Analytical closed-form solution for fluid flow through microchannel heat sinks including axial conduction

Abstract

An analytical study on the convective heat transfer through a rectangular microchannel heat sink including solid axial conduction, has been performed. The system has been split into two coupled boundary value problems, each addressing the heat transfer to the fluid through different routes (namely, the sidewall or fin and the base wall or substrate). The results are derived in the form of a net wall and fluid temperature rise. The validation of the proposed analytical model has been done using existing experimental data and a three-dimensional conjugate computational model. The results show excellent agreement in terms of solid and fluid temperature distributions. The parametric studies show an increasingly non-linear behaviour in the solid and fluid temperature profiles in the microchannel, if axial conduction is dominant. The simulated results are consistent with the CFD and experimental outcome. It has also been noted that a uniform heat flux applied at the bottom of the microchannel (substrate) cannot ensure the transfer of heat uniformly to the fluid. If axial conduction is high, a significant fraction of the applied heat influx is transmitted to the fluid near the channel entry region with a corresponding reduction in the flux distribution at the channel exit.