Lubrication-type analysis of thermo-hydraulic transport in a model grooved heat pipe

The objective of this work is to achieve a rigorous resolution of the coupled hydraulic and thermal problems (including the solid) within a single triangular axial groove of a heat pipe in microgravity conditions. This is done by modeling the phenomena of transport of matter, momentum and heat, starting from the equations of continuity, Navier-Stokes and energy conservation. By combining the lubrication approximation and the one-sided approach, our approach leads to a 2nd-order differential equation for the scaled height of liquid. Through solving numerically this equation for a given heat flux input distribution, we can establish the profiles along the heat pipe for the scaled height of liquid and for the scaled averaged axial velocity of the flow. The equation of energy conservation can then also be solved, for the scaled liquid height distribution just determined. It leads to the scaled temperature field in each section of the heat pipe, and hence to the 3D temperature field, both in the solid and in the liquid. The proposed approach also enables determining the maximum heat flux that can be applied in the evaporator section without reaching dryout. Finally, the parametric sensitivity of this maximum heat flux to both geometrical and thermodynamical parameters is also analyzed.