d2C/ dy2= [dC2/dȳ2. (1/√(y)) + dC/dȳ .d/dȳ (1/√(y))]
please try to bring the equation a modified Bessel Equation of appropriate order. Identify the the order and write down the analytical solution for the concentration distribution C= f (ȳ) and thus C= f(z) using modified Bessel Functions.
The values are given if you need it.
reaction rate constant (k) =0.05 cm/s
Diffusion coefficient of ‘A’ (D) = 0.01 cm2/s
The cavity opening at the top (a)= 0.1 cm
Concentration of ‘A’ at z=0 (C0)= 1 mol/cm3
Length (L)= 1 cm
Graph with solution is given below: