This work analyzes the non-isothermal electro-osmotic fluid flow in a microchannel considering the Soret effect and temperature-dependent properties. The constitutive equation that models the fluid rheology corresponds to the generalized Phan-Thien–Tanner (gPTT) model. Temperature and pressure gradients are induced due to the interaction between an ionized fluid and the electrical field imposed at the microchannel's ends, resulting in Joule heating. The temperature-dependent physical properties of the fluid modify the ionic distribution in the electric double layer and its thickness change along the microchannel walls. The generalized Phan-Thien–Tanner (gPTT) model is used as a constitutive equation that describes the fluid rheology, where the trace-stress tensor is based on the Mittag–Leffler function, which represents the destruction of physical junctions and entanglements in the Lodge–Yamamoto network of viscoelastic fluids, through the inclusion of two fitting parameters: α and β. The gPTT model allows better fitting and flexibility to experimental data and a wider range of variation in the description of rheological responses of complex fluids. The hydrodynamics and thermodiffusion obtained through the gPTT model are compared against that using the linear form of the Phan-Thien–Tanner model (lPTT).

The influence of the temperature-dependent viscosity on the electroosmotic flow through a porous medium in a microchannel of parallel flat plates. At the end, an imposed electric field induces Joule heating and temperature gradients, modifying the viscosity of the fluid. The Phan-Thien–Tanner and Darcy–Forchheimer models describe the viscoelastic fluid through the porous media. Consequently, the electric double layer (EDL) overlaps at the center plane of the microchannel, causing an electrically charged porous matrix and modifying the zeta potential along the microchannel walls. Therefore, we define a zeta potential ratio of the porous matrix and that at the microchannel walls. Unlike similar investigations, the boundary condition for the zeta potential varies locally due to the temperature field, modifying the interaction among hydrodynamics, electrical, viscoelastic, thermal and porosity effects. A modified Péclet number is defined as a function of the porosity and thermal conductivity of the fluid and an effective charge density is determined based on the Poisson–Boltzmann equation, accounting for the pore size and the zeta potential ratio. The set of equations are solved numerically considering the lubrication approximation theory. We found that the influence of the temperature-dependent viscosity increases the shear stresses at the EDL region, particularly where the temperature rises to maximum values. Also, the overlapping of the EDL occurs mainly for low values of permeability. Finally, the pressure gradient involved in the Darcy law can be altered through the zeta potential ratio.

The operation of an inverted pendulum and its respective type of control are affected by the change of the values of its internal parameters. Changes with high uncertainty result in responses with undesirable outputs. In this work, a comparison is presented for the control of an inverted pendulum to determine the operation and characteristics of three types of control systems: Neuro-Fuzzy Control (NFC), Indirect Adaptive Control (IAC) and a Proportional Integral Derivative control (PID). The study considers several indices such as stabilization time, rise time, mean square error, overshoots, convergence, computational load, error, mathematical requirements, and performance indices for control systems. To demonstrate its operation, the controls are implemented in hardware, one for the NFC and another for the IAC under an Arduino UNO platform. The results indicate that the NFC and IAC controls do not generate a transient or impulse response, only a small delay and the rise and stabilization time are minimal. While PID presents a transient response and overshoot, as well as a stabilization time to reach the steady state response.