An annular design heat exchanger is formed from an arrangement of wedge-shaped stacks of wafers. Each wafer includes sheets of material separated by peripheral and supporting walls that define interior flow channels through which a first fluid can flow. Holes in the sheets provide inlets and outlets to the channels, and walls surrounding the holes mate with neighboring wafers in the stack, forming integral inlet and outlet manifolds, while ensuring uniform spacing between the wafers. A second fluid can flow around the manifolds and through the spaces between the wafers in a counterflow pattern. In the annular assembly, the manifolds are oriented substantially axially, and the flow channels are oriented substantially radially. The heat exchanger can be formed from a ceramic material, and can be incorporated into an engine assembly or a heat-recirculating combustor.