First law analysis for viscous dissipation in liquid flows in micro-channels

This paper focuses on temperature rise due to the viscous dissipation in liquids flowing through micro-channels. In the past, equations for the prediction of the temperature rise have been obtained as a function of the friction factor, Reynolds number and Eckert number or a similar form, starting from Navier–Stokes equation and energy equation under the assumption of fully developed laminar flow by researchers. The temperature rises calculated from the equations have been compared with experimental data and the equations have been validated. However, in this paper, a new equation for the prediction of the temperature rise is simply obtained from the first law of thermodynamics without restriction of fully developed laminar flow.