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

The potential advantages of triangular micro-channels incorporated into hea t generating small devices are discussed. A simple one dimensional model of boiling two-phase flow and heat transfer in a single triangular micro-chan nel is investigated. The flow of the liquid phase inside the micro-channels is driven by surface tension and friction forces that exist at the interfa ce 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 diminishe s 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 ons et of liquid flow. Along the micro-channel the increasing amount of generat ed vapor causes vapor velocity to increase and friction forces exerted on t he liquid phase become significant until dry-out occurs. Since in the dry-o ut zone the heat transfer is drastically diminished, dry-out length estimat es are of major concern in micro-channel design. A solution of a first orde r 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 ve rtical channel of equilateral triangular cross-section. Hydraulic diameters from 0.1 to 1 mm, heat fluxes from 10 to 600 W/cm(2) and contact angles of 5 degrees to 40 degrees were assumed. The results validate the basic assum ption that vapor pressure along the micro-channel is almost uniform. In man y practical applications the differential equation can be simplified and so lved analytically and the dry-out length are determined via a solution of a n algebraic equation. Finally, it was demonstrated that the dryout lengths seem to fit the dimensions of microelectronic devices. (C) 2000 Elsevier Sc ience Ltd. All rights reserved.