Coupled Vapor and Liquid Flows in Regular-Polygonal Micro Heat Pipes at Zero Viscosity Ratio

Abstract

Micro heat pipes have been used to cool microelectronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. A typical micro heat pipe has a long and narrow cavity of polygonal cross section sealed at both ends. A long vapor bubble occupies the center of the cavity, while the liquid fills the rest. As one end of the pipe is heated, the liquid evaporates into the bubble and the vapor flows to the cold end where it condenses to regenerate the liquid and releases the latent heat. The liquid flows along the corner channels back to the hot end to complete the cycle. Since the pipe is long, the vapor and liquid flow almost uni-directionally along most part of the pipe. The coupled fluid-flow problem contains a small parameter , which is the ratio of vapor to liquid viscosity. We perturb the problem in the limit and obtain leading order solutions for the axial vapor and liquid velocity fields in triangular, square and hexagonal micro heat pipes. To leading order, the vapor exerts no shear stress on the liquid and we find that the vapor flow depends on the densities of the vapor and liquid. The leading order vapor and liquid velocity fields are solved by a finite-difference method. Our results indicate that the vapor and liquid flow rates are maximum in the triangular micro heat pipe and minimum in the hexagonal micro heat pipe. The fluid flow in a micro heat pipe is responsible for carrying heat from the hot end to the cold end by evaporative heat transfer. Thus the flow rate is an indicator of the thermal performance of these devices.