Viscous dissipation effect in trapezoidal microchannels at constant heat flux

Abstract

Present paper is dealt with the steady state, laminar and hydrodynamically and thermally developed flow in a trapezoidal channel under H2 boundary condition is investigated. Slip flow, temperature jump and viscous dissipation effects are considered. Firstly, Navier-Stokes equations are transformed from physical plane to square domain, and then solved using finite difference method. Also, it is possible to obtain fluid flow and heat transfer characteristics for a rectangular microchannel with this method. The effects of aspect ratio, rarefaction, base angle and viscous heating on Nusselt number are discussed. The results of the numerical method are verified with the conventional theory of macrochannels (i.e. Kn=0, Br=0). Also, the friction factors and the Nusselt numbers for Br=0, Kn≠0 are in a good agreement with the available results of flow and heat transfer of rectangular microchannels in the literature. The results showed that the increase in rarefaction reduces the Nusselt numbers in trapezoidal and rectangular microchannels. When the Kn number is fixed and the Br number is small, the microchannel with the higher aspect ratio has the greater Nu, but for higher Br numbers, the greater aspect ratio results in smaller Nu. Also, at the same rarefaction, when Br number is large, the difference between Nu number of different aspect ratios decreases.