Heat exchanger design optimization of size, weight and cost usually requires that at least one, and sometimes both surfaces of the wall separating the two heat exchange fluids, be extended in area. This objective is easily accomplished by raising fins on the outside surfaces of tubes. When it is necessary to increase (or extend) the inside surface of a tube, without unacceptable interference with the fluid flow, the problem is compounded. The commercially available tubes with extended inner surfaces are of limited utility and designers usually opt to use a large number of small, smooth-bore tubes. These designs are costly and easily damaged. This research proposes to develop the design of a new heat transfer matrix which will have extended surfaces without the problems associated with the currently available materials. The new matrix is particularly well suited for encapsulation in tubes, but is also useful in other void volumes