General Correlations for the Sherwood Number

Particles and bubbles. Using the method of asymptotic analogies, we shall derive formulas for the calculation of the Sherwood number in a laminar flow past spherical particles, drops, and bubbles for an arbitrary structure of the nonperturbed flow at infinity. We assume that closed streamlines are lacking in the flow. 

We start from the approximate formula (4.7.1). Let us transform (4.7.1) by using the procedure described in Section 4.1. We take into account the fact that the asymptotic expansions of Shp at small and large Pe have the form 

These formulas coincide with (4.1.2) and (4.1.3) up to notation (ui = Shp, r == Pe) for A = 1, B - 0.624, k = 0, and m =. Let us substitute these values into (4.1.5), where the function F is determined from (4.7.1). We take into account the fact that the equation Shpo = 1 holds for spherical particles, and obtain the following result [359]  

Formula (4.7.9) can be used for the calculation of the mean Sherwood number in laminar flows of various types without closed streamlines past a solid spherical particle. The auxiliary value Shpoo must be chosen equal to the leading term of the asymptotic expansion of the Sherwood number as Pe - oo. 

Similarly, for an arbitrary flow past a spherical bubble, one can derive the approximate formula 

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For an isothermal situation at 600 K, develop a general correlation for the Sherwood number versus the spin Reynolds number, which should be generally in the form... 

General correlations for the Sherwood number. In [364], the following approximate equation was suggested for the mean Sherwood number ... 

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