Optimisation of a model internal combustion engine with linear phenomeno-logical heat transfer law

The optimal motion of a model internal combustion engine with a piston fitted inside a cylinder containing an ideal gas is examined. The gas is heated at a given rate f(t) and coupled to a heat bath with linear phenomenological. heat transfer law q proportional to Delta (T-1) for a finite amount of time. The optimal motion of the model internal combustion engine with linear phenomenological heat transfer law and maximum power output objective is obtained, as well as the optimal motion of the model internal combustion engine with linear phenomenological heat transfer law, fixed power output and maximum useful work output objective. The maximum useful work output per cycle, the maximum power output and the corresponding efficiency are obtained. Numerical examples are provided and the obtained results are compared with those obtained with Newton's heat transfer law. The results presented herein can provide the basis for both determination of optimal operating conditions and design of real systems operating with linear phenomenological heat transfer law.