Abstract

In this paper, we investigate analytically the first and the second law characteristics of fully developed gaseous slip flow with the H1 boundary condition through elliptical microchannels. The closed-form solution of temperature distribution was obtained with the separation of variables method. Expressions for the Nusselt number, the nondimensional entropy generation rate, and the Bejan number were further deduced. The influences of crucial factors, including viscous dissipation, rarefaction, aspect ratio, and fluid axial heat conduction, have been carefully evaluated. The results indicated that viscous dissipation has a dramatic impact on heat transfer characteristics. But the rarefaction effect was found to significantly reduce the effect of the viscous dissipation on the Nusselt number, and the former may not deteriorate the heat transfer performance when considering the viscous dissipation. The main source of the entropy generation rate is controlled by fluid axial heat conduction when the Peclet number is less than one. The impacts of the viscous dissipation, the rarefaction, and the aspect ratio on entropy generation are magnified when fluid axial conduction dominates the irreversibility. The analytical solutions of the current study will make it possible to compare, evaluate, and optimize alternative elliptical microchannel heat exchanger design options.

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