Entropy Generation Analysis of Electro-Osmotic Flow for a Power-Law Fluid in a Microchannel

Abstract

In this work the entropy generation in a parallel flat plate microchannel under a purely electro-osmotic flow with a non-Newtonian fluid is analyzed. We considering a fully-developed flow in the velocity profiles; the fluid obeys a constitutive relation based in a power-law model. The temperature fields were obtained by the steady-state analysis of a conjugate heat transfer problem in the fluid and solid walls; the governing energy equation was solved firstly using the numerical successive-over-relaxation method with central finite differences scheme and then an asymptotic solution was introduced to validate the numerical process. Analytical expressions for dimensionless local and global entropy are obtained. The goal of this paper is show the influence of dimensionless parameters involved in the analysis on the temperature profiles, entropy distributions and the Bejan number. The dimensionless parameters are: a flow behavior index, to describe the power-law fluid behavior; an electrokinetic parameter, to indicate the thickness of the Debye length; the Peclet number, as indicator of heat transfer convection; a normalized power generation term, being the ratio of heat flux from the external wall to the Joule heating; a conjugation term, which represents the competition between the longitudinal conductive heat in the microchannel wall to the convective heat transfer in the fluid; a characteristic temperature difference and finally the aspect ratios of the microchannel system, respectively. Additionally is observed the excellent agreement between the numerical and asymptotic solution to the Nusselt number for different conditions in the conjugated heat transfer process.