The effect of substrate conduction on boiling data on pin-fin heat sinks

Heat-transfer experiments for a copper heat sink containing pin-fins with a cross section of 1 mm by 1 mm and a height of 1 mm have been reported previously. The pin-fins were manufactured on a 5 mm thick, 50 mm square base plate in a square, in-line arrangement with a pitch of 2 mm. Data were produced while boiling R113 and water at atmospheric pressure. The heat sink was heated from below through a 5 mm thick aluminium wall by an electrical heating method that is normally associated with the uniform heat flux boundary condition. However, variations in the heat-transfer coefficient and the liquid subcooling interacted with the high thermal conductivity of the aluminium and copper materials to produce a near isothermal wall boundary condition. Thus, heat conduction effects had to be taken into account when determining the heat-flux distribution required in the analysis of the data. Many experiments like these have used the uniform heat-flux assumption to analyse the data. The discrepancies produced from this approach are explored. Single-phase flows across a pin-fin surface produce a reasonably uniform distribution of heat-transfer coefficient. However, the liquid temperature increases as it moves across the heat sink. This produces a non-uniform heat flux distribution at the solid-fluid interface. The uniform heat-flux assumption is shown to lead to errors of +/- 17% in the estimation of the heat-transfer coefficient. The original boiling flow experiments found that the water data were confined and that the majority of the R113 data were not. The confined and unconfined data are processed with the thermal conduction in the walls taken into account and by assuming a uniform heat flux at the solid fluid interface. The uniform heat-flux distribution analysis for unconfined flows shows errors in the heat-transfer coefficient to be typically +/- 17%. Confined flows produce smaller errors, typically +/- 12%, close to the onset of nucleation. However, these damp out as the distance from the onset increases. The effect of test-section design is investigated by repeating the analyses with smaller wall thickness and lower wall thermal conductivities. Lower wall thermal conductivity is shown to produce a uniform heat flux distribution at the expense of reduced extended surface effectiveness. Thinner substrate thicknesses are found to give limited improvements. These analyses demonstrate that an applied uniform heat flux to the heat sink base will not result in a uniform heat flux at the solid liquid interface. (C) 2014 Elsevier Ltd. All rights reserved.