A general analytical model for the design of conventional heat pipes

An analytical solution is presented for the 3D temperature field and the 2D pressure and velocity fields within a conventional heat pipe either flat or cylindrical. Several heat sources and heat sinks can be located on the heat pipe. The model is a generalization of a previous analytical solution developed for a flat plate heat pipe fully insulated on one of its face. The equivalent thermal conductivity and the permeability are the main parameters of the capillary structure. A Fourier series expansion is used to solve the 3D heat conduction equation in the heat pipe wall. A similar approach enables to solve the 2D balance equations within the liquid and the vapor. The thermal and the hydrodynamic models are coupled together. The model can be used to determine the thermal resistance and the different limits of the heat pipe. As the model is analytically derivable, it is straightforward to use it to optimize heat pipe parameters and the locations of the heat sources and the heat sinks. An inverse formulation can be derived easily to estimate the capillary structure parameters using wall temperature measurements. In the case of the classical problem of a cylindrical heat pipe heated on one side and cooled on the other side, the simplification of the general solution enables to establish the well-known theory of heat pipe modeling, which validates the approach.