The rate of heat transfer into highly viscous fluids can be enhanced significantly by chaotic advection in both batch and continuous processes where the flow is dominated by viscous forces. In batch operations, such as liquid flow between concentric, rotating cylinders, the heat transfer rate is first increased by a geometry modification which creates a vortex zone. This is achieved simply by moving the inner cylinder into an eccentric position, thus separating the flow into two or more independent zones. Afterwards, by varying time-periodically the angular velocity of one boundary, while the other one moves at constant velocity, fluid can be transported from one flow zone into another. This is the mechanism of chaotic advection and leads to a further rise in the heat transfer rate if the modulation is appropriately selected. In three-dimensional open flows created by superposing an axial flow onto the cross-sectional batch flow, the heat transfer rate can also be enhanced by a suitable modulation of the boundary motion. A method of analysis for these flows and a way to determine the most suitable operating conditions are given here. It is shown that in both batch and continuous processes there is an optimum frequency of the sinusoidal modulation of the boundary for which the heat transfer rate and the mixing of a passive scalar are a maximum.