First and second law analysis of fully developed gaseous slip flow in trapezoidal silicon microchannels considering viscous dissipation effect

Fully developed gaseous slip flow in trapezoidal silicon microchannels is studied. Friction factor, Nusselt number and entropy generation in the microchannel is obtained, effect of rarefaction, aspect ratio and viscous dissipation is explored and, the range of Brinkman number in which viscous dissipation effect is important and cannot be neglected is specified. The continuum approach with the velocity slip and temperature jump condition at the solid walls is applied to develop the mathematical model of problem in the trapezoidal microchannel. Transformation of trapezoidal geometry to a square provided ease of application of finite difference method in solution of the mathematical model. The effect of viscous dissipation is quantified by Brinkman number. The calculated Brinkman number for common engineering applications even with limiting operational and geometric conditions is found less than 0.005. It is observed that viscous effect for applications with Brinkman number less than 0.005 can be neglected. The region in which viscous dissipation effect cannot be neglected is specified as Br > 0.005. Decreasing effect of rarefaction and increasing effect of Brinkman number on irreversibility due to all sources, excluded axial conduction, is established. The dominant source of irreversibility in total irreversibility is specified as a function of Brinkman number.