In this paper microwave heating a liquid rotated and stirred by paddle wings is investigated numerically. In order to feed electromagnetic energy into this rotating system directly, we proposed to use the rotating metal shaft as a coaxial antenna. A set of multiphysics equations representing this system was solved by using finite-element method. In the actual computation, commercial software, COMSOL Multiphysics, was utilized. This software enables us to simultaneously solve frequency domain Maxwell equations and time-dependent Navier-Stokes and heat-transfer equations. The flow and temperature fields were extensively visualized as a result of this investigation.