The uniform internal heating of a solid slab and the viscous flow between two parallel walls, are used to illustrate the possibility of minimizing the global entropy generation rate by cooling the external surfaces convectively in an asymmetric way. The known analytic expressions for the temperature field, in the first case, and the velocity and temperature fields, in the second case, are used to calculate the global entropy generation rate explicitly. In dimensionless terms, this function depends on the dimensionless ambient temperature and convective heat transfer coefficients (Biot numbers) of each surface which, in general, are not assumed to be the same. When the Biot numbers for each surface are equal, the entropy generation rate shows a monotonic increase. However, when the Biot numbers are different this function displays a minimum for specific cooling conditions. (C) 2003 Elsevier Science Ltd. All rights reserved.