Verify that the concentration profile in a slab is linear, whereas that in a hollow cylinder is logarithmic, and for a spherical shell it is an inverse function of \(r\) for the three geometries in Fig. 10.1.

Also verify the expressions for the numbers of moles transported across the system, \(\mathcal{W}_{\mathrm{A}}\).

10.1 Steady-state diffusion: no reaction Slab WA WA = DA A(CA,i- CA,O) Ax 2 DAL(CAI-CAD) In(R/R;) Concentric cylinder O Concentric sphere W = 4 DARR (CA, i-CA,o) Ro-R