Geothermal Heat Pipes - Just How Long Can They Be?

Abstract

Steady heat pipe solutions with capillarity and conduction effects included are considered. Phase plane trajectories of temperature vs. saturation typically approach zero capillarity solutions, one liquid-dominated and one vapor-dominated. Previous studies on the way in which choice of boundary conditions selects from these solutions are generalized, computer visualization techniques are used to cope with complexity, and accurate numerical solutions of the steady-state equations are presented. It has been speculated that the length of a gravity driven heat pipe may go to infinity. The maximum possible lengths of heat pipes are calculated here for a variety of values of the critical parameter, heat flow divided by permeability. It is found that liquid-dominated heat pipes can be more than 2 km long, and vapor-dominated heat pipes can be up to 100 km long in theory.