The science
The pipe is a lumped three-state model: evaporator temperature Te, condenser temperature Tc and wick wetness w. Heat is carried by latent heat of the circulating vapour, limited by the capillary pressure ΔPcap = 2σ cosθ / r against gravity ρ g L sin(tilt) and the Darcy liquid and Poiseuille vapour losses, and by a rough sonic cap. If demand exceeds the limit the wick dries out (w falls) and the pipe stalls.
Energy is stored in the two thermal masses and lost through the cooler and an insulation leak: Ce dTe/dt + Cc dTc/dt = Q - h(Tc - Ta) - leak.
Simplifications: fluid properties from correlations valid for roughly 15 to 105 C, no boiling or entrainment limits, effective length fixed at 0.74 L, wick permeability from a Carman-Kozeny-style estimate, linear conduction through the wall. Illustrative orders of magnitude, not a design tool.
Made with ChatGPT · 2D companion of the 3D page; same solver and numbers.