**Background:** It is well known that the counter-flow scheme is more efficient than the direct-flow scheme of heat carrier motion. Earlier, by using the developed model of multi-current heat exchange, we analyzed heat carrier motion schemes in the three-stream heat exchanger. It is now urgent to determine the effective structures of heat carrier flows for heat exchangers with three or more heat carriers for various industrial technologies.

**Materials and methods:** The model for multi-current heat exchangers was built based on the system of differential equations representing heat balance equations for each heat carrier. The analytical solution to the system of linear differential equations was found using the method of trial functions.

**Results:** We propose a mathematical description of heat exchangers with four heat carriers with different flow structures. It represents a system of linear differential equations. We have obtained and analyzed the analytical solutions to eight possible schemes of heat carrier motion, and found the most effective flow structure with the minimum heat loss.

**Conclusions: **The proposed mathematical model is the basis for developing more effective methods of heat transfer organization in technological units for various purposes with an arbitrary number of heat carriers.

**Key words: **heat transfer, heat carrier flow, direct-flow, counter-flow, multi-current heat exchanger, heat loss, flow structure.