Present day heat exchangers might not effectively exchange heat with hot or cold fluid flowing through a constrained operational space, such as an annulus. For maximum heat recovery in gas turbine engines, a heat exchanger needs to be placed immediately after the exhaust turbine in the annulus of engine's exhaust system. In case of heat recovery in the family of shaft-powered aircraft engines, any additional component to the aircraft needs to be compact and should weigh less. An innovative design of a compact heat exchanger is presented in this paper. This heat exchanger is specifically designed to be used in applications (including gas turbine engines), where the hot or cold fluid (which act as a heat source or sink relative to the working fluid flowing through the heat exchanger), flows through an annulus. This paper, at a conceptual design phase, presents the construction, orientation for best efficiencies, solution to manufacture the complex geometry of the heat exchanger, and the materials that can be used in its fabrication.