Heat Transfer and Fluid Dynamics Modeling in Shear-Driven Liquid Film Cooling System of Microelectronic Equipment

Analytical and numerical solutions were obtained for the problem of combined liquid film and gas flow in a flat channel with a local rectangular heat source located at the channel bottom. A linear approximation of the problem was derived, and an exact solution was obtained, which can be used to test numerical algorithms and codes. The solution is valid for small film surface deformations and small deformation curvatures. Numerical calculations were performed in the thin-layer approximation for the flow of FC-72 liquid and gaseous nitrogen. The model proposed takes into account convective heat transfer, the effect of liquid surface tension and the Marangoni effect, as well as the dependence of liquid viscosity on temperature. The influence of gas pressure and shear surface stress induced by the gas flow on the deformation intensity at the liquid-gas interface as well as the effect of heating on pressure variations in the gas flow and generated shear stress were studied. It has been established that, in contrast to the case of an infinite flow or a large channel height, for a direct gas and liquid flow in a microchannel, the influence of liquid film deformations on the pressure and velocity in the gas phase is significant.