Second law analysis for a mixed electro-osmotic and pressure driven flow of a viscoelastic fluid in a micro-channel

In this work the entropy generation rate in a parallel flat plate micro-channel under mixed electro-osmotic and pressure driven flow with a non-Newtonian fluid is analyzed. A fully developed flow is considered and the fluid obeys a constitutive relation based in a simplified Phan-Thien-Tanner model. The temperature distributions of a conjugate heat transfer problem in the micro-channel were solved asymptotically in steady-state, then, expressions for dimensionless local and average entropy generation rate are obtained. The aim of this paper is to show the influence of dimensionless parameters involved on the entropy generation rate : The viscoelastic parameter, the ratio of pressure forces to electro-osmotic forces, the Ṕeclet number, the normalized power generation term, the dimensionless temperature difference, the ratio of micro-channel thickness to length, the ratio of micro-channel wall thickness to length and the conjugation parameter; this set of parameters controls directly the thermal performance of this micro-channel. We can predict that the entropy generation rate is basically dominated by the Joule heating effect.