Stationary Mass and Heat Exchange

Statement of the problem. Following [367, 368], let us consider stationary diffusion to a particle of finite size in a stagnant medium, which corresponds to the case Pe = 0. We assume that the concentration on the surface of the particle and remote from it is constant and equal to Cs and C), respectively. The concentration field outside the particle is described by the Laplace equation 

The unknown quantity which is of most practical interest in these problems is the mean Sherwood number, which is determined by (3.1.28) and is related to the mass transfer coefficient ac by 

From the mathematical viewpoint, the diffusion problem (4.3.1)-(4.3.3) is equivalent to the problem on the electric field of a charged conductive body in a homogeneous charge-free dielectric medium. Therefore, the mean Sherwood number in a stagnant fluid coincides with the dimensionless electrostatic capacitance of the body and can be calculated or measured by methods of electrostatics. 

Shape factor. In what follows, it is convenient to introduce a shape factor II, which has the dimension of length, as follows  

One can interpret the table data as follows. Let us project a body of revolution on the plane perpendicular to the symmetry axis. The projection is a disk of 

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