Model-Based Method of Theoretical Design Analysis of a Loop Heat Pipe

Abstract

Mathematical models accepted so far for loop heat pipes (LHPs) are mentioned, with a brief account of the operating characteristics. The necessity of an analytical model formed in a consistent way is stressed from the viewpoint of design practices. An ordinary differential equation, expressing the heat and mass transfer in a thick-walled porous cylinder, is solved to give a radial temperature distribution of the cylindrical wick, from which the outside-to-inside wick diameter ratio is derived. This ratio depends on the number of transfer units and is finally expressed in terms of the evaporator temperature effectiveness, which serves as a performance index. Positive-powered expressions, including the specified critical Bond number and specified linear pressure loss gradients, are then given to determine the wick inside, vapor line, and liquid line diameters. A pressure-loss model, consisting of theoretically or empirically obtained practical expressions, is presented to specify the wick pore radius. Derived expressions for the wick permeability and conductivity are combined to find an optimal wick porosity. The degree of subcooling, determined from the heat leak and the heat loss or gain, is given in a binominal expression dependent on the heat load, operating temperature, ambient temperature, and modeled coupling conductances. That degree is then converted into the pump efficiency, serving as another performance index. A reasonable method for reservoir sizing is proposed, considering both hot and cold startups. A two-region model representing the surface activity of a condensing radiator is introduced to determine the condenser/subcooler tube diameter, the total tube length, and the radiator half feeder spacing. All the expressions are arranged to develop into an LHP design code of convenience. Results of numerical computations done over a possibly wide range of parameters are graphically shown in the figures with a view to offering LHP design curves of interest.