A steady state, one dimensional, model for boiling two phase flow in triangular micro-channel

The potential advantages of triangular micro-channels incorporated into heat generating small devices are discussed. A simple one dimensional model of boiling two-phase flow and heat transfer in a single triangular micro-channel is investigated. The flow of the liquid phase inside the micro-channels is driven by surface tension and friction forces that exist at the interface between the fast moving vapor and liquid. The flow of the vapor phase is controlled by the heat flux generated and removed from the device. As the liquid flows through the channel it evaporates, its cross-section diminishes and the radius of curvature at the liquid vapor interface decreases. Thus, according to Young–Laplace equation, the liquid–vapor pressure difference increases along the channel. Consequently, a large decrease in the liquid pressure along the channel is obtained if the vapor pressure remains almost uniform. That pressure drop in the liquid phase is responsible for the onset of liquid flow. Along the micro-channel the increasing amount of generated vapor causes vapor velocity to increase and friction forces exerted on the liquid phase become significant until dry-out occurs. Since in the dry-out zone the heat transfer is drastically diminished, dry-out length estimates are of major concern in micro-channel design. A solution of a first order non-linear differentiated equation is required to predict dry-out lengths and their dependence on the dimensionless parameters governing the flow. A numerical simulation was carried out for the case of water flowing in a vertical channel of equilateral triangular cross-section. Hydraulic diameters from 0.1 to 1 mm, heat fluxes from 10 to 600 W/cm2 and contact angles of 5° to 40° were assumed. The results validate the basic assumption that vapor pressure along the micro-channel is almost uniform. In many practical applications the differential equation can be simplified and solved analytically and the dry-out length are determined via a solution of an algebraic equation. Finally, it was demonstrated that the dry-out lengths seem to fit the dimensions of microelectronic devices.