Analysis of cylindrical heat pipes incorporating the effects of liquid–vapor coupling and non-Darcian transport—a closed form solution

Abstract

This paper presents a two-dimensional analytical model for low-temperature cylindrical heat pipes. A closed-form solution which incorporates liquid–vapor interfacial hydrodynamic coupling and non-Darcian transport through the porous wick for the first time, is obtained for predicting the vapor and liquid velocity and pressure distributions. In addition, the steady-state vapor and wall temperatures for a given input heat load in the evaporator region and a convective boundary condition in the condenser region, are obtained. The effects of liquid–vapor interfacial hydrodynamic coupling and non-Darcian transport through the porous wick on the vapor and liquid velocity and pressure distributions as well as the heat pipe capillary limit are discussed and assessed. The analytical solutions of the axial vapor and wall temperature distributions, the vapor and liquid pressure distributions, and the centerline vapor velocities compare very well with both experimental and numerical results. This work constitutes for the first time a comprehensive analytical solution which provides closed form solutions for the vapor and liquid flow as well as the operating temperature and the maximum heat removal capability of the heat pipe.