Heat exchangers are basic components of industry and daily living. The paper deals with the optimization of some special heat exchangers used in electronics and in the process industry. There are some kinds of heat exchangers even in mobile phones, where small heat generating components should be located on a printing board so that the allowed temperatures are not exceeded, whilst simultaneously the total length of wires connecting them is small. In power electronics heat generating components are located at the base plate, which is cooled by natural or forced convection-using fins. The flow can be laminar or turbulent. The main problem is to prevent the overheating of components. In addition, these exchangers, called heat sinks, must have a small weight and volume. Thus, we have a multi-objective optimization problem in both the above applications.

There are similar types of optimization problems in industrial processes, where the size scale of equipment is much larger than in the above applications. For example, in the pulp and paper industry the length of the economizer in a recovery boiler can be as much as 30 meters, and the total weight one million kilograms. High pressure water in tubes is heated by flue gases from burning black liquor. Heat exchanger tubes are connected together with welded fins between the tubes to form walls, which are located parallel to each other, forming clusters that contain hundreds of pipes. Hot flue gas from burning black liquor flows in channels between the walls. The weight of this type of counter-flow heat exchanger is important in addition to the heat transfer.

The most challenging problem in the above applications is the evaluation of convection. Though numerical modelling of the flow (CFD) is a useful tool, it is not suitable in the above cases, especially if there is a turbulent flow. The results in the paper are obtained using analytical correlations of convection, which are utilized in the optimization of heat transfer. The main goal is to derive analytical equations for the performance of a new type counter-flow heat exchanger to be used in optimization, where there are at least two criteria: improving heat transfer and reducing size. Analytical equations of convection are needed if multi-objective optimization is to be performed in a reasonable time. Practical examples are given to show the usefulness of the proposed approach in the design of practical heat exchangers.