In this study, we focused on the convective heat transfer for water flowing in a small diameter tube. Quasi-steady state and transient heat transfers were measured in vertical small tube with exponentially increasing heat inputs.The heat generation rate was raised through an exponential function. The flow velocities,the inlet liquid temperatures and the inlet pressure were ranging from 2.3 to 24.1 m/s, 285 to 350 K, and 180 to 1262 kPa.The effects of various parameters such as flow velocity, inner diameter of the tube, and e-folding time of heat generation rate were investigated, and the relations between convective heat transfer and these parameters were clarified. It was obtained that the heat transfer coefficient increased with the decreasing of inner diameter of tube.The heat transfer coefficient also increased with decreasing of the e-folding time of the heat generation rate when the e-folding time is smaller than about 1 second. The heat transfer coefficient also increased with an increase in flow velocity.Moreover, the Nusselt number under the quasi-steady state was affected by the Reynolds number and the non-dimensional diameter of tube.