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with where is a constant. The boundary conditions specify
the concentration on r = 1 and that the flux of oxygen must be zero at r = 0;
these are expressed as

(a) Find the size of the boundary layer near r = 1 (in the form
for suitable and hence show that satisfies

where we have assumed that and as (which
is consistent with the equation).
(b) From the result in (a), deduce that is exponentially small as
for 1 – r = O(1), seek a solution (which is exponentially small) in terms
of the scaled variable and show that where
satisfies

Solve this equation, apply the relevant boundary condition, match and hence
show that

where is a constant (independent of which should be identified.