Analytical study of two-layered mixed electro-osmotic and pressure-driven flow and heat transfer in a microchannel with hydrodynamic slippage and asymmetric wall heating

We investigate the fluid flow and heat transfer characteristics for a combined electro-osmotic and pressure-driven flow of two immiscible fluids through a straight planar microchannel considering the interfacial wall slip and slip-dependent zeta potential with asymmetric wall heating. Closed-form expressions are derived for the electrical potential distribution induced in the electrical double layer (EDL), velocity, temperature, and Nusselt number of both the layers after analytically solving the Poisson–Boltzmann equation, the mass, momentum, and energy conservation equations along with suitable boundary conditions for a steady incompressible hydrodynamically and thermally fully developed flow. The results for both the layers are presented for a broad range of parameters, such as dielectric constant ratio, pressure gradient, interfacial zeta potential difference, Debye–Hückel parameter, slip length, Joule heating parameter, Brinkman number, and heat flux ratio. The flow velocity is found to attain a higher value after considering the slip effect on zeta potential for all the parameters and for both fluids, and the enhancement in the velocity is more for thinner EDL. The heat transfer characteristics for the two layers are different, where the absolute value of the Nusselt number with the slip effect on zeta potential is always higher than that for the no-slip case for the bottom layer. Contrarily, the absolute value of the Nusselt number shows an opposite trend for the upper layer. Critical values of Brinkman numbers are obtained for the bottom layer beyond which the Nusselt number is higher for thicker EDL.