Effects of flow slip and temperature jump on heat transfer in a ribbed microfluidic channel using lattice Boltzmann method

Abstract

As the dimension of electronic devices approaches micrometers, the slip velocities and temperature jumps may play a pivotal role in their thermofluidic performance. Some studies report that the thermal performance increases with Knudsen number (Kn) while others show the opposite observations. The rationale for the discrepancy has not been clarified. In this study, a thermal lattice Boltzmann method is developed to study the effects of flow slips and temperature jumps on heat transfer in a ribbed microfluidic channel filled with air. Varied parameters are respectively the rib height ($H_r^{\ast }$), pitch ratio (PR), Kn, and Reynolds number (Re). It is observed for the first time that there exists a critical $H_r^{\ast }$ = 0.35 beyond which $\overline{Nu}/{Nu}_0$ decreases with increasing PR below which $\overline{Nu}/{Nu}_0$ rises with increasing PR because of the combined effect of interfacial thermal resistance caused by temperature jumps on the wall and disturbed thermal boundary due to the ribs. For a fixed rib height (${H_r}^{\ast }$ = 0.25), the heat transfer enhancement ($\overline{Nu}/{Nu}_o$) is observed to increase with increasing PR and Re and decrease with increasing Kn. In contrast, the pressure loss ($\bar{f}/f_o$) is found to decrease with increasing PR and Kn and increase with increasing Re. In addition, for the convenience of engineering application, the empirical correlations of $\overline{Nu}/{Nu}_o$ and $\bar{f}/f_o$ versus PR, Kn and Re are proposed.