An unreported model of the cylindrical thermophotovoltaic cell (TPVC) composed of an emitter and a photovoltaic (PV) cell is proposed and used to recycle the waste heat released by the automobile exhaust pipe to generate electricity. To theoretically analyze the performance of this system, expressions of the power output and the conversion efficiency of the thermophotovoltaic cell driven by the automobile exhaust are derived analytically. The optimal functions of the temperature distributions of the automobile exhaust pipe and TPVC are obtained by the variational method and the modified Lagrangian formulation. The maximum power output is calculated. The performance characteristics of the whole system at the maximum power output are represented. The optimal regions of the voltage output of the PV cell, the energy gap of the material in the PV cell, and the inlet heat flow of the gas pipe are determined. The effects of the size of the gas pipe on the performance of the TPVC are discussed. The theoretical efficiencies of the TPVC and thermoelectric generator driven by the automobile exhaust are compared. The advantages of the TPVC are revealed. The results obtained show that the optimally designed TPVC can significantly harvest the waste heat of the automobile exhaust.

提出了一种由发射器和光伏电池组成的圆柱形热光伏电池（TPVC）的未报告模型，该模型可用于回收由汽车排气管释放的废热来发电。为了从理论上分析该系统的性能，分析得出了由汽车尾气驱动的热光电电池的功率输出和转换效率的表达式。通过变分法和改进的拉格朗日公式，获得了汽车排气管和TPVC温度分布的最佳函数。计算出最大功率输出。表示了整个系统在最大功率输出下的性能特征。PV电池电压输出的最佳区域，PV电池中材料的能隙，确定燃气管道的入口热流量。讨论了气管尺寸对TPVC性能的影响。比较了汽车排气驱动的TPVC和热电发电机的理论效率。揭示了TPVC的优势。获得的结果表明，经过优化设计的TPVC可以显着地收集汽车尾气的废热。