Analytic solutions of heat and mass transfer in flat heat pipes with porous wicks

Abstract

Flat heat pipes have been used in cooling computer chips. However, previous models impose heat rate through the pipe as an input parameter, preventing optimization of heat transfer. We consider a horizontal flat heat pipe with an idealized porous wick on either one or both walls. A constant temperature difference is imposed across the two ends of the pipe, and we seek a steady-state solution. The pores in the wick are straight circular capillaries running along and across the wick, and are filled with a partially-wetting liquid. Its vapor fills the center region of the pipe and is connected to the liquid through circular pore openings on the wick surface. At the hot end, the liquid evaporates from the pore openings into vapor, which moves to the cold end where it condenses and the condensate flows in the wick to the hot end to complete a cycle. The mass evaporation rate at each pore opening on the wick surface is found from evaporation kinetics. This pore-level result is incorporated into pipe-level mass, momentum, and energy balances. The mass evaporation rate is found to depend only on the pipe temperature and is essentially independent of the vapor pressure. Consequently, the pipe behaves like a fin with evaporative cooling instead of convective cooling. Thus, the analytic fin solution holds for the pipe temperature and contains only one dimensionless number S (S2 is the ratio of evaporative to conductive heat rate through the pipe). It is observed that in heat pipes, S≫1 and thermal energy is chiefly transferred by vapor flow. Analytic solutions are subsequently found for the evaporation rate, the heat rate through the pipe, and the liquid and vapor flows along the pipe. Our idealized-wick parameters are converted to the porosity and permeability of a porous medium, so that we can compare directly with two published flat heat-pipe experiments. We analyze the effects of pipe length and wick thickness on the heat rate through the pipe, and provide guides for future design of flat heat pipes.