An Analytical Model for Thin Film Heat-Transfer Gauges

A theoretical study was conducted to evaluate the transient thermal response of a thin film heat transfer gauge (HTG) attached to a thermally insulating substrate material. The substrate material is assumed to be significantly longer than the thin film so that the temperature at the rear end of the substrate remains constant. The temperature distribution in the HTG was obtained by solving the governing one-dimensional heat conduction equation for the thin film and the substrate. At the boundary of the domains, i.e., the thin film and the substrate, various initial and boundary conditions were applied as follows. Initially, the entire probe is assumed to be at room temperature. Subsequently, the temperature at the surface of the thin film is raised instantaneously to an arbitrary value higher than the initial temperature. At the interface between the thin film and the substrate the temperature is always assumed to be continuous. As mentioned earlier, the temperature at the rear end of the substrate is assumed to be constant throughout the duration considered in the analysis. Additionally, the heat-flux at the interface between the thin film and the substrate is the same as the heat-flux at the surface of the thin film. The governing equations and the initial/boundary conditions were then non-dimensionalized and Laplace transformation was applied to the system of equations. With the considered initial/boundary conditions, the general solutions to the system of equations were further simplified to obtain analytical solutions for the temperature distribution in the thin film and the substrate. The results of the analysis were then used to determine the thickness of platinum thin films required for a HTG probe. In the sample case, platinum thin films were assumed to be mounted on a MACOR substrate. For an imposed response time of 0.1 microseconds, the analysis shows that the required platinum thickness must be 1 micron. These results provide useful insight into the dynamic thermal behavior of the HTG system and suggest its potential application in the design and development of thin-film sensors, especially under conditions of high temperature. Acknowledgements: EB is supported by The Republic of Turkey Ministry of National Education. AJ is partially supported by NASA MSTAR with Professor Liwei Zhang as the Principal Investigator. Insights and contributions of Ashton Short and Professor Frank Lu to the analysis are acknowledged.