Micro Thermal Engines: Is There Any Room at the Bottom?

Richard P. Feynman introduced the field of microscale and nanoscale engineering in 1959 by giving a talk on how to make things very small. Feynman’s premise was that no fundamental physical laws limit the size of a machine down to the microscopic level. Is this true for all types of machines? Are micro thermal devices fundamentally different than mechanically-based machines with respect to their scaling laws? This paper demonstrates that micro thermal engines do indeed suffer serious performance degradation as their characteristic size is reduced. A micro thermal engine, and more generally, any thermally-based micro device, depends on establishing a temperature difference between two regions within a small structure. In this paper, the performance of a micro thermal engine is explored as a function of the characteristic length parameter, L. In the development, the important features of thermal engines are discussed in the context of developing simple scaling laws predicting the dependency of the operating efficiency on L. After this is accomplished, a general model is derived for a heat engine operating between two temperature reservoirs and having both intrinsic and extrinsic sources of irreversibility, i.e. thermal conductances and heat leakage paths for the heat flow. With this model and typical numerical values for the conductances, micro heat engine performance is predicted as the characteristic size is reduced. This paper demonstrates that under at least one particular formulation of the problem, there may indeed be some room at the bottom. However, heat transfer does play a critical role in determining micro engine performance and depending on how the heat transfer through the engine is modeled, vanishingly small efficiencies can result as the characteristic engine size goes to zero.