# Modeling of heat and mass transfer in flat heat pipes

## Degree

Doctor of Philosophy (PhD)

## Department

Mechanical and Industrial Engineering

Dissertation

## Abstract

Phase-change phenomenon is ubiquitous in nature and widely utilized in thermal management of computer chips. Flat heat pipes have been extensively used in thermal management of microelectronic devices. However, existing research mainly concentrates on developing numerical models and lacks a systematic analytical approach to elucidate the working mechanism of flat heat pipes. We consider a horizontal flat heat pipe with an idealized porous wick. The pores in the wick are straight circular capillaries running along and across the wick and are filled with a liquid. The rest of the pipe is filled with its vapor. The mass evaporative rate at each pore opening is found from evaporation kinetics. This pore-level result is incorporated into pipe-level mass, momentum, and energy balances. The mass evaporative rate is found to depend only on the pipe temperature and is essentially independent of the vapor pressure. 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. We also consider the effect of the vapor-pressure difference on evaporation rate and revisit the analytic solutions for heat and mass transfer along the pipe. The evaporator and condenser regions are then incorporated into modeling of the flat heat pipe. The steady-state problem is solved for two cases: (1) a specified heat flux q'' at the evaporator, and (2) a specified temperature difference \$2\Delta T\$ between the two ends of the pipe. We find for the first time an analytic relation between q'' and \$\Delta T\$ and demonstrate that the modified model significantly improves the heat-rate predictions. Finally, We consider the problem of evaporation from the spherical meniscus at a circular pore opening in a cylindrical pore and derive analytically an expression for the evaporation rate from the spherical-cap meniscus.

8-17-2023

Wong, Harris