The Phase-III Outboard Pump Limiter is a heat sink made of pyrolytic graphite armor brazed to water-cooled copper tubes. Around the inner wall of the tube wall, some of the water can be in the subcooled boiling regime. The central issue analyzed here is how the heat flow in the tube changes when the thermal resistance along the heated portion of the tube is redistributed. Cracks or braze flaws in the joint between the tile and tube cause this redistribution. Severe cracks or flaws reduce the power-handling capability of this assembly because the local peak heat fluxes increase and, for a given critical heat flux (CHF), the safety margin decreases. There were some surprises. The increase in local peak heat flux for the most common type of flaw encountered in the fabrication of this limiter was negligible up to a flaw size of ∼50%. The examples presented are intended as a case study that illuminates the more general problem of how correlations for heat transfer and for CHF developed for uniform circumferential heating are applied to a case of one-sided heating.