<p>The authors have obtained parameters of prototype heat-transfer structures, that correspond to the minimum entropy production (dissipation) at prescribed heat load and heat-transfer coefficient. The latter is related to the contact surface, which is in turn correlated with the cost of the heat-exchange system. Dissipation, at prescribed heat load and heat-transfer coefficient, is bounded below, and the heat load corresponding to this bound is the highest possible for this heat-transfer coefficient. Account has been taken of the influence of the hydrodynamics of flows and of the change in their phase state.</p>