Deducing flux from single point temperature history when relative spatial variation of flux is prescribed

• Geometry and surface flux distributions affect reliability of semi-infinite models. Improved deduction is demonstrated using heat kernel methods. Utility the new approach illustrated transient temperature data. Surface transfer in convective radiative environments sometimes measured by recording history a experiment interpreting this with aid suitable model for conduction within substrate. The one-dimensional often adopted, several well-developed techniques application to data are available. However, when spatial variation exists across surface, may not always be reasonable approximation because errors typically increase time. In paper we introduce method treatment that more accurate than substrate lateral significant relative distribution known priori . This uses so-called Neumann , which evolves over an insulated domain unit energy initially deposited at specified point. A useful impulse response function formed integrating against domain. By applying result sphere analysis hemispherical-nosed probes, demonstrate how theoretical results enhance practical measurements. current superior former methods relying on semi-empirical approximations multi-dimensional modelled greater fidelity analysis.