The oxidation of wine in a wooden barrel proceeds by a series of reactions that can be lumped into the rate expression ? = ? ?? in units of mol/m3s, where\ is an exponent that depends on the wine. Oxygen (species A) enters the cylindrical barrel by permeating the wood from the sides, but the top and bottom of the barrel are insulated by barrels stacked above and below. The radius of the barrel is R, its length is L and the diffusion coefficient of oxygen in wine is DAB.