Rheological impact on thermofluidic transport characteristics of generalized Maxwell fluids through a soft nanopore

The time-dependent electroosmotic flow (EOF) and heat transfer characteristic of a generalized Maxwell fluid through the polyelectrolyte layer (PEL) grafted nanopore are investigated while considering different permittivity between the PEL and electrolyte solution. The ion partitioning effects arise due to the different permittivity among these regions. Taking the ion partitioning effects, the analytic solution for the induced potential is established within and outside the PEL from the modified Poisson–Boltzmann equation assuming the Debye–Hückel approximation for a low surface charge. The Cauchy momentum equation with a suitable constitutive equation for fractional Maxwell fluids is derived, and the corresponding analytic solution is presented to provide the axial fluid flow distribution in the full domain. The energy fluxes that have major contributions to the energy equation mainly depend on axial conduction, convection due to electrolyte transport, and Joule heating effects for the external electric field. The analytical solutions of the energy equation for hydro-dynamically fully developed flow with constant thermophysical properties are presented to provide the temperature distribution considering constant heat flux at the nanopore wall. The influence of several important factors for characterizing heat transfer behavior is investigated in the present study. The maximum fluid velocity occurs when the permittivity between the PEL and electrolyte region is the same. The increasing values of fluid velocity imply higher convective heat transfer and make the Nusselt number higher. This study makes a conscious effort toward highlighting the modality controlling the heat transfer characteristics for the ion partitioning effects.