An improved method to manage the flow of heat in an active regenerator in magnetocaloric or an electrocaloric heat-pump refrigeration system, in which heat exchange fluid moves synchronously with the motion of a magnetic or electric field. Only a portion of the length of the active regenerator bed is introduced to or removed from the field at one time, and the heat exchange fluid flows from the cold side toward the hot side while the magnetic or electric field moves along the active regenerator bed.
 This invention was made in part with US Government support under Small Business Innovative Research (SBIR) Department of Energy Contract No. DE-FG02-07ER84943. The Government has certain rights in the invention.