2020/04/29 by David Buttsworth, Buttsworth, David, Timothy Buttsworth +1
Engineering · Mathematics · #FOS: Physical sciences #Heat Transfer and Optimization #Instrumentation and Detectors (physics.ins-det) #Numerical methods in inverse problems #Radiative Heat Transfer Studies
paper · pdf · doi:10.48550/arxiv.2004.14558
openalex publication_date 2020/04/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Surface heat transfer in convective and radiative environments is sometimes\nmeasured by recording the surface temperature history in a transient experiment\nand interpreting this surface temperature with the aid of a suitable model for\ntransient conduction within the substrate. The semi-infinite one-dimensional\nmodel is often adopted, and several well-developed techniques for application\nof this model to surface temperature data are available. However, when a\nspatial variation of heat flux exists across the surface, the application of\nthe semi-infinite one-dimensional approach may not always be a reasonable\napproximation. In this paper we introduce a method for treatment of the\nmeasured surface temperature history that is more accurate than the\nsemi-infinite one-dimensional approximation when substrate lateral conduction\nis significant and the relative spatial distribution of the flux is known a\npriori. This new method uses the so-called \Neumann heat kernel, which\nevolves a temperature over an insulated domain with unit energy initially\ndeposited at a specified point. A useful impulse response function is formed by\nintegrating this Neumann heat kernel against the spatial variation of flux over\nthe surface of the domain. Neumann heat kernels are constructed for the solid\nbox, cylinder, and sphere. By applying the heat kernel result for the sphere to\nthe analysis of a convective experiment using hemispherical-nosed probes, we\ndemonstrate how the theoretical results enhance the practical analysis of\ntransient surface temperature measurements. The current approach is superior to\nformer methods relying on semi-empirical approximations because the\nmulti-dimensional heat conduction within the substrate is modelled with greater\nfidelity using the heat kernel analysis.\n