Phase change material modules for use in a heat exchanger are described. The phase change material module comprises two or more set of a plurality of substantially aligned hollow structures arranged to form a porous structure. A phase change material capable of undergoing a phase change as a result of heat exchange between it and a fluid is housed within the hollow tubes. Also described is a phase change material module with hollow tubes having a cross-sectional area through the phase change material selected from elliptical, rectangular, stadium-shaped, teardrop-shaped, airfoil-shaped, rounded rectangle and ovoid. A heat exchanger comprising a plurality of the phase change material modules, a first fluid inlet and outlet, and a second fluid inlet and outlet, wherein the phase change material modules are repeated circulated from alignment with the first fluid inlet and the second fluid inlet is also described.