Analyzing and modeling on optimized L-ratio of evaporator section to condenser section for micro heat pipe heat sinks

This paper is focused on modeling and analysis on the determination of the optimized L-ratio, or L_e/L_c, for the length of evaporator section to the length of condenser section of cylindrical heat pipes, for a heat sink in the horizontal position. The independent variables (for an equipped heat pipe on which all fixtures are firmed) in the function of the total thermal resistance are L_e and L_c. Given the fact that this function has a local minimum between two fixed end points, the minimum extremal of the thermal resistance function can be obtained by taking the derivative of this functions and setting it to zero. Since the total length of a heat pipe, L, is constant, therefore L_c may be replaced by L-L_e, then the differential equation can be solved. In this paper, a formula to analyze the optimal L_e/L_c ratio is established. Table 2 to table 4 show analyzed results for diameters from 4 mm to 6 mm micro heat pipes in assemblies which are currently quite popular in applications.