An efficient hybrid system integrating a direct carbon fuel cell (DCFC) with a vacuum graphene-anode thermionic converter (VGTC) is proposed for cogeneration. The VGTC efficiently recycles waste heat released from the DCFC and generate additional electricity, significantly improving energy utilization efficiency and economic performance. A comprehensive mathematical model is developed to quantitatively assess the thermodynamic performance of the hybrid system, taking into account the overpotential losses of the DCFC and the irreversible energy losses occurring within the system. The results show that at an operating temperature of 923 K, the hybrid system can achieve a maximum power density of 466 W/m2, which is approximately 1.34 times that of a single DCFC, indicating a significant improvement in output performance. Besides, the optimal operating region and parameter selection criteria for the hybrid system are determined using finite-time thermodynamic optimization theory. Furthermore, the effects of essential parameters on the output performance of the hybrid system, such as the operating temperature of the DCFC, the heat transfer coefficient, the Fermi level of graphene, the work function of the cathode, the thermal emissivity, and the reflectivity of the back mirror, are investigated. Finally, the comparative study shows that the proposed hybrid system outperforms other previously reported hybrid systems regarding output electric power and conversion efficiency due to the efficient high-grade waste heat recovery and energy conversion by the VGTC.
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