Analysis of streamwise conduction in forced convection of microchannels using fin approach

The effects induced by streamwise conduction on the thermal characteristics of forced convection for single-phase liquid flow in rectangular microchannel heat sinks under imposed constant wall temperature have been studied. By employing the fin approach in the first law of analysis, models with and without streamwise conduction term in the energy equation were developed for hydrodynamically and thermally fully-developed flow under local thermal non-equilibrium for the solid and fluid phases. These two models were solved to obtain closed form analytical solutions for the fluid and solid temperature distributions and the analysis emphasized details of the variations induced by the streamwise conduction on the fluid temperature distributions. The effects of the Peclet number, aspect ratio, and thermal conductivity ratio on the thermal characteristics of forced convection in microchannel heat sinks were analyzed and discussed. This study reveals the conditions under which the effect of streamwise conduction is significant and should not be neglected in the forced convective heat transfer analysis of microchannel heat sinks.