Forced convection in electro-osmotic/Poiseuille micro-channel flows of viscoelastic fluids: fully developed flow with imposed wall heat flux

Abstract

The analytical solution for heat transfer in a dynamic and thermally fully developed channel flow of the simplified Phan-Thien-Tanner fluid induced by combined electro-osmosis and pressure gradient was obtained assuming that material properties are independent of temperature. The flow forcing was quantified by an appropriate dimensionless parameter and its effect and that of all other relevant dimensionless numbers is presented and discussed. Specifically, the forced convection occurs under conditions of constant wall heat flux and the solution includes the effects of Weissenberg number, electric double layer (EDL) thickness, forcing ratio parameter, viscous dissipation as well as of Joule heating due to the electric currents and was obtained under the simplifying Debye-Huckel approximation. Generally speaking, the Joule effect is stronger than the viscous dissipation except in very narrow channels, but these fall outside the validity of the Debye-Huckel conditions. For pure electro-osmosis, viscous dissipation is restricted to the near-wall region and virtually nonexistent elsewhere, so it is irrelevant for thin electric double layers and Joule heating is more relevant. As the EDL thickens and/or the pressure gradient contribution increases, the role of viscous dissipation grows and shear-thinning effects also appear more clearly on the Nusselt number. Generally speaking, an increase in internal heating results in lower Nusselt numbers and this effect is stronger than the effect of shear-thinning, which is responsible for a slight increase in the Nusselt number.