This paper deals with density-based topology optimization considering fluid and thermal interactions, in which the Navier-Stokes and heat transport equations are coupled. We particularly focus on designing heat exchangers. In the engineering context, heat exchangers are designed while considering a certain amount of input power. Therefore it is important to maximize the performance of a heat exchanger under a constant input power. In this paper we propose a way to control the input power by introducing an extra integral equation. To be more precise, in the fluid analysis, the inlet pressure is determined by solving the extra integral equation together with the Navier-Stokes equation. By doing this we can keep the inlet power constant even when the flow channels are changed in the optimization process. Consequently, the system of equations of the fluid field takes an integrodifferential form. On the other hand, in the heat transport analysis, a single governing equation is defined for simultaneously modeling both the solid and fluid parts. The design variable is a fluid fraction whose distribution represents the topology of the solid and fluid domains. When designing heat exchangers, two different heat conditions are considered in the formulation of the optimization problems, namely temperature-dependent and temperature-independent heat sources. Through the numerical examples for designing flow channels in a heat exchanger, it is shown that distinct topologies can be obtained according to the input power and the heat source conditions. © 2013 Springer-Verlag Berlin Heidelberg.