Optimization of an irreversible Carnot engine in finite time and finite size

Abstract

In this work, we consider the class of irreversible Carnot engines that results from combining the characteristics of two models found in the literature: the model in finite time and the model in finite size. The performance of the resulting model, including three irreversibilities, was doubly-optimized in finite time and finite size. The first optimization of power and efficiency, maintaining the thermal conductances fixed, was performed in finite time. Since the optimum time ratio from the first optimization, is the same for both maximum power and maximum efficiency, this means that the model can be newly optimized but now in finite size. Then, the second optimization, maintaining the overall heat transfer coefficient constant, was performed. For both optimizations, analytical expressions for the efficiency that maximizes the power and maximum efficiency were obtained. Changing the order in which partial optimizations were carried out, a remarkable optimal property was obtained: the resources of total contact time and the total area of heat transfer are proportional.