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Surface heat transfer in convective and radiative environments is sometimesmeasured by recording the surface temperature history in a transient experimentand interpreting this surface temperature with the aid of a suitable model fortransient conduction within the substrate. The semi-infinite one-dimensionalmodel is often adopted, and several well-developed techniques for applicationof this model to surface temperature data are available. However, when aspatial variation of heat flux exists across the surface, the application ofthe semi-infinite one-dimensional approach may not always be a reasonableapproximation. In this paper we introduce a method for treatment of themeasured surface temperature history that is more accurate than thesemi-infinite one-dimensional approximation when substrate lateral conductionis significant and the relative spatial distribution of the flux is known apriori. This new method uses the so-called \textit{Neumann heat kernel}, whichevolves a temperature over an insulated domain with unit energy initiallydeposited at a specified point. A useful impulse response function is formed byintegrating this Neumann heat kernel against the spatial variation of flux overthe surface of the domain. Neumann heat kernels are constructed for the solidbox, cylinder, and sphere. By applying the heat kernel result for the sphere tothe analysis of a convective experiment using hemispherical-nosed probes, wedemonstrate how the theoretical results enhance the practical analysis oftransient surface temperature measurements. The current approach is superior toformer methods relying on semi-empirical approximations because themulti-dimensional heat conduction within the substrate is modelled with greaterfidelity using the heat kernel analysis.

Deducing Flux from Single Point Temperature History when Relative Spatial Variation of Flux is Prescribed