Correlation For Convective Mass Transfer Coefficient | Mass Transfer - Chemical Engineering PDF Download

3.4 CORRELATION FOR CONVECTIVE MASS TRANSFER COEFFICIENT 
In this section various correlations that are used to estimate the convective mass transfer coefficients for various cases are presented. The various correlations are generally formed in terms of different dimensionless groups associated with the mass transfer. The definitions of mostly useful dimensionless groups associated with the mass transfer are given in Table 3.1 as follows:

Table 3.1: Dimensionless groups for mass transfer:



3.4.1 Correlation of mass transfer coefficients for a single sphere 
3.4.1.1 Mass transfer coefficients for a single sphere in case of natural convection
In presence of natural convection the mass transfer from single sphere were studied by Steinberger and Treybal (1960) and they recommended the mass transfer coefficient as follows:
Sh = Sh_nc + 0.347(ReSc^0.5)^0.62                                                          (3.34)
In the range of 1 < Re < 3×10⁴ and 0.6 < Sc < 3200 
Sh_nc = 2.0 + 0.569(Gr_DSc)^1/4                                                    (3.35)
in the range of Gr_DSc < 10⁸
and
Sh_nc = 2.0 +.0254(Gr_DSc)^1/3  Sc^0.244                                      (3.36)
in the range of Gr_DSc >10⁸

3.4.1.2 Mass transfer coefficients for a single sphere in case of forced convection 
Different investigators have performed the experiment on the mass transport from a single sphere and developed correlations based on mass transfer in the environment of forced convection along with the consideration of mss transfer by molecular diffusion in the general form of:
                                                          (3.37)
where m and n are correlating constants. As per Bird et al. (1960), for low Reynolds number, the effects of natural convection is negligible which results Sherwood number theoretically to a value of 2.0. Then the generalized correction becomes:
                                                         (3.38)
At Reynolds numbers ranging from 2 to 12000 and Schmidt number ranging from 0.6 to 2.7, Froessling (1939) and Evnochides and Thodos (1959) developed the mass transfer coefficient for a single sphere and represented as follows:
                                             (3.39)

3.4.2 Correlation of mass transfer coefficients for flat plates 
There are several investigations in literature regarding the evaporation from a free liquid surface or the sublimation from a flat solid surface into air stream under both laminar and turbulent conditions. Wilty et al. (1984) developed correlations for the average mass transfer coefficient during evaporations from a flat solid surface of characteristic length of L under laminar and turbulent conditions as follows:
at laminar condition and Re < 3×10⁵
                                                      (3.40)
at turbulent condition and Re > 3×10⁵
                                                       (3.41)
The Reynolds number and the Sherwood number are defined based on the characteristic length /. The range of Schmidt number for the above correlations is 0.6< Sc < 2500