Abstract
The problem of entropy generation due to heat transfer in an electro-osmotic flow with circular type area section micro-channels for small values of electro-kinetic parameterΞΊΞ±(whereΞΊis the Debye length andais the radius of the micro-channel) is investigated analytically. The momentum and energy conservation equations in cylindrical coordinates for an electro-osmotic flow are derived in non-dimensional form. The momentum equation is solved and velocity distribution in terms of modified Bessel function of the first kind is obtained. An approximation is used for the Bessel function of first kind. Considering the approximate velocity profile, the energy equation including viscous dissipation effects is solved to obtain the temperature distribution in terms of parametric values of the electro-kinetic parameter and the Brinkman number. A uniform surface heat flux boundary condition is considered. The importance of this investigation is development of an engineering simple method of design for electro-osmotic circular micro-electronic cooling systems and possible optimizations of these kinds of flows with respect to the second-law of thermodynamics through the micro-coolers.
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