An exact analytical solution was derived for the concentration of solute or the temperature of the fluid ina constant molar flow semi-batch well-stirred vessel in contact with permeable core-shell composites. The linear equi-libria at both the fluid-particle interface and the core-shell interface are assumed and the extraparticle film resistanceis included. Several particular solutions can be readily degenerated from the solution derived in this work. By takingthe contact affinity at the core-shell interface to zero, the solution in case of impermeable core-shell composites canbe degenerated. By taking both the contact affinity at the core-shell interface and the ratio of mass or thermal effectivediffusivities in the core and the shell to unity or by taking the size of the core to zero, the solution in case of homo-geneous particles can be degenerated. The solution for the batch vessel is also degenerated by the differentiation ofthe solution for the constant molar flow semi-batch vessel with respect to time.