A coupled electrical-thermal-fluid simulation technique is developed based on the finite element method. The coupled simulation, which integrates the full-wave electromagnetic, fluid, and transient conjugate heat transfer analyses into an iterative scheme, is devised for circuit designs with integrated micro channel cooling. The motion of fluid flow is decoupled from temperature under the assumption of incompressible and fully developed flows. The full-wave electromagnetic and the transient conjugate heat transfer analyses are coupled through temperature-dependent material properties. The efficiency of the coupled simulation is enhanced through several numerical techniques including an adaptive time stepping scheme, a domain decomposition scheme called the finite element tearing and interconnecting (FETI), and FETI-enabled parallel computing. The capability and the efficiency of the coupled simulation are demonstrated through a numerical example.