• $\lambda$    the thermal conductivity ($W/m.K$)
• $D$    diffusion coefficient of the vapour in the air ($m^2/s$)
• $\rho_S$    mass concentration of vapour at the interface ($kg/m^3$)
• $\omega$    mass fraction of vapour in the air with $\omega= \frac{\rho_v}{\rho_v+\rho_a}$
• $\dot{m}$    mass flow rate ($kg/s$)
• $h_{lg}$    latent heat ($kJ/kg$)
• $h_c$    thermal exchange coefficient
• $h_m$    mass exchange coefficient
• $D_h$    hydraulic dimension

Subscript :

• $v$    for the vapour
• $S$    for the vapour at the interface
• $in$    for the input condition
• $w$    for the wall condition
• $l$   for the liquid

2- Assumptions related to the vapour- state :

We consider a layer of liquid in a ventilated box. The following figure represents the problem: Figure: Problem modeling & Simplifications

During this study, we simplify the problem by considering the following assumptions:

• Bidirectional incompressible turbulent flow.
• Liquid film thin in relation to the reservoir but sufficient thick for neglect the interfacial resistance.
• Air charged in vapour is in thermodynamic balance : the phase change happens in saturation conditions.
• Viscous dissipation and pressure work is neglected.
• Soret effect ( temperature gradient dependence for the mass flow) and Dufour effect (mass gradient dependence for the heat flux) neglected.
• Radiation phenomena neglected.
• Boussinesq approximation considered.

In further, the conservation equations are presented below.