In this research, the transient heat transfer due to exponentially increasing heat input was experimentally measured for upward water flowing in a vertical small tube. The heat generation rate was increased exponentially with a function of Qoexp (t/τ), where, Qo is an initial heat generation rate, t represents time and τ is e-folding time. The heat generation rate was controlled by high speed computer system. The test tube was heated with exponentially increasing heat input by direct current. The average temperature of test tube was measured by resistance thermometry using a double bridge circuit. The experimental apparatus consists of a test section, a cooler, a heater, a pump, a tank and a pressurizer. The working fluid was distilled and deionized water. The inlet fluid temperature of test tube was controlled by the cooler and the heater. The system pressure was up to 800 kPa. The test tube was 0.7 mm in inner diameter and 12.0 mm in heated length respectively. The ratio of heated length to inner diameter was 17.1. The test tube was electrically isolated from experimental loop by Bakelite plates. The experimental data were compared with previous correlations of nucleate boiling. It was obtained that the experimented data agree well with full-developed flow boiling correlation by Rohsenow. Moreover, the transient critical heat flux (CHF) and nucleate boiling with onset of nucleate boiling (ONB) values increased with the increase in flow velocity. The transient CHFs and ONBs increased with a decrease in e-folding time at τ < 1 s, and they approached steady-state value at τ > 1 s. It was understood that the heat transfer is in steady-state at τ > 1 s, and it is in transient state at τ < 1 s.