Evaporative heat transfer system. The system includes a substrate and a plurality of substantially parallel, spaced-apart ridges extending from the substrate forming vertical liquid manifolds therebetween. A nanoporous membrane is supported on the ridges and a pump delivers a dielectric fluid across the ridges. The fluid is drawn through the liquid manifolds via capillarity provided by the nanoporous membrane and evaporates to dissipate heat flux through the substrate. A preferred dielectric fluid is pentane. It is preferred that membrane porosity vary across the membrane to tailor thermal resistances to limit temperature rises.