The heat exchange between hot brine (4 wt% NaCl) and cold water as well as between condensing steam and cold water without direct fluid-fluid contact using modules made out of solid polymeric hollow fibers of polypropylene (PP) and polyetheretherketone (PEEK) has been studied. The solid hollow fiber dimensions were 425μm/575μm (ID/OD) for PP and 420μm/570μm (ID/OD) for PEEK. Extensive heat transfer measurements have been performed and the experimentally-determined overall heat transfer coefficients utilized to isolate the wall heat transfer coefficient, the inside heat transfer coefficient and the outside heat transfer coefficient. The heat exchange between hot brine and cold water was evaluated at hot brine temperatures between 82 °C and 99 °C and cold water temperatures between 5 °C and 41 °C. The tube-side Reynolds Number was varied in the range of 58-2464 and 3-160, respectively for the hot brine-cold water and condensing steam-cold water systems. The maximum U (overall heat transfer coefficient based on the inside area) values attained in the hot brine-cold water system for PEEK and PP-based modules were 1914 W/m²-K and 2076 W/m²-K respectively. The maximum U value attained in the two-phase heat exchange system was 1700 W/m²-K. Overall, the PP-based module HEPP2 showed the highest conductance per unit volume (CUV) value (2.92x10⁶ W/m³-K). The highest CUV value achieved was approximately 19 times higher than what can be achieved in conventional metallic shell and tube heat exchangers. The results for hot brine-cold water heat exchange demonstrated thermal efficiencies very close to 97% and up to four transfer units for devices having height of transfer unit (HTU) values as low as 5 cm. Those results were attained under conditions of lower tube-side Reynolds numbers.