Equation (12.265) indicates that the magnitude and direction of mass transfer can have a large effect on the Sherwood number. It is interesting to explore this a bit. Consider two situations. In the first we have a saturated sugar/water solution that is being transported to the surface of a plate. A reaction at the surface consumes all the sugar that reaches it. In the second scenario, we have a flat plate made of sugar that is dissolving into water. At a temperature of \(25^{\circ} \mathrm{C}\) the mole fraction of sugar in water at its solubility limit is \(9.65 \times 10^{-2}\). The molecular weight of sugar is \(342.3 \mathrm{~kg} / \mathrm{kg}\)-mole. The diffusivity of sugar in water is \(0.52 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\). Estimate the maximum difference in the Sherwood numbers for the two cases.

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Sh = CfRex 2 0.37Rex Mwa (Ca-Kegcas) p(1Xao) (12.265) -Sc