In this study, a new topology optimization method is developed to design heat-dissipating structure with forced convection. To cool down electrical devices or mechanical machines, two types of convection models have been widely used: the natural convection model with a large Archimedes number and the forced convection with a small Archimedes number. In these days, lots of engineering application areas such as electrochemical conversion devices (Fuel cell) or rocket propulsion engines adopt the forced convection to dissipate the generated heat. Therefore, to our knowledge, it becomes an important issue to design flow channels inside which the generated heat dissipate. Thus, this paper studies optimal topological designs considering fluid-heat interactions. To consider the effect of the advection in the heat transfer problem, the incompressible Navier-stokes equation is solved. This paper numerically studies the coupling phenomena and presents optimal channel design considering forced convection.