Role of the thermal entrance length on the viscous heating in microchannels

Abstract

The present work is devoted to experimental investigations on the viscous heating associated with fluid flows in microchannels with non-adiabatic walls. A very simple model is proposed that demonstrate the relative influence of the thermal entrance length $L^*$ on the temperature rise of a fluid flowing through a rectangular or trapezoidal microchannel. By resolving directly the 1D energy conservation equation, we get an explicit relation describing the evolution of the temperature along the direction of the flow. That model shows that the adiabatic solution is realistic especially when the length of the channel is much lower than $L^*$. It also demonstrates that when reducing the hydraulic diameter $D_h$, a steady-state thermal profile is reached and heat losses through the walls considerably limit the temperature rise. Experimental data have been recorded through hybrid silicon–Pyrex trapezoidal microchannels for a large range of hydraulic diameters (73 ≤ D _h  ≤ 353 μm) and aspect ratio $(0.05 \le \chi \le 0.5)$ with isopropanol and ethanol as the working fluids. The experimental data match the values expected from the model that can be useful to predict the order of magnitude of the longitudinal viscous heating in any configuration.