A general analytical model for the design of conventional heat pipes

Abstract

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 generalisation 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 vapour. 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 modelling, which validates the approach.

Effect of mesh wick geometry on the maximum heat transfer rate of flat-micro heat pipes with multi-heat sources and sinks

“…The Young-Laplace equation has been previously used to determine the maximum heat transfer rate of FMHPs using the capillary limit [5][6][7][8]10,26]. However, previous research did not consider whether the maximum surface temperature of FMHPs at the maximum heat transfer rate exceeded the allowable maximum temperature of the electronic components, which is crucial for ensuring the longevity of these components.…”

“…In recent years, continuous improvements in thermal management technology for electronic devices, such as tablet PCs, smart-phones, and various kinds of mobile electronic devices, have been developed to meet the increasingly higher heat flux requirements due to their dramatic reduction in size [1][2][3]. 1 One solution that has been devised by researchers [1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to meet the high heat flux duty is flat-micro heat pipes (hereafter FMHPs). FMHPs have a thickness of less than 1 mm; however, there are several challenges in developing devices at this scale.…”

Study of Miniaturization of a Silicon Vapor Chamber for Compact 3D Microelectronics, via a Hybrid Analytical and Finite Element Method

“…The basic assumptions are two-dimensional, constant material properties, constant saturation temperature and linear temperature profile across the structure of the wick. -Conduction in wall [9] The non-dimensional temperature, heat flux and coordinates can be defined as:…”

“…A second axis of very important work, these last years, consists in designing the chips in a more effective way compared to thermal dimension. Thermal models can thus be integrated into DK-like with the tools of floorplaning for an either electronic or thermoelectric design [4][5][6][7][8][9][10]:.…”

Complete analytical model of a loop heat pipe with a flat evaporator

“…Both solutions enable to determine parasitic heat losses through the wick and the evaporator body, the sensible heat given to the liquid flowing through the porous structure as well as the heat dissipated by evaporation at the wick-groove interface. A similar approach was implemented in the case of conventional heat pipes by Lefèvre and Lallemand [10] and later extended by Lips and Lefèvre [11]. These features, coupled with energy balances and thermodynamic relationships in the rest of the LHP, give a simple solution for the operating temperature.…”