Analysis of time-dependent heat transfer with periodic excitation in microscale systems

This study investigates time-dependent heat transfer with periodic excitation in micro-scale systems. Specifically, this study sheds light on time and length scales relevant to periodic heat transfer in micro systems. First, a system's substrate is modeled as a slab of finite thickness, in which the heat conduction equation is solved analytically for a periodic temperature boundary condition over the entire range of transient-periodic process. Using the analytical solutions, the system reaction in time is characterized for time scales and material properties typical for micro-systems. A "penetration depth" is defined as a parameter which indicates the maximum distance from the periodically-heated boundary/surface at which the periodic-thermal excitations are still noticeable. Then, as a case study, an experimental device is examined that uses a round, impinging water jet to cool a surface heated by pulsing laser. Finally, a three-dimensional numerical simulation, validated versus experiments, is used to elucidate the system's expected thermal behavior, including spatial and temporal temperature field variation, relevant time scales for measurements, and the spatial distribution of the heat transfer coefficient. It is demonstrated that the analytical findings can serve to characterize the real behavior rather accurately. The findings can assist in the design of systems with unsteady heating, and in future studies aiming at understanding more complex physically-driven transient phenomena, like flow boiling in micro-systems.