An experimental inverse problem in determining spatially varying surface heat flux using measured temperature readings

Abstract

An experimental investigation to estimate the unknown spatially dependent surface heat flux of a flat plate based on the surface temperature readings taken by a thermography camera and the conjugate gradient method (CGM) is examined in this study. In the present three-dimensional inverse problem, the functional form of the heat flux is considered to be initially unknown; thus, the functional form of the heat flux is classified as the category of function estimation. In addition, air velocity is specified as the working condition, not the heat transfer coefficient; therefore, it is defined as an inverse heat conduction-convection conjugated problem (IHCCCP). The experimental study for estimating the unknown spatially dependent surface heat flux has not been examined previously in the IHCCCP. The estimations of the inverse solutions are conducted experimentally with two designed plate heaters and various inlet air velocities and plate thicknesses, and the total heat losses are found to be approximately 5% of the original design heating power. The experimental results indicated that for a uniform heating design (Design A), the estimated heat fluxes are always very accurate if the heat losses are deducted from the design power. For the nonuniform heating design (Design B), due to the existence of two discontinuities in the heating power, the estimated relative errors for heat fluxes are found to be between 16% and 18% using 6 to 8 iterations, reflecting the nature of the inverse problem, i.e., a small measurement error will amplify the error of the estimates; in addition, the estimated heat flux becomes less accurate as the plate thickness increases. Finally, numerical simulations with errorless measurements are performed, and the results reveal that the estimated errors for heat fluxes can be decreased to approximately 8% with 150 iterations for Design B.