Heat Flux from Surface Temperature Visualizations

This chapter describes extraction of the surface heat flux from a time sequence of surface temperatures obtained in time-resolved surface temperature measurements with temperature sensitive paint (TSP) in high-speed flows. First, the analytical inverse heat transfer solution of the 1D heat conduction equation for the heat flux is derived for a polymer coating layer on a finite base (a semi-infinite base as a reduced case). This analytical solution is expressed as a convolution-type integral of the surface temperature history. Next, the numerical inverse heat transfer solution is described for the temperature-dependent polymer and base materials, which is useful for TSP measurements in high-enthalpy hypersonic wind tunnels. Further, based on the analogy between the 3D and 1D solutions of the heat conduction equation, the image deconvolution method is developed for correcting the lateral heat conduction effect on 1D heat flux calculation. As examples, the inverse heat transfer methods are applied to cone and wedge models in hypersonic wind tunnels and obliquely impinging sonic jets.