Temperature is a key parameter of fuel cell efficiency. In air cooled fuel cell stacks, large temperature disparities are observed. This temperature distribution has a significant influence on cell behavior in the stack, resulting in voltage disparities. The aim of this study, thus, is to correlate the temperature distribution in the stack to local voltage degradations, such as membrane drying and electrodes flooding. Indeed, the temperature has a strong impact on the water distribution in the cells because the saturation pressure is thermo-dependent. As a result, the hottest cells are prone to drying, whereas the coolest cells tend to be flooded, depending on the operating conditions. Measurements show that while drying, cell voltages decrease slowly and continuously until complete shutdown of the cells, whereas flooding results in quick voltage drops. Under drying conditions, voltage can be improved by increasing the inlet gas humidity or decrease in the stoichiometric ratio. In the case of flooding cells, purging the stack or reducing the inlet gas humidity is necessary to avoid complete shutdown of the cells. Consequently, small cell temperature variations through the stack can be responsible for large voltage variations from one cell to another. The cooling device must thus be optimized to reduce stack temperature nonuniformity.
This paper proposes important and useful results relating to the minimization of the sum of the flow time and the tardiness of tasks or jobs with unequal release dates (occurrence date), with application to maintenance planning and scheduling. First, the policy of real-time maintenance is defined for minimizing the cost of tardiness and critical states. The required local optimality rule (flow time and tardiness rule) is proved, in order to minimize the sum or the linear combination of the tasks' flow time and tardiness costs. This rule has served to design a scheduling algorithm, with O(n 3 ) complexity when it is applied to schedule a set of n tasks on one processor. To evaluate its performance, the results are compared with a lower bound that is provided in a numerical case study. Using this algorithm in combination with the tasks' urgency criterion, a real-time algorithm is developed to schedule the tasks on q parallel processors. This latter algorithm is finally applied to schedule and assign preventive maintenance tasks to processors in the case of a distributed system. Its efficiency enables, as shown in the numerical example, the cost of preventive maintenance tasks expressed as the sum of the tasks' tardiness and flow time to be minimized. This corresponds to the costs of critical states and of tardiness of preventive maintenance.
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