Analytical solution to heat transfer for mixed electroosmotic and pressure-driven flow through a microchannel with slip-dependent zeta potential

Abstract

The use of hydrophobic surfaces in electrokinetic flows results in an intricate analysis due to the coupling of surface potential and interfacial slip which challenges their independent measurement. Thus, it becomes significant to consider the slip-dependent surface potential which can decouple the interfacial slip from the zeta potential. In this article, we develop an analytical model to investigate the heat transfer characteristics for combined electroosmotic and pressure-driven flow through a plane microchannel considering the slip-dependent zeta potential. We solve analytically the Poisson–Boltzmann (PB) equation, the mass, momentum and energy conservation equations for hydrodynamically and thermally fully developed flow with appropriate boundary conditions to obtain closed form expressions for the induced potential within the electrical double layer (EDL), the velocity and temperature profiles and the Nusselt number in terms of different physico-chemical parameters. The results reveal that interfacial slip-dependent surface potential has a strong influence on the thermal transport phenomenon along with other parameters, like Joule heating, applied pressure-gradient, electrokinetic parameter, slip length and viscous dissipation. The velocity in the core region is always under-predicted considering the slip-independent surface potential and the under-prediction is amplified for thinner EDL and pure electroosmotic flow. Beyond the critical values of the slip length, the consideration of the slip-independent surface potential in the paradigm of thermal transport dynamics for electrokinetic flows, over-predicts the Nusselt number and the over-prediction is amplified for thinner EDL. Moreover, a critical Brinkman number, Brk is also identified such that for Br < Brk, Nusselt number increases with Debye parameter, while the opposite effect is observed for Br > Brk. The relative enhancement in Nusselt number due to the interfacial slip increases with the applied pressure-gradient and slip length at smaller values of Brinkman number. Furthermore, the sensitivity of Nusselt number on slip is highly dependent on the Debye parameter, Brinkman number and applied pressure-gradient.