Page 104 - Modelling in Transport Phenomena A Conceptual Approach

84 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

4.3.3 Mass Transfer Correlations

When a sphere is immersed in an infinite stagnant fluid, the analytical solution for
the steady-state diffusion is possible2 and the result is expressed in the form

Sh = 2 (4.3-32)

In the case of fluid motion, contribution of convection must be taken into con-
sideration. Correlations for convective mass transfer are as follows:

hz-Marshall correlation

For constant surface composition and low mass transfer rates, Eq. (4.3-29) may be
applied to mass transfer problems simply by replacing Nu and Pr with Sh and Sc,
respectively, i.e.,
I Sh = 2 + 0.6 Re;’’ Sc1I3 I (4.3-33)
Equation (4.3-33) is valid for

2 2 Rep 5 200

0.6 5 Sc 5 2.7
Frossling correlation

Frossling (1938) proposed the following correlation:
I Sh = 2 + 0.552 Re? Sc1I3 I (4.3-34)

Equation (4.3-34) is valid for

0.6 5 Sc 5 2.7
Steinberger and Treybal (1960) modified Frossling correlation as
I Sh = 2 + 0.552 Re%53 Sc113 I (4.3-35)

which is valid for
1500 5 Rep L 12,000
0.6 5 Sc 5 1.85

2See Example 8.13 in Chapter 8.