A combustor-heat exchanger system comprising a plurality of cans. Each can includes an inner cylinder and an outer cylinder forming an annular space in between, wherein the inner cylinder is configured to receive and combust a fuel and compressed oxidant to generate heat and a hot gas. The outer cylinder is configured to receive a portion of a gas lean in carbon dioxide from a turbine system and utilize the heat from the inner cylinder to generate a heated gas. The combustor-heat exchanger further includes an inlet volute along the surface of the inner cylinder configured to receive the portion of the gas lean in carbon dioxide and distribute the gas lean in carbon dioxide into an axial flow through the annular space of each can. The combustor-heat exchanger also includes an outlet volute along the surface of the outer cylinder configured to receive the heated gas from each can, a first manifold to distribute the gas lean in carbon dioxide stream into each inlet volute and a second manifold to receive the heated gas from each can and generate a hot discharge stream.