Electroosmotic flow in a thin microchannel when the slippage condition and the viscosity of the electrolytic solution depend on the temperature

Based on a perturbative scheme, we treat in the present work, a non-isothermal electroosmotic pattern flow in a rectangular microchannel. For this purpose, we consider that a non-uniform slip regime prevails, controlling simultaneously the main characteristics of the velocity field induced externally by a uniform electric field. Taking into account the proper limitations of the asymptotic analysis, we add full numerical solutions of the governing equations, which basically are composed of the continuity, momentum, and energy equations for the electrolyte flow, and the related with the electrical phenomenon: the equation of Poisson-Boltzmann. A direct comparison between both asymptotic and numerical solutions shows favorable results for those particular cases when the viscosity of the fluid and the slip condition depend on the temperature. The impact of the temperature is readily appreciated through the well-known Joule heating effect, which is yielded by the external electric field on the electrolyte solution. Due to that, the previous effect heats the electrolyte solution in the entire domain, and to avoid overheating for the electroosmotic flow, we impose on the boundaries of the microchannel, a cooling convective condition. Therefore, the full set of the dimensionless equations depends on several parameters that determine between them the different scenarios for the induced volumetric flow rate. In addition, we complete the results by adding the corresponding velocity, pressure, and temperature fields. The results show clearly that the variable effect of slippage favors notably the increment of the volumetric flow rate.