An optimization method to find the thermodynamic limits of convective mass transfer for fixed viscous dissipation is developed. The method applies the principle of extremum entropy generation to the mass transfer problem. The mass transfer-induced entropy generation in the fluid flow is defined as the criterion. By maximizing or minimizing the criterion under the constraint of fixed viscous dissipation, a velocity field and associated body force field can be obtained, which can enhance the mass transfer process to the thermodynamic limit. By applying the optimization method, the dependence of the maximum convective mass transfer enhancement on viscous dissipation can be found. Such a mass transfer limit is shown to be useful for setting a target for mass transfer enhancement in practical applications. The analysis is demonstrated using three examples. (C) 2016 Elsevier Ltd. All rights reserved.