Numerical simulation was conducted on the heat transfer process in a two-dimensional flow field imposed by a sinusoidal oscillation of fluid. When gravitational force was ignored, the heat transfer at the wall was similar to a forced- flow turbulent heat transfer. On the other hand, under gravity, two modes of mixed convection heat transfer were observed depending on the thermal boundary conditions. For high-viscosity fluids, the bifurcation of the flow pattern appeared, which was mainly determined by the oscillation amplitude.