Joule heating, viscous dissipation and convective heat transfer of pressure-driven flow in a microchannel with surface charge-dependent slip

The present work develops closed form expressions of Joule heating, viscous dissipation and Nusselt number for steady, laminar, hydrodynamically and thermally fully developed pressure-driven flow (PDF) in a microchannel considering the combined effect of surface charge-induced electric double layer (EDL) and surface charge-dependent slip. On basis of these, the effects of zeta potential in a large range limited by the steric effect of free ions to valid the nonlinear Poisson-Boltzmann equation, surface charge-dependent slip, ionic concentration of the electrolyte and the microchannel height on the Joule heating, viscous dissipation and Nusselt number of the PDF are analyzed. The results reveal that the electric field strength generated from the motion of the net free charges within the EDL moving with the PDF shows a valley trend with the continually increasing absolute value of zeta potential, and it is a key factor to affect the thermal performances of the PDF. Both the Joule heating and viscous dissipation of the PDF show a non-monotonic variation with the continually increasing zeta potential because of the non-monotonic electric field strength. Additionally, the zeta potential can lead to the reduction of Nusselt number by reducing the velocity of PDF. However, when the magnitude of zeta potential increases to a high value, the Nusselt number shows a non-monotonic variation because of the non-monotonic velocity field of the PDF arising from the non-monotonic electric field strength. Furthermore, slip, ionic concentration and microchannel height can also significantly affect the Joule heating, viscous dissipation and the Nusselt number of the PDF in different manners. The underlying mechanisms of the corresponding results are analyzed. The subject of the paper is the theoretical results and the corresponding analysis.