Overlapping of free and forced flow

In simultaneous heat and mass transfer in binary mixtures, mean mass transfer coefficients can likewise be found using the equations from the previous sections. Once again this requires that the mean Nusselt number Num is replaced by the mean Sherwood number Shm, and instead of the Grashof number a modified Grashof number is introduced, in which the density p(p,T, ) is developed into a Taylor series, 

As Saville and Churchill [3.51] showed, the results obtained with this method are only sufficiently accurate if the Schmidt and Prandtl numbers of the mixtures are the same. In any other case the mutual influence of the mass transfer and the flow field will not be sufficiently taken into account. 

In the discussion of forced flow we neglected the influence of free flow and in reverse the effect of forced flow was neglected in our handling of free flow. However, frequently a free flow will overlap a forced flow as a result of density gradients. As we have already seen in 3.9.1, eq. (3.308), the decisive quantity for this is Gr/Re2. If it is of the order 1, the buoyancy and inertia forces are equal, whilst for Gr/Re2 -C 1 the forced, and for Gr/Re2 1, the free flow predominates. 

Forced and free flow can, depending on the direction of the inertia and buoyancy forces, either mutually stimulate or dampen each other. In a forced flow overlapping a free flow, the heat and mass transfer can either be improved or inhibited. As an example of this we will look at a heated plate, Fig. 3.51. A free flow in the upwards direction develops, which can be strengthened Fig. 3.51a, or weakened, Fig. 3.51b, by a forced flow generated by a blower. Experiments have shown that the heat transfer coefficient can be calculated well by using equations of the form 

3 Convective heat and mass transfer. Single phase flow 

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Fig. 3.51 Overlapping of free and forced flow, a Strengthening b Weakening of the free flow by the forced flow...

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