A steady-state inverse heat conduction-convection conjugated problem in determining unknown spatially dependent surface heat flux

Abstract

The unknown spatially dependent surface heat flux is estimated for a three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP) in this study. Air with a specified velocity flows over a flat plate which was subjected to an unknown heat flux on the bottom surface and the simulated temperature measurements on the top surface were used for the estimations. As the functional form of the heat flux is considered to be initially unknown, this inverse problem falls within the category of function estimation. Optimization is performed using the conjugate gradient method (CGM) because this method does not require a priori information regarding the functional form of the unknown functions, enabling a large number of unknowns to be corrected and estimated in each iteration to always yield good estimates. This efficient algorithm has never been applied to the IHCCCP. The results of the inverse solutions are verified using numerical simulations with various inlet air velocities and plate thicknesses. The results show that using exact measurements always produces accurate boundary heat fluxes under thin plate conditions since the maximum error for the estimated heat flux using error measurements was found to be only 6.43%, and the air velocity does not affect the estimates. The measurement errors and their influence on the inverse solutions are analyzed. Finally, it is concluded that because the inverse problem is ill-posed, the estimated heat flux becomes less accurate as the plate thickness increases.