**2. The relation between convective heat and mass transfer coefficient**

All types of DCHME mentioned above can be assumed that each exchanger has similar geometry and boundary conditions for heat and mass transfer process so convective mass transfer is analogous to convective heat transfer, and that can be applied for both laminar and turbulent flows [19]. Bird et al. [21] and Incropera and DeWitt [22] defined the analogy Nusselt (*Nu*) and Sherwood (*Sh*) number for the calculation of mass transfer coefficient *hM* [m/s] from the heat transfer coefficient *α<sup>a</sup>* [W/m<sup>2</sup> .K]. Nusselt (*Nu*) number, related with *αa*, is a function of Reynold (*Re*) and Pantanal (*Pr*) number, expressed in Eq. (1). Sherwood (*Sh*) number, related with *hM*, is a function of Reynold (*Re*) and Schmidt (*Sc*) number, stated in Eq. (2).

$$Nu = \frac{a\_d \ D\_H}{k\_d} = a \left[ Re \right]^b \left[ Pr \right]^{\dagger \beta} \tag{1}$$

$$\text{Sh} = \frac{h\_M \, D\_H}{D\_v} = a \, [\text{Re}\, ]^b \, [\text{Sc}\,]^{1\zeta} \tag{2}$$

where *a* and *b* are coefficient numbers, *DH* [m] is characteristic length of exchanger, *ka* [W/m.K] is thermal conductivity of air, and *Dv* [m2 /s] is mass diffusivity. Division of Eq. (1) with Eq. (2) are called the Reynold analogy, and it gives the relation of Lewis (*Le*) number which can be seen in Eqs. (5) and (6).

$$\frac{a\_a}{h\_M} = \left[\frac{Pr}{\text{Sc}}\right]^{\frac{1}{\dagger}} \frac{k\_a}{D\_v} \tag{3}$$

$$\frac{a\_d}{h\_M} = \left[\frac{Pr}{\text{Sc}}\right]^{\frac{1}{5}} \frac{\text{Cp } \mu}{Pr} \frac{\rho \text{ Sc}}{\mu} = \text{Le}^{-\frac{1}{5}} \text{Le } \rho \text{ Cp}\_m \tag{4}$$

$$\frac{a\_d}{h\_M \rho \text{ C} p\_m} = L e^{\frac{2}{5}} \approx 1\tag{5}$$

where *μ* [N s/m2 ] is dynamic viscosity, *Cpm* [J/kg.K] is specific heat capacity of moist air, and *ρ* [kg/m3 ] is density of air. For the humidity ratio is taken as a driving force in mass transfer process, mass transfer coefficient should be defied with the term *KM* = *hM ρ* [kg/m2 .s]. The Lewis relation equation Eq. (5) can be written as follows:

$$\frac{a\_d}{K\_M C p\_m} = L e^{\frac{2}{7}} \approx 1\tag{6}$$

Similarly, Chilton and Colburn [23] proposed Chilton-Colburn j-factor analogy using this similarity to relate Nusselt number to friction factor by the analogy. The j-factor analogy has some limitation that is it can be only reliable when the surface conditions are identical. Bedingfield and Drew [24] also proposed the relation equation between heat and mass coefficients. Many others relation equations that can be found in literatures to calculate mass transfer coefficient *hM* from heat transfer coefficient *αa*, but in this study, Lewis relation will use in this model development due to its simplicity.
