Heat and mass transfer in a cylindrical heat pipe with a circular-capillary wick under small imposed temperature differences

Previous models of heat pipes use the heat rate through the pipe as an input parameter, and therefore lack predictive capabilities. Here, we demonstrate, using a simple heat pipe, that if the evaporation and condensing kinetics are properly modeled, then the heat rate is predicted. We consider a cylindrical heat pipe with the inner wall lined with a circular-capillary wick. The capillaries are filled with a partially wetting liquid, and the center of the pipe is filled with its vapor. The equilibrium vapor pressure at the hot end is higher than that at the cold end, and this pressure difference drives the heat transfer in the heat pipe. We assume that the wick’s pore size is infinitesimal compared with the pipe dimensions. Thus, pore-level events can be treated separately from pipe-level events. Analytic solutions are obtained for the pipe temperature, vapor pressure, and all the other variables. For maximum evaporative heat transfer, we find an optimal pipe length for fixed pipe cross-sectional dimensions, and an optimal wick thickness for a fixed pipe length. These optimal pipe length and wick thickness can help to improve the design of heat pipes and are found for the first time.