The present problem is on the mass transport process through an annular tube, where a chemical species is discharged into a flowing stream driven by a harmonic pressure gradient. The species may undergo linear reversible and irreversible reactions at the outer boundary of the annulus. Also, two non-linear chemical decay are assumed within the bulk flow and at the outer wall. However, the degree of the non-linearity of these reactions are different. The problem is analyzed based on the three-time scale, and thus the homogenization method is utilized to average the two-dimensional mass transport problem. We establish analytical expressions for different transport coefficients in terms of rigorous mathematical calculations. The results exhibit some paradoxical behavior with the radius ratio. The transport coefficients linearly increase with the associated reactions rate but decrease with the wall absorption rate. © 2019 Elsevier Ltd