Surface Model

The heat pipe concept is based on the recirculation of the condensate liquid to the evaporator, which would be impossible without the capillary pressure head supplied by the wick. The capillary pressure relationship is therefore of utmost importance in heat pipe modeling. This relationship,

$$\Delta {\frac{{2 \sigma}}{{r_c}}}$$ (16)

allows for axial counter flow of the liquid and the gas through the variation of r_c, the radius of curvature of the surface of the liquid-vapor interface.

In steady state, r_c varies from a value of infinity, which represents a flat surface, in the condenser to a small value in the evaporator section. The radius of curvature is strictly tied to the amount of liquid present. There will be a flat surface, r_c = $\infty$, if there is enough liquid present to cover or overflow the wick. As the liquid recedes into the wick, the radius of curvature becomes smaller and smaller until it reaches the limiting value of the pore radius in the wick. This condition usually exists in the evaporator.

In order to make Equation 16 as implicit as possible, the radius of curvature is related to a system variable, the gas mixture volume fraction $\alpha_{m}^{}$, using geometric arguments. The resulting equation is linearized to yield an implicit representation of the capillary pressure relationship that is included in the Axial Model Equation Set. For a full description of the wick surface model, see ##hall91b (##hall91b) or ##hall88b (##hall88b).