An analytic linear relation between the imposed heat flux and the pipe-end temperature for flat heat pipes with porous wicks

Abstract

Flat heat pipes have been extensively used in thermal management of microelectronic devices. However, their heat-transfer mechanism has not been analyzed rigorously. A flat heat pipe can be separated into three sections: evaporator, adiabatic, and condenser. Heat is supplied to the evaporator and removed from the condenser. We consider a horizontal flat heat pipe with an idealized porous wick on either one or both walls. The pores in the wick are straight circular capillaries running along and across the wick and are filled with a partially-wetting liquid. The rest of the pipe is filled with its vapor. We assume that the heat transfer is one-dimensional, and the pore size is extremely small compared with the pipe length. Therefore, the pore-level phenomena can be studied separately from those at the pipe level. The analytic solution for the mass evaporative rate in a single pore is incorporated into the mass, momentum, and energy balances along the pipe. We take the evaporator to have the same length as the condenser which leads to skew-symmetric solutions. Hence, we only need to focus on the heated half of the pipe, and solve the steady-state problem with a specified heat flux $q^{\prime \prime }$ at the evaporator. We find for the first time an analytic linear relation between $q^{\prime \prime }$ and $\Delta T$, where $2\Delta T$ is the temperature difference between the two ends of the pipe. This analytic relation is validated by comparing with four published experiments. The analytic relation shows that to optimize the performance, a flat heat pipe should be designed with maximum wick porosity, liquid thermal conductivity, and number of evaporative pores, and minimum wick permeability.