Analysis of Conjugate Heat Trasfer Problem in a Microchannel for a Mixed Electro-Osmotic/Pressure Driven Flow of a Fluid with a Reological Power Law Model

Abstract

In this work we solve numerically the conjugated heat transfer problem in steady state of a non-Newtonian fluid and solid walls in a microchannel under the influence of pressure and electroosmotic forces. The velocity field is determined taking into account a hydrodynamically fullydeveloped flow and a constitutive relation based in a rheological power law model. The numerical process results in: velocity profiles of the flow and in the solid-fluid temperature distributions. It is shown the influence of nondimensional parameters involved in the analysis on the conjugated heat transfer problem: the Peclet number, a normalized power generation term being the ratio of heat flow from the external wall to the Joule heating, a conjugation term which determines the basic heat transfer regimes between fluid and solid sections in the microchannel. For the flow field: an indicator of non Newtonian behavior, an electrokinetic parameter and a ratio of pressure forces to the electroosmotic forces, the last acts on the flow as a drag reducer and drag increaser under favorable and adverse pressure gradients, respectively. An asymptotic solution was introduced to validate the numerical process.