A mathematical investigation of the influence of physical parameters on local surface heat flux of thin films

In engineering applications, comprehending thermal issues arising from local heat fluxes in thin films has gained significant attention in recent times. For heat transfer processes in applications, it is important to determine physical parameters of the films for which the temperature outside the heating zone does not increase rapidly. For example, microelectronics packages are facing an increased demand for processing large amounts of data, leading to higher energy consumption. Dissimilar materials are used as thin films in these packages, and their thickness is becoming increasingly smaller. These conditions lead to thermal management issues, as local heat flux may occur in the thin films, making heat management more critical. Although some experimental studies have been conducted, in the case of thin films with very small thickness, the difficulty in temperature measurement of thin films increases, resulting in insufficient research. To clarify their physical significance and for studies in situations where measurement is challenging, research through validated mathematical models is necessary. This paper investigates this problem based on an asymptotic analysis for solutions to the heat equation with Robin boundary condition. We show that the temperature outside the heat flux region can be lowered by reducing the film’s thickness, reducing the thermal diffusivity or by increasing the heat convection. The theoretical result is also supported by the numerical experiments. It means that thermal energy may not be released effectively, and the temperature in localized areas, such as heat spots, could rise drastically. Therefore, in engineering applications where the thickness of thin films decreases, thermal management becomes more challenging, and more efforts are needed to increase thermal diffusivity.