Hydrodynamics and thermal analysis of a mixed electromagnetohydrodynamic- pressure driven flow for Phan-Thien-Tanner fluids in a microchannel

An analytical study of the flow and temperature fields of a viscoelastic fluid in a rectangular microchannel under the simultaneous influence of electroosmotic (EO), magnetohydrodynamic (MHD) and pressure driven forces (PD) is presented. The non-Newtonian fluid obeys the constitutive relation based on the simplified Phan-Thien-Tanner model (sPTT). The analysis is primarily motivated by the need for increasing the volumetric flow rate in a microchannel by attenuating the inevitable Joule heating effect in electrokinetic flows. The governing equations are presented in dimensionless form containing six dimensionless parameters that control the flow and temperature fields: a parameter representing the viscoelasticity of the fluid, εDe _κ, the ratio of the pressure to electroosmotic forces, Γ, the ratio of magnetic to electroosmotic forces, ΩHa², the ratio of the thermal resistances, Λ, the ratio of the applied electric fields, γ, and the ratio of the thickness to the length of the microchannel, β₁. We report the conditions under which it is possible to take advantage on the simultaneous application of EO, MHD and PD forces. In addition, we determine the conditions that must be met to prevent the lateral flow when EO and MHD forces are considered simultaneously [1,2]. The volumetric flow rate is observed to increase in about 40% and the maximum temperature diminishes when MHD and EO forces are present in comparison with the case of a purely EO flow.