Optimization of AMTEC-TIEC cascade and analysis of the algorithm used for solving the non-linear system of equations in the thermal model

A mathematical modeling of a system consisting of Thermionic Energy Converter (TIEC) and an Alkali Metal Thermal to Electrical Converter (AMTEC) is performed to optimize the efficiency of the cascade. The TIEC is heated by electron bombardment, which converts heat partially into electrichy and rejects the remaining. The AMTEC utilizes the rejected heat. A thermal model of the cascade converter has been developed to analyze the key parameters such as power level, heat fluxes, and temperatures. The efficiency of the cascaded cell is improved and h is greater than any of the individual efficiencies of the cells and smaller than the sum of the individual efficiencies. The problem is divided into two smaller segments and then MATHCAD was used to solve 12 non-linear system of equations. Algorithms for solving the system of non-linear equations are also analyzed. The order of two of the algorithms are calculated and recommendation is made for a custom made program which can be used for solving the whole 16 node system of non linear equations.